Berkeley’s Direct Tactile Realism In His NEW VISION

Oddly enough for those of us used to thinking of Berkeley as a thoroughgoing idealist, Berkeley maintains in his AN ESSAY TOWARDS A NEW THEORY OF VISION a direct realism regarding tactile perception.  Whereas the objects of vision — for example, the visible moon — do not exist outside the mind, the objects of touch — what is touched, tangible physical objects — do exist outside the mind in external space.  As George Pitcher puts it, speaking of what Berkeley is claiming in black and white in the NEW THEORY OF VISION:

What we feel are the tangible objects — i.e., the objects that are spread around us at various points in physical space.  What we see are objects that exist only in the mind.

George Pitcher, BERKELEY: THE ARGUMENTS OF THE PHILOSOPHERS  (Routledge, London and New York), p. 28. Henceforth BERKELEY

Tangible objects, in the system of the Essay, exist around us in real physical space.

George Pitcher, BERKELEY, p. 43.

And from the Master himself (passage 1):

Passage 1

For all visible things are equally in the Mind, and take up no part of the external Space.  And consequently are equidistant [in the next sentence Berkeley says ‘Or rather to speak truly…are at no Distance, neither near nor far…] from any tangible thing, which exists without the Mind.

George Berkeley, AN ESSAY TOWARDS A NEW THEORY OF VISION, paragraphs CXI and CXII, in The GEORGE BERKELEY COLLECTION: 5 CLASSIC WORKS, Amazon Print-On-Demand Edition, no pagination.  Henceforth A NEW THEORY OF VISION. 

Perceiving/sensing/understanding (for now I will take these terms to be more or less equivalent, as I think they are for Berkeley) for Berkeley is always a two-place relation between a Mind that perceives something and the thing that is perceived — the object of perception.  Berkeley calls the direct, that is to say, the immediate object of sensing/perceiving/understanding an ‘idea’:

Passage 2a

… I take the word idea for any immediate object of sense, or understanding — in which large signification it is commonly used by the moderns.

George Berkeley, AN ESSAY TOWARDS A NEW THEORY OF VISION, in BERKELEY Essay, Principles, Dialogues With Selections From Other Writings (Charles Scribner’s Sons, New York) 1929) p. 36.  Henceforth A NEW THEORY OF VISION when referring to that Essay in this volume.

So henceforth I will be treating the terms ‘idea’ and ‘object (of touch, of vision, of hearing, etc.)’ as equivalent, except when the context makes it obvious that ‘idea’ is being used in another way.

Visible things, visual ideas — the objects of vision — for example, the Visibile Moon … these things have visible properties. The Visibile Moon, for example, has a round shape, is flat, luminous, and is of a kind of non-saturated yellow color. That this should be so ought not perhaps be too surprising. Things have properties, right? Shouldn’t visible things have visible properties? And should their bearing properties be gainsaid by the fact that these things exist only in the mind? I can see a wine red or viridian green or burnt sienna afterimage, right?

Vision is, I have said, assuming for the moment the guise of Bishop Berkeley, a two-place relation between the Mind and an object that exists only in the mind, a visual Idea. In the case of touch, this relation is a two-place relation between the Mind and a hard or soft or rough or smooth or sharp or rounded…physical object existing in external space. [By ‘physical object’, I mean ‘object that obeys the laws of physics,’ and I take it this is what Berkeley is also thinking of when he talks about things existing in ‘external space’.] Shortly, I will be talking about what these relations might be.

As regards vision, I do perceive an extra-mental object existing in external space — but only indirectly, or mediately, in a three-place relation. This relation comprises my Mind (me), the Visibile Idea (e.g., the Visibile Moon) to which my Mind is related directly, and the external object (the physical, tangible Moon) for which the Visibile Moon serves as a sign.  So with regard to vision, Berkeley maintains in the NEW VISION a representational theory of perception.  He is an indirect realist with regard to vision:  we see the physical object in external space just indirectly, in a way mediated by the mental object of color and shape that we do see directly.

But with regard to touch, Berkeley is a direct realist.  We perceive the physical object directly through touch.  We don’t perceive it by ‘touching’ or ‘feeling’ a mental object that represents the physical tangible object.  We are in contact with the object itself.  Put another way, our perception reaches all the way to the felt object.  In the case of touch, the perception is a two-place, not a three-place relation.

This direct realism in the case of touch comes as a bit of a surprise to those of us who think of Berkeley as a thoroughgoing idealist who thinks that everything is mental.  And in fact Berkeley apparently claimed in later writings that he theorized touch this way only to prevent his readers from freaking out from far too much counterintuitive idealism (Pitcher, BERKELEY, p. 28) which would only have served to distract his readers from what he wanted to focus on, namely, vision. In his own thoughts, ostensibly kept to himself at the time of A NEW THEORY OF VISION, he regarded the objects of touch as in fact mental.

But regardless of what the historical George Berkeley thought or did not think inwardly as he wrote that tract, treating touch in a direct realist fashion as involving direct perceptual contact with the touched/felt physical object is strongly motivated by two things.  First, Berkeley’s treatment of the objects of vision as being both mental and possessing visual properties leads to absurdities if applied to the objects of touch.  The absurdity disappears once one regards the objects of touch as being extra-mental, existing outside the mind.  Second, reflecting on the nature of vision and the nature of touch motivates (without forcing!) a direct realist theory of touch and an indirect realist theory of vision.  .

I’ve been speaking of the objects of vision and the objects of touch, whether these be the same [be sure to cash this out], or different, as Berkeley thinks. The object of vision is what is seen; the object of touch is what is touched. Berkeley calls the former the visual Idea, and the latter … well, to anticipate, I think one is likely to feel some discomfort in calling what is touched, the physical object, an ‘Idea’, given that Ideas are normally regarded as mental, as Berkeley regards the (direct) objects of vision. Be that as it may, objects have properties.

So it is not terribly surprising to see (as I have discussed in a previous post, The Truth Of Bishop Berkeley (Part 0)) Berkeley treating the visible object as having visual properties (what other kind would it have? [Yes, this is a trick question]).  The Visibile Moon, for example, is round, flat, luminous, and (although Berkeley never assigns it a specific color) of a certain pale cheese-like yellow. If I may be permitted to go at least a little distance out on a limb, I ascribe to Berkeley the idea that for a mind to sense ‘moon yellow’ and the other sensed properties of the Visibile Moon is simply for that object to have those properties and to exist in the mind.

But we run immediately into trouble if we try to apply that idea to the objects of touch. It seems rather strange to say that for a mind to sense rough, smooth, hard, soft and so on is for a rough (or smooth, hard, soft) object to exist in the mind. But surely no mental things can be rough etc.  Only physical objects — for example, the bark of a tree, the cool smoothness of marble — can have these properties.  Thus conceptualizing Ideas, the objects before the Mind, as having properties puts Berkeley straightway on the road to regarding physical objects existing in extra-mental space as the objects of touch.

But what happens, then, to the idea that to sense an object with its properties directly is for that object with its properties to exist in the mind? The object of touch with its roughness etc. exists outside, not inside the mind. How, then, can it be an Idea? An Idea, surely, is something that exists in the mind. And an Idea, remember, is what is sensed, what is perceived — the object of touch or of vision. If one ever suffered from the delusion that the Berkeleyan Idea was not a problematic concept, they should be stripped of that delusion now. [ It would seem that Berkeley would either have to jettison either the notion that an Idea is a mental object (with properties) in the mind, or that it is an object, mental or not, before the mind. the notion we have ascribed to him that ]

[What is this relation? At least in the case of vision, Berkeley seems to conceive of this relation in quasi-spatial terms — and he is not, of course, the only one to do so.  For him, to sense wine red, for example, is for wine red (deep crimson red) to be “in” (yes, do note the scare quotes) the mind. The origin of this spatial metaphor doubtlessly lies in a causal story of perception. Light bounces off the object (say, a translucent wine-red paper weight), strikes the retina, triggering other events that end up quite literally in the brain…and from there (though no story about the pituitary gland) ideas somehow slip into the mind. That Bishop Berkeley easily flips from talking about brains and physical processes to talking about minds and the ideas contained therein. As shown here, he starts out talking about retinas and brains, then suddenly corrects himself midstream and starts talking about minds. These easy flips make it more likely he will apply in a metaphorical or derived way to minds and mental objects spatial terms such as ‘in’ whose use is quite literal when applied to brains inside skulls. ]

[For now, I will leave the terms ‘mind’ and ‘mental’ as primitives, and assume that I and my readers understand them in roughly the way Bishop Berkeley understood them. We are all, after all, still swimming the still-powerful current of Cartesian dualism.]

[What is this relation? At least in the case of vision, Berkeley seems to conceive of this relation in quasi-spatial terms — and he is not, of course, the only one to do so.  For him, to sense wine red, for example, is for wine red (deep crimson red) to be “in” (yes, do note the scare quotes) the mind. The origin of this spatial metaphor doubtlessly lies in a causal story of perception. Light bounces off the object (say, a translucent wine-red paper weight), strikes the retina, triggering other events that end up quite literally in the brain…and from there (though no story about the pituitary gland) ideas somehow slip into the mind. That Bishop Berkeley easily flips from talking about brains and physical processes to talking about minds and the ideas contained therein. As shown here, he starts out talking about retinas and brains, then suddenly corrects himself midstream and starts talking about minds. These easy flips make it more likely he will apply in a metaphorical or derived way to minds and mental objects spatial terms such as ‘in’ whose use is quite literal when applied to brains inside skulls. ]

[For now, I will leave the terms ‘mind’ and ‘mental’ as primitives, and assume that I and my readers understand them in roughly the way Bishop Berkeley understood them. We are all, after all, still swimming the still-powerful current of Cartesian dualism.]

[But why doesn’t regarding the objects of vision likewise put one right on the road to viewing the objects of vision as extra-mental entities? Can a mental object be yellow, luminous, round, and flat?]

Whether such a reading is historically accurate or not, I am tempted to read the following passage (passage 2) as motivated by a discomforting sense on the part of Berkeley that there is something problematic about the notion of an Idea. What better way to eliminate the discomfort than to say the opposite? ‘There is nothing problematic about the notion of tangible ideas’, my psycho-analyzed version of Berkeley would say. ‘I am just using the phrase as everyone else among us moderns uses it’.

Passage 2

Note that, when I speak of tangible ideas, I take the word idea for any immediate object of sense, or understanding — in which large signification it is commonly used by the moderns.

George Berkeley, AN ESSAY TOWARDS A NEW THEORY OF VISION, in BERKELEY Essay, Principles, Dialogues With Selections From Other Writings (Charles Scribner’s Sons, New York) 1929) p. 36.  Henceforth A NEW THEORY OF VISION when referring to that Essay in this volume.

But what is directly, i.e., immediately, i.e., im, that is to say, not mediately touched is the extra-mental physical object itself.  Given the passage just quoted, that would mean the physical object is an Idea — a tactile Idea — , at least when it is being touched.  Visual Ideas may be mental, but it would seem that tactile Ideas are not.  But surely, in the large signification the word ‘Idea’ is used by the moderns, as well as by all of us captive to what is still a Cartesian common sense, an Idea is something mental, something in the Mind.  Passages 1) and 2) are clearly in tension with one another.

One way to reconcile 1) and 2) is to reinterpret the concept of an Idea by applying to it a distinction between the content of intentional states such as seeing and touching and the object of these states.

A Berkeleyan Idea, I propose, is ambiguous between content and object.  In the case of feeling/touching [I shall use ‘feeling’ interchangeably with ‘touching’], the Idea is a mental content without properties but describable by seeking answers to the question ‘how’, or adverbially.   The intentional state with this content has a physical thing with properties as its object.  In the case of vision, the Idea is an “inner” mental object [I will take ‘inner’, ‘mental’, and ‘mind’ as primitives and pretend, at least for now, that there is nothing problematic about these terms] with properties.

Let me explain this distinction by making an analogy to the (commonly made in this context)  distinction between kicking a tree (an action directed towards an object) and kicking a kick (an action that may or may not be directed towards an object).  Let’s say that Dr. Johnson kicks a tree (while exclaiming ‘I refute Berkeley thus!’)  This event can be described in two ways:  ‘Dr Johnson kicked a tree’, and ‘Dr. Johnson kicked a kick’.  The kick, is of course, identical with Dr. Johnson’s action of kicking the tree and is, in spite of the direct-object grammatical role played in the sentence by the word ‘kick’, not the object of the kick.

Dr. Johnson is both kicking a kick and kicking a tree.

Now suppose that  Bruce Lee is demonstrating a particular martial art move which includes a kicking action.  The kick is directed towards the air, towards anything that might [the futural dimension] meet its thrust, in other words, to nothing in particular.  It is not directed towards any actual existing object.  Bruce Lee is kicking a kick, but the kick is not directed towards an object.

Continuing with this analogy, let’s say that the tactile Idea is like kicking a kick that may or may not have an object.  Suppose I am resting my elbow on a marble countertop.  I feel the coolness of the marble.  At the same time, I feel the equal and opposite force of the cool, smooth, hard marble as it meets my weight at my elbow while I lean into it. In feeling this equal and opposite force impinging upon my body, I  feel the marble’s hardness and resistance to my body.  Likewise, I feel the pressure on my somewhat rubbery skin as both the marble and the bone of my elbow press into it.   Oh no!  I have placed too much pressure on the countertop!  A piece of it has broken off and smashed into my toe! I feel the marble’s force, and my toe throbs painfully with such a salience that it becomes difficult to attend to anything else.

In the course of all this, I have enjoyed/suffered the following:  a coolness feeling, a force feeling, a hardness feeling, a resistance feeling, a pressure feeling, a pain feeling.  Some of these, although named by different words, may be identical events (e.g., hardness feeling, resistance feeling, force feeling).  These start, continue for a while, then end (I stop leaning on the counter; my toe eventually stops throbbing painfully).  They are, in short, events that have the same structure as the event kicking a kick.  I was feeling a hardness feeling, feeling a resistance feeling, feeling a coolness feeling, feeling an equal-and-opposite-reaction-comprising-a-force feeling, feeling a toe-throbbing-painfully feeling.

These ‘feeling a feeling’s I will call the content of the intentional state of feeling the marble countertop. In each case, the feeling is not the object of the various tactile events, but is identical with those events.  The object of  the events is the marble countertop itself and its various properties and capacities:  its hardness, its resistance to forces impinging upon it, its presenting those forces with equal and opposite reactions, its temperature. Dr. Johnson kicks a tree; I feel a marble countertop.

It is fairly safe to place the marble countertop in extra-mental space.  With just a little bit of work, I think, we can plausibly place the feeling inside the mind as a mental event.  I say ‘plausibly’ for now because later I hope to chip away a bit at any such clean separation of ‘mental’ from physical as would seem naturally intuitive to Berkeley and to anyone still caught up in the general thralldom of what is still common-sense Cartesian dualism.

Suppose I am now hallucinating the marble countertop.  I seem to be leaning my elbow on the countertop.  But there is in fact no marble countertop for me to lean on.  Instead, there are just the following:  a feeling a hardness feeling, a feeling a resistance feeling, a feeling a coolness feeling, a feeling an equal-and-opposite-reaction-comprising-a-force feeling, a feeling a toe-throbbing-painfully feeling.  These are, plausibly, events taking place inside me and only inside me.  They are taking place inside no one else.  If I am a Mind, a Spirit, then these events are taking place inside my mind.  They are mental events.

They are tactile Ideas.  When there is a marble countertop that I am feeling, they are tactile Ideas with both an object and a content — Dr. Johnson kicking a tree (object) and kicking a kick (content).  When I am hallucinating and there is no marble countertop that I am feeling, they are tactile Ideas with a content but no object.  They are Bruce Lee kicking a kick without kicking anything. Tactile Ideas are mental contents identical with events that may or may not have an object.

Regarding them as mental events, we need not think of them as objects with properties standing in front of the felt object and hiding it from our direct tactile view. Instead, they are best described by phrases that answer the question ‘how?’ and sometimes adverbially.  How am I feeling?  I am feeling impinged upon by a force that is equal and opposite to the force I am exerting on the countertop.  I am feeling impinged upon by the temperature of the marble.  I am feeling throbbingly/painfully in that area of space occupied by my toe.  Answers to the how question and (sometimes) adverbs better describe these events than do properties, states and capacities of objects (wine-red, translucent, cubical).

Thank goodness, because, as suggested above, if the tactile Idea had tactile properties such as hardness etc. by analogy with visual Ideas having visual properties such as luminosity and a particular shade of bright-moon-cheese-yellow, we would be in very strange territory indeed.  We would be faced with slabs of mental marble floating around (would something that has the property of heaviness float? — Maybe mental space is gravitation-free) in my mind possessing the properties of smoothness, coolness, and hardness, and capable of  exerting any force, whether gravitational or equal-and-opposite-reactional, upon any physical object, including upon that physical object that I am.  Were these allegedly non-physical objects actually capable of exerting/undergoing such forces, they would in fact be physical, that is to say, describable by the laws of physics. [By ‘physical’ I mean ‘describable by the laws of physics.]

(Later, however, I hope to submit to the consideration of my gentle reader the idea that maybe we should include the force exerted by the marble as part of the tactile sensation, the tactile Idea. )

By treating tactile Ideas as mental contents, Berkeley can retain his claim that touch gives us direct access to the physical object, without the mediation of any objects at all standing in the way — much less strange entities such as tactile Ideas seen as objects with tactile properties.  The tactile Idea is not an object mediating our access to the felt object in a three-place relation comprising mind, mediating mental object with properties, and physical object.  Rather, it is this access.

Of course, if visual Ideas are to be treated the same way, we would end up with a direct perception theory of vision, not a representational theory.  Visual perception would be a two-place relation between a mind and the physical object (when the visual experience has an object), not a three-place relation comprising mind, visual Idea, and physical object.  In the case of after-images and hallucinations, the visual experience would have a content (identical with the the event that is that experience), but it would have not object.  To the exclamation ‘surely you are seeing something when you see a wine-red afterimage or hallucinate that magenta rhinoceros grazing at your feet as you write this screed’, the proper rejoinder is ‘no, I am not seeing anything.’  For there is no inner, mental object that is wine red (in the case of the afterimage) or magenta (in the case of the hallucinated rhinoceros).

So if Berkeley is to retain his indirect, or representational theory of visual perception and admit the existence of physical objects as well, he has to retain the notion of a visual Idea as a mental, inner object possessing properties such as wine red, magenta, yellow ocher, or burnt sienna.  These objects stand in the way, between the mind and the physical object.

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When I “see” a wine-red afterimage, it may seem odd to deny the existence of something that has the property wine-red.  As a matter of my personal biography, I have found this denial a bit counter-intuitive to make. I see this wine-red thing, dammit!  It’s right there before me!  (Even though no one else can see it.)  Likewise, when I hallucinate a magenta rhinoceros grazing peacefully at my feet (this is my study rhino) … er … I mean … were I to hallucinate a magenta rhinoceros, I see all this rather powerful vivid magenta, dammit!  (Even though no one else can see what I see.)  How could a color exist without being the property of a colored thing?  So how could there not be something magenta before me?  Do you really want to deny that magenta exists (er, I mean, would exist) in my visual field?

But neither the afterimage nor the hallucinated rhinoceros are physical objects.  Were I to try to touch the rhinoceros, no equal and opposite reaction would meet my action.  And there is no way I can even try to touch the afterimage — it does not exist in a space in which reaching for it can make sense.  If these objects are not physical objects, they must be mental objects.  These are “inner” mental objects with properties, such as wine red or magenta or  yellow ocher.

Add to this line of thought the fact that every perceptual or quasi-perceptual event has a cause, and you get a theory of visual perception that renders visual perception indirect in the way articulated above.  [Combine this line of thought with the idea that the object of perception must be present, not just on the sensory surface, but inside it (the sensory object must be where the causal chain ends), and you end up with the notion that every object of visual perception must be an inner, mental object.]  In the case of visual perception, the event of kicking, which it is without exception describable as kicking a kick, is always also kicking a tree.  Visual perception always has a mental entity as its direct object; at best, a physical thing can be just the indirect object of perception.

Would the same type of argument pack any punch at all in showing (or seeming to show) that tactile perception has just an indirect “grasp” of the physical object?  Since there does not seem to be anything like an “aftertouch” that would correspond to an afterimage, I will focus on the possibility of tactile hallucination.

Suppose that I am hallucinating the following:  I am resting my elbow on a marble countertop.  I seem feel the equal and opposite force of the cool, smooth, hard marble as it meets the weight I press into it via my elbow — that is to say, I seem to feel the (ostensible) marble’s hardness and resistance to my body.  Likewise, I seem to feel the pressure on my somewhat rubbery skin as both the marble and the bone of my elbow press into it.   Oh no!  I have placed too much pressure on the countertop!  A piece of it has broken off and smashed into my toe!

But I am hallucinating.  There is no physical marble outside my mind that my body is leaning against.  Nor is there any slab of mental marble floating around (would something that has the property of heaviness float?) in my mind possessing the properties of smoothness, coolness, and hardness, and capable of  exerting any force, whether gravitational or equal-and-opposite-reactional, upon any physical object, including upon that physical object that I am.  Were these allegedly non-physical objects capable of exerting/undergoing such forces, they would in fact be physical, that is to say, describable by the laws of physics.

I am hallucinating the events occurring in my body as well.  My body exists, thank God, but I am hallucinating the various events that are ostensibly taking place within it and to it:  my elbow bone pressing into my skin and other flesh that is ostensibly in contact with the ostensible marble countertop; the ostensible marble pressing into that same flesh from the other side; the piece of marble dropping onto my toe.  None of these events is actually happening.  For the same reasons there is no mental marble slab floating around in my mind like an object in the opening of the TWILIGHT ZONE — but wait!  One of the ostensible properties of the ostensible marble is weight — so this mental slab couldn’t be just floating —  there is no mental ‘my body’ floating around there either.

To feel an object is to impinge one’s physical flesh-and-blood-and-bone self upon it, or to suffer its impinging upon this flesh-and-blood-and-bone self.  This is why any completely convincing tactile hallucination — if any such ever occur — would need to include hallucinatory (and ostensible) events occurring in and to one’s physical body.  And it is also why any object of a tactile Idea has to be physical.  It is not possible to get one’s hands upon, impinge upon, a mental, non-physical entity.  The smoothness, coolness,  hardness, resistance, capacity to exert or suffer a force of an object become tactilely perceived properties of an object only given the impact/suffering of tactically sensitive flesh.

What we are left with is an event, an action that looks less and less “mental” (I shall now start placing this word in quotes in order to cease pretending I really know what this word means).  If the ostensible object of my touching does not exist “outside the mind”, it does not exist.  There is something occurring, however — an event of feeling.  Idea. This Idea, however, is similar in structure to a kick, which usually is directed towards an object but sometimes is not.  When the marble countertop exists, the tactile Idea is akin to kicking a tree (which act is also describable as kicking a kick).  But when the marble countertop does not exist because I am hallucinating, the tactile Idea is akin to just an objectless kicking a kick.  In a sense that will be clarified later on [promissory note], I am not feeling anything.

On the kicking a kick side, the force-feeling, the hardness-feeling, the coolness-feeling, the resistance-feeling.

But then have to bring in the physical — the fingers and elbows and toe getting smashed, and it starts getting a bit problematic to call this an Idea.

Nonetheless:

It is not at all plausible (to repeat the point already made in paragraph x above) to argue:  ‘There are no non-physical slabs of marble existing only in my mind possessing  the properties of smoothness, coolness, and hardness and capable of of exerting forces upon another

My body does exist, thank God, but it is not exerting/receiving any forces from material objects.  That body exists only in my mind — so I will say, but only as a first approximation.

Afterimages don’t push back.

Think of as having same structure as kicking a kick | kicking a tree.  Touch is both.  No mental slab of marble.  Vision is always kicking a kick according to the above.  What would be possible reasons for thinking this.

*********

Of course, this interpretation of Berkeley is ever so slightly (just slightly, I hope!) tendentious.  So far as I know, Berkeley never explicitly says that Ideas have colors or have other properties.  The interpretation relies on the his seeming to equate the objects of vision (for example, the Visibile Moon) with conglomerations of Ideas.  The Visibile Moon is luminous, implying that it has some color or other.  It is difficult to see how Ideas could be conjoined to form a conglomeration with luminosity and a color unless they were themselves luminous and colored; therefore it would seem that visual Ideas have to have properties.

But there are interpreters, such as George Pitcher, who argue that we can make more pieces of what Berkeley says cohere with one another if we think of his Ideas not as objects of sensation (and therefore not as entities with properties), but as events or “acts”.

An Idea on this interpretation would be an event that has the same structure as a kick.  Let’s say that Dr. Johnson kicks a tree (while proclaiming ‘I refute Berkeley thus!’)  This event can be described in two ways:  ‘This person kicked a tree’, and ‘this person kicked a kick’.  The tree in the first description of of course the object towards which the kick was directed; the kick in the second description is not such an object, but is identical with the kicking event itself.

A kick may have an object towards which it is directed, as when Dr. Johnson kicks the tree.  Or it might not.  Bruce Lee, for example, may be demonstrating a particular martial art move without actually kicking anything.  Just so, the tactile Idea of cool, smooth marble may have an object towards which it is directed — the marble counter top over which I am passing my hands, or it might not.  I might be hallucinating the feeling of cool, smooth marble.  If I am hallucinating, the noun phrase ‘tactile Idea of cool, smooth marble’ names not some object to which the sensation is directed, but a sensory event.  [I will try to claim the event normally has “non-mental” aspects, my physical fingers passing over the marble.]

Because of the grammatical similarity between ‘tree’ and ‘kick’ in the above kick sentences, both serving as grammatical objects in the sentences, one could theoretically think that there is some sort of special object called a ‘kick’ towards which the event of kicking is directed.

Practically speaking, I rather suspect this sort of confusion is unlikely to occur when we are talking about kicks.  But this confusion may be occurring should one think that sensing a wine red color and sensing an oblong shape , say, is to be analyzed in terms of an event, sensing, that has as its object an entity that is both wine red in color and oblong in shape.  In short, a thing with properties.  If one “sees” a wine-red, oblong afterimage, or hallucinates a magenta rhinoceros, there is clearly nothing present in extra-mental space that is wine red, oblong, magenta, or shaped like a rhinoceros.  But (it would seem) there is something that is wine red and oblong (in the afterimage case) or magenta and rhinoceros-shaped (in the hallucination case).  Since these things do not exist in extra-mental space, they must exist “in the mind” — maybe even in some sort of “internal space”.  I know — let’s call these things ‘Ideas’.  Visual access to the physical objects available to us via touch would then have to be mediate in character — accomplished not directly but through the intermediary of visual Ideas.

As we have seen in the section above, this kind of analysis falls apart in the case of tactile sensations — tactile Ideas. Should one hallucinate the tactile presence of a slab of cool, smooth marble, or the tactile presence of rough bark, there is surely no mental, i.e., non-physical object that is cool and smooth in a marble-like way, or rough in a bark-like way.

In these cases, sensing coolness and smoothness | sensing roughness would need to be treated along the lines of an objectless kicking a kick.  At a first approximation, the coolness and smoothness | roughness would be identical with the events ‘sensing coolness and smoothness | sensing roughness.  [footnote:  I say ‘at a first approximation because later I intend to modify this claim substantially into a quite different claim.  For now, however, I will let it stand and use it as a kind of guide-post helping to lead one into a more complete analysis]

In the case of touching a physical object that does exist, thank you very much (the slab of marble, the bark), the treatment would be that of kicking a tree.  Kicking a tree is also kicking a kick, but now the event has an object it is directed towards.  There being no mental object with the requisite tactile properties, there is nothing that serves as a mental intermediary between the sensing events and their objects.  There would be a direct perception of the marble | bark.

Because Berkeley holds in the NEW VISION (at least in black and white) that that we do enjoy/suffer direct tactile perception of physical objects, applying to tactile Ideas the kicking a kick/kicking a tree analysis just given seems like a good way to interpret his tactile Ideas.

George Pitcher thinks there are additional reasons as well to interpret Berkeley’s Ideas generally in this manner.  [Link to this and to my digestion of it.]  Certainly one would want a consistent interpretation of Berkeley’s notion of an Idea that holds good both for visual and tactile Ideas, especially given this:

Note that, when I speak of tangible ideas, I take the word idea for any immediate object of sense, or understanding — in which large signification it is commonly used by the moderns.

George Berkeley, AN ESSAY TOWARDS A NEW THEORY OF VISION, in BERKELEY Essay, Principles, Dialogues With Selections From Other Writings (Charles Scribner’s Sons, New York) 1929) p. 36.  Henceforth A NEW THEORY OF VISION when referring to that Essay in this volume.

Berkeley’s use of the word ‘object’ here presents problems for those proposing a violent reading of the text, to say the least.  But it does seem plain that he wants an interpretation of ‘idea’ that would hold good both for visual and for tactile (or “tangible”) ideas.  If tactile ideas are events rather than objects with properties, visual ideas should be as well.

[Direction.  The physical body. Kicking.]

So subjecting sensing tactilely to a kicking a kick vs. kicking a tree type analysis removes

Clearly, Berkeley’s tactile Ideas would need to be interpreted this way if he is to make physical objects existing in extra-mental space their direct objects.

overOne can kick a kick, and one can kick, say, a tree (perhaps as a way of saying ‘I refute Berkeley thus’).  Sticking to the Berkeleyan framework, having an Idea of wine red, for example, that is to say, sensing wine red,  is more like kicking a kick than it is like kicking a tree:  there is no mental object (and, for Berkeley, there are no other kinds) towards which the event is directed.  What is meant by a kick in ‘kicking a kick’ is exhausted by the act of kicking; what is meant by ‘wine red’ in ‘sensing wine red’ (having an Idea of wine red) is exhausted by ‘sensing wine red’.

Of course, kicking a kick may also be an act of kicking tree rather than an objectless act (done say, to demonstrate a particular move in a martial art). Likewise, unless one is a Berkeleyan idealist, one is likely to think that there normally exists an extra-mental wine-red object one is directed towards when the event ‘sensing wine red’ occurs.  The Berkeley of the NEW VISION thinks that there is no such extra-mental object in the case of sensing wine red, but there

When an event of sensing the smoothness and coldness of polished marble occurs (when there is a tactile Idea of marble smoothness and roughness, to state things in a Berkeleyan way),

Distance and Location

Apart from what Berkeley said in black and white and what he may or may not have actually been thinking as he put down his sentences in black and white, a brief look at touch and vision themselves show that touch and vision invite, tempt us towards, the sort of treatment Berkeley gives them in the NEW VISION, whether or not we accept that invitation.  There is something about touch that wants, so to speak, to be direct, and something about vision that wants to be indirect.

Touch lends itself to a direct realist interpretation in a way that vision does not.  The felt object makes its presence … well … felt … directly on the sensing surface, the skin.  There is no gap to leap across, so to speak, to get access to the felt object.  It presents itself right here as it impinges upon and transfers energy to this sensory surface, one’s skin, whether by its motion towards and into one (say as one is catching a ball) or by the opposite and equal force it directs into one as one leans on their elbow at the desk, or as they stroke silk, pressing ever so lightly and delicately into the silk.

But the seen object at least seems to be at a distance from the sensing surface of the see-er.  It makes its presence apparent (feel the weakening of the adjectives as I go from ‘makes its presence felt’ to ‘makes its presence apparent’) via what at first sight looks like an intermediary, i.e., photons reflected from the object that enter the sensing surface, the retina, and transfer their energy to that other important part of the sensing surface, the brain.

It would seem then that what is seen directly are photons — light.  What we normally take to be the objects of vision — tables, tea pots, chairs, trees, houses, pineapples, cacti, cliffs and stars — would seem to be seen just indirectly.  (In the cases of the stars, however, perhaps a case could be made that what we are seeing is indeed light.)  [Footnote:  if I am not mistaken, in certain moods Berkeley thinks that what we see is light.]  This is the path we are led into if we have the intuition that the direct object of a sense must impinge upon the sensory surface.  The greater-than-zero distance from the sensing surface of what is normally taken to be the object of vision beckons us to enter that path, is extending an invite.

As I suggested above, we do not necessarily have to accept this invitation.  One way to politely decline it is    But wait — shouldn’t the objects of vision be regarded as the sensed wine-red, sensed sea-glass viridian green etc. inside my brain?  Well no — not if we think of sensing wine red or sea-glass green as kicking a kick as opposed to kicking a tree.  All right, then, let’s regard the sensing event as comprising the events going on in the brain and what is going on in the retina and what is going on at the lenses and what is going on with the photons bouncing off the table, pineapple, cactus etc.   Then we can get back out tables and trees etc as direct objects of vision.

By contrast, there is no such question     there is zero distance between the sensing surface of my skin and the rough bark of the tree as I run my hand along the bark’s surface. Through touch, I am in contact with the physical object itself.  There is no question of the tactile experience having to “reach out” to the object because a physical me — an entity with weight and heft –, engaging my physical hand, has already done the reaching out.  Touch is the direct realist sense par excellence. There is something about touch that wants to be direct.

And, as I hope to show (soon, or at least sometime before I die), the visual experience actually does reach out (in some sense of ‘actually does reach out’) to the physical object (Merleau-Ponty), or at least seems to so reach out (Berkeley) because of the way touch is implicated in the visual experience.  Touch informs the direct realist character (real or ostensible) of visual experience.

Impression.  Presentation as opposed to mere representation:  the object has a presence because it, in its fullness, is impinging upon one.  Felt impingement.

Given this, that the seen object is (with the exception of that portion of one’s body that is in their view) at a distance from one can seem a bit paradoxical.

*********

This time my homage to Plato’s SYMPOSIUM takes the form of Brad Pitt in THE FIGHT CLUB.  This image seems appropriate for a disquisition on touch and brutal physical reality.

Brad-Pitt-Fight-Club

If Plato can have a thing for Alkibiades, I can have a thing for gorgeous rednecks.  This particular redneck needs to stop smoking, however.


Protestant Theologians Peddling Coronavirus Conspiracy Theories

Yes, John Schneider is a crank and a fool with a predilection for conspiracy theories. Why do you ask?

It is beginning to look like the virus that causes COVID-19 has been around for some decades now, lurking inside bats and pangolins, already equipped with the biological tools needed to infect human beings. The evidence comes from the ability to detect the number of times the virus has undergone “recombination” with the DNA of other virues. “‘That [evidence] means SARS-CoV-2 has been circulating in bats for decades’, Boni says. ‘What’s more, one of the older traits that SARS-CoV-2 shares with RaTG13 and other close relatives is its receptor-binding site, the genetic mechanism that enables the virus to recognize and bind to receptors inside the human lung. The receptor binding site was not acquired by recombination from another virus,’ he explained. ‘That’s something that just exists in bats—and in pangolins, it turns out. It’s just a trait of these specific bat coronaviruses that they can also infect humans.'” Link.

But not so long ago Schneider was trying on Facebook to peddle to a working virologist a conspiracy theory, stemming from the right-wing fever swamps (this one was an attempt to discredit Dr. Fauci), to the effect that the virus escaped from a lab near Wuhan that was engaging in Gain of Function experiments on viruses. ‘The connection between the start of the pandemic in Wuhan and the presence there of a lab performing Gain of Function experiments on viruses is EXTREMELY SUSPICIOUS!!! he breathlessly announced to the world on a Facebook page. One can just hear the conspiracy theorist say in their nasally tone: “Now is that a coincidence? I don’t think so.

For a while the virologist patiently tried to explain why this, although possible, was not likely. It is extremely difficult to effect the slightest change in a virus, even in Gain of Function experiments employing a kind of controlled evolution. By contrast, there are there are countless Gain of Function experiments occurring in nature every day in those bat caves. The virologist finally lost patience with him and asked him to please bother reading to the end the articles that he, Schneider, had linked to. I would suggest that Mr. Schneider save himself from embarrassment by attempting to argue with a working virologist on a subject he knows nothing about.

This article also presents evidence that the virus arose from natural selection, and not from human intervention.

Maybe the virus came from bats or pangolins living near Wuhan and brought to a wet market in that city. Maybe it had infected a researcher studying bats and viruses in a cave thousands of miles from Wuhan; perhaps the researcher, infected without symptoms, went to Wuhan to talk to fellow researchers in the labs there and ended up infecting people unknowingly. Whatever happened, it is beginning to look like the connection between the start of the pandemic and the Wuhan labs is rather tenuous, not some Frankenstein’s monster cooked up and let loose by the evil and careless Asians existing in the fevered imaginations of the right-wingers Schneider hangs out with.

Novel Coronavirus SARS-CoV-2 Transmission electron micrograph of SARS-CoV-2 virus particles, isolated from a patient. Image captured and color-enhanced at the NIAID Integrated Research Facility (IRF) in Fort Detrick, Maryland. Credit: National Institute of Allergy and Infectious Diseases, NIH

What Part Of Treachery Do You Not Understand?

Cross-posted from a comment on an FB page. The ‘you’ in question is the controversial Protestant Theologian John Schneider, who behaved shamefully in general as a concern troll during those dark Trump years, and has behaved shamefully to me personally.

I am reading him the riot act.

“What part of ‘treachery’ do you not understand?

“Deep into the election, Trump was trying to close a deal to build a tower in Moscow. All throughout, he was blatantly lying to the American public by claiming he had nothing to do with Russia. The deal would have required the approval of Putin, the head of a hostile foreign power whose government lacks clear boundaries to separate it from organized crime.

The deal would have required lifting our sanctions against certain Russian banks. In other words, Trump’s truly massive corruption was determining what he thought our foreign policy should be. All of this rendered Trump vulnerable to blackmail. “All of this was quite possibly legal. I trust Mueller’s integrity (as opposed to Barr’s) enough to believe him should it turn out Mueller thought Trump’s actions were legal.

But the mere absence of an indictable crime does not preclude those actions from being instances of treachery in the service of corruption. And I really do look askance at those trying to normalize this treachery and corruption, whatever their motivations. “‘Russia Gate” will continue to be a live issue as long as there exist people who are outraged by treachery in the service of gross corruption. No attempted whitewash by Trump’s minion of an Attorney General will alter this fact. I don’t intend to let you forget this.

J’Accuse.”

Compare with Jonathan Chait’s essay here:


Protestant Theologians Behaving Badly (This Time It Is Personal)

Of course, Protestant theologians behaving badly have been very much in the news lately.

Given the tone and tenor of the remarks John Schneider, the controversial and influential Protestant Theologian, has made about political candidates of the XX persuasion, I have often wondered if some animosity embracing more than just policy disagreements underlies his disparagement of those candidates. I am not the only person to have wondered this.

Now when I accuse someone of being a misogynist, I want something more to go on than just the tone and tenor of a series of remarks, no longer how long the time span of this series may have been strung out. Recently, however, Schneider has shown himself to be well-acquainted with at least one tool employed by misogynists to put women in their place: insisting on referring to them by their first names in contexts in which this is clearly inappropriate. The employment of this tool was a prominent feature of the January 6 insurrection, as described here in the Washington Post. Let me dwell on this insurrection a bit, since it displays the character of this tool in a very clear and very stark way.

Searching for Vice President Mike Pence, the mob yelled out “Pence” in a tone that suggested ‘come out, stand up and fight’. Searching for Speaker Nancy Pelosi, they cooed out “Naaaaaaaaaaaancy”, the tone suggesting she has become their toy and is about to be subjected to that kind of violence meant to demean rather than allow her the status of a worthy opponent.

Oh, Naaaaaaancy is a very specific scene from a horror movie. Oh, Nancy is what the protagonist hears when she is hiding in a parking garage, or in a stairwell, or crouched under her desk, or pressed flat on the ground in a damp cornfield. Her terror is played out for entertainment, whether that means a narrow escape or a bloody death.

Oh, Naaaaaaancy is said in a singsongy voice. It is the same voice that a child would use to say, Come out, come out, wherever you arrrrre in a backyard game of hide-and-seek tag. It is playful. It is sinister. It says, I am planning to take my time, and it will not be pleasant, and it will not end well for you. The men looking for Pelosi in the Capitol were strolling, not running.

The “Nancy” part is intentional. Footage shows us that the rioters were also looking for male lawmakers; they were looking for Vice President Mike Pence. They referred to him as “Pence,” not “Mike.” They yelled his name instead of cooing it. They wanted to show they were angry with him. Her? They wanted to show she was their toy.

Some women — and I won’t say all, but I think it is closer to all than none — have heard their own first names called out in this singsong tone. Maybe a woman heard it when the front door clicked open, announcing the homecoming of the boyfriend who hits her sometimes. Or maybe she heard it intoned with flirtation and menace by the unnerving guest at a party; maybe she was hiding in the pantry at the time, concocting her excuse to leave. Or maybe she heard it while lying in bed, eyes wide-open, wishing she hadn’t told the pushy date he could sleep it off on the sofa.

Oh, Naaaaaaancy. A woman who hears it thinks of a specific kind of danger, and a man who says it thinks of that danger, too. That’s why he says it. To make clear that he is the hunter, and guess what you are?

After watching the newly released footage from the Capitol siege — a cornerstone of the House impeachment managers’ case against former president Donald Trump — it is hard to imagine there is a man, woman or nonbinary individual inside the Capitol who did not fear for their lives that day. But to be a woman in the Capitol then meant fearing for your safety in a specific way.

Monica Hesse, Washington Post, Feb. 10, 2021 at 8:37 p.m. CST

Add to list

The terror the rioters inflicted on women that day was clearly meant to demean them and to place them lower than they in the status heap. The mob employed one implement in the misogynist’s toolbox to accomplish this: calling someone by their first name in an egregiously inappropriate familiar tone meant to demean and to degrade. The rioters did not do this to Vice President Pence, a man, because whatever violence they intended to inflict on him, they were not intent on demeaning and degrading him and placing him lower in the status heap. But this was precisely their intent with Speaker Pelosi.

Misogyny is one species of bigotry, the nature of which I explore here.

To be a bigot is to assert oneself as part of an in group by casting another group (defined by some characteristic such as religion, race, gender, or sexual orientation) as an out group whose status of whose members is inferior to one’s own status and deserving of contempt. The out groups are regarded this way partly in order to fill a need for status (to have some place in the hierarchy other than the very bottom), partly for other reasons, such as the desire to obtain cheap or even free labor (race) or to have someone serve as a scapegoat to draw away one’s own sins (sexual orientation). Sometimes the reason is simple fear of otherness (religion, culture) which serves as fertile ground for the imagination to come up with all sorts of horrors. Typically members of the out groups are faced with a constant threat of violence in order to keep them in their place. Obstacles are placed in the way of their attempts to thrive as human beings (employers can refuse to hire them on the basis of the characteristic that defines their membership in the out group; they are always at risk of getting fired, getting evicted, getting red-lined, getting refused service at a lunch counter or cake shop, getting socially quarantined through Jim Crow laws, prevented from entering into (an inter-racial or same-sex) marriage). Often the bigot expresses a violent, obstinate hatred of members of the out group, especially when bigot feels their status slipping away, or feels even the slightest theoretical possibility of such a threat.

Cliff Wirt, https://cliffengelwirt.wordpress.com/2019/07/14/what-it-is-to-be-a-bigot/

The misogyny expressed by the rioters took the form of violence and threat of violence. But misogyny need not always be expressed that way. One can be a misogynist who is perfectly friendly with this or that woman — as long as the woman does not threaten his status at the top of the heap. It is therefore no defense against the charge of misogyny to say “some of my best friends are women”, or “my daughter-in-law is a woman”. All that is needed for misogyny is the desire to keep the status of women in general lower than one’s own. Even here, there may be exceptions when the accomplishments of a woman are too great. The misogynist, for example, might place Marilyn McCord Adams as a theologian superior to himself when her accomplishment simply cannot be denied, and yet still want — perhaps unconsciously — to grant women in general a status lower than that of men in general.

I choose this particular extreme example — the Capital Building Insurrection — because, as I said, it very clearly and very starkly reveals the misogynist character of referring to someone by their first name in an inappropriate context. This particular implement in the misogynist’s tool box obviously need not always be employed in such a violently dramatic fashion. It is normally part of the background hum of everyday existence in which women get devalued and demeaned. So when I accuse Mr. Schneider of employing this tool to demean and degrade a person, I do not mean to imply that he is a Capitol Hill Insurrectionist — though I certainly do believe that he did grease the skids leading to January 6 by acting as a concern troll. I am sure Mr. Schneider’s intent was much more humdrum and quotidian.

I am the person he intended to demean. In a recent exchange on Facebook, I had asked him to please not call me by my first name. “Cliff Wirt” or “Mr. Wirt”, but not “Cliff”. I did not care to be thought of as being on familiar terms with a person like him. So what does he do? Affirming the very reasons I did not want to be on a first-name basis with him, in the very next post, he calls me “Cliff”. I am fortunate that, if he meant it with the sing-songy intonation of “Naaaaaaaaaaaaaaancy”, that intonation did not make it through the internet wires. Nonetheless, his action was amazingly childish, more expected from a five-year-old than from a former professor at Calvin. It was grossly inappropriate, given that I had just asked him not to do this. Clearly, he meant to show disrespect for that request, and, by extension, for me. He meant to “place me lower” just as he would a woman.

I am, of course, of the XY persuasion. A woman is far more likely to be met with this kind of demeaning behavior than a man is, but of course the point of pulling this nonsense on a man would be to demean him in the way one demeans a woman. I do believe this was Mr. Schneider’s intent. At any rate, his reaching for this particular tool of misogyny shows that it is a ready-to-hand tool for him, always there to be used should the occasion require.

Does this show that Mr. Schneider is a misogynist? Maybe it is just another item of tone and tenor to be added to the tone and tenor of his Facebook discussions of female candidates starting from 2016. Maybe it is not enough to apply the label “misogynist” to him with complete confidence; maybe he is merely guilty of acting like a child. Your mileage may vary. I report: you decide.

Either way: J’Accuse.


The Protestant Theologian As Concern Troll

J’Accuse.

The divide is not between Democrat and Republican, but between those who have some share of decency and those who are vile. The Never-Trumpers, the people in the Lincoln Project, are Republicans, but they, like anyone else with any moral bearings at all, knew and feared Trump was capable of something like January 6. No one could see he would perform this particular act of treason, but everyone not in the Basket of Deplorables knew he would do something equally consequential and equally hideous. If not nuke Iran, then something else.

Let’s say that Mr. Schneider, concern troll, was NOT not in the Basket of Deplorables.

Had John Schneider, the controversial and influential Protestant Theologian, achieved the aim of his concern trolling, everyone would have been lulled into a general complacency regarding Trump that would have made the success of the insurrection much more likely. No, Trump isn’t really that bad, Schneider was trying to lull us into thinking. What makes you think he is? If you think he is simply vile, you are showing a deplorable lack of respect for the Deplorables, these salt-of-the-earths who put him in office.

Had Schneider succeeded completely, no one would have enlisted beforehand in call lists to show up in force for massive protests on the streets in case Trump tried to steal the election. Labor leaders would not have discussed the possibility of strikes hitting key sectors. We would have been like the unprepared immune system attacked by COVID-19, never having encountered that virus before. Trump’s attempt to become a dictator would have had a substantially greater probability of success because it would have faced less resistance. Fortunately, Mr. Schneider did not succeed completely. Even had the Capitol insurrection succeeded, the call lists I was included in would have ensured that I, at least, would have been on the streets. I strongly suspect crippling strikes would have been in the offing.

Everyone else could see that Trump was likely to attempt something as horrifying as the attack on the Capitol. Why did Mr. Schneider not see this? Instead, wallowing in endless grievances of the right-wing sort, he attacked and demeaned those who did see this, all the time pretending to be a progressive concerned about his allegedly fellow progressives.

Speculating what motivated Mr. Schneider to engage in his concern trolling is beyond my pay grade. Speculation that he is in the payroll of Vladimir Putin or earning a very comfortable living from funds ultimately supplied by Betsy DeVos would of course be wild. Myself, I think that comparisons with the behavior of compromised public intellectuals in communist regimes who have been made very comfortable by those regimes is at least one avenue to explore. Even though the aim of instilling complete complacency regarding Trump would not have been practically accomplishable, Schneider remains morally responsible for doing what he could towards that end. And while he probably did not intend this particular act of treason — the Capitol Insurrection — Schneider’s concern trolling remains an objectively treasonous endeavor. He greased the skids that brought us there, even if he did not know the exact destination. For this reason, the Capitol Insurrection will stain Mr. Schneider forever.

He, along with the others, is responsible. The blood is on his hands just as much as it is on the others.


Kamp Houston: Putting Profits Before Human Lives

Really, nothing more needs to be said than this:

http://lawyersgunsmoneyblog.com/2021/02/there-is-no-reasonable-defense-for-permitting-indoor-dining-under-covid-and-there-is-no-reasonable-defense-for-dining-indoors-under-covid

If Jonathan Reitzell and Moheed Martins have an answer to the question posed in the link above, I have not seen it. They are, however, doubtlessly too busy adding to Houston’s Wall Of Shame to be thinking too hard about an answer.

The sheer amorality of keeping a club open during the COVD-19 pandemic is worsened by the fact that the club caters largely to members of the community hardest-hit by the pandemic. Many of the comments made here are apropos:

https://www.lipstickalley.com/threads/bow-wow-apologizes-after-crowded-houston-club-backlash.4319735/page-4

It would be amazing if the normally crowded Kamp Houston did not spawn numerous super-spreader events, and the African American mayor of Houston, Sylvester Turner, would almost certainly dearly love to shut this potential swamp of disease and noise pollution down. Arresting and fining everyone from the venue owners (that is to say, Messrs. Reitzell and Martins) to the artists to the patrons would be a plus.

…he’s [Mayor Turner has] been trying to shut these clubs down for months but because of the governor he can’t. He’s done everything he could do to stop the spread

Contributor Kgyal20

Governor Abbott took the power away from local officials to put a capacity limit in these places otherwise everyone from the venue owners to the artists to the patrons should have been arrested and fined.

Having said all this these people are reckless and stupid and if they get sick all of them should be treated with the lowest priority.

Contributor Miza

The Republican governor of Texas, of course, is sure to see reducing the African American population as a feature and not a bug. That way he need not have to work so hard to prevent the African American vote from being counted:

the republican governors don’t care that the black communities/cities aren’t following guidelines bc they are waiting for covid to wipe them out.

they know white peoples will be fine lol

Contributor njessie1

And although I am no critic of rap music, I really do have to wonder if those who catch COVID-19 at a Bow Wow concert hosted by Kamp Houston might die of embarrassment first:

Crowd full of clowns. How you risk your health to see a Bow Wow concert in 2021?

Contributor Helwa

Wait. Ppl actually paid money and risked their lives to see a Bow Wow concert in 2021?Crowd full of clowns. How you risk your health to see a Bow Wow concert in 2021?

Contributor OriginalDonDada

I can only imagine how many folks will lie on their contact tracing from sheer embarrassment. A BOW WOW CONCERT?!

Contributor SouthernNotCountry

Imagine having to say your loved one died because he got Covid at a Bow Wow concert.

I’d lie. I’m not gon’ let my people go out like that. Say they got it somewhere more respectful. Like, the grocery store. 

Contributor gossiplover4044

The grocery store, however, is not likely to be hosting a packed maskless crowd:

No this fool [Bow Wow] didn’t try to make himself a victim because he was called out for promoting & performing to a packed maskless crowd during a pandemic.

Contributor LalaSharp

who in the hell is risking they life to go see Bow Wow.

Contributor anonyme

The situation is sad. The primary tool local officials have is public shame [such as Mayor Turner’s Wall Of Shame] since the southern governors are more committed to Trump than public health.

I don’t have time to post them right now but the – you willing to die, kill your grandmother, meet Peter at the Pearly Gates before your time for Bow Wow? jokes and memes are funny.

Contributor LalaSharp

“Folks in Houston got some explaining to do. What’s wrong with your city??!!” contributor Nikki Brady remarks. Should I provide a list, starting with Governor Abbot’s interference, and continuing with the greed and irresponsibility of certain entrepreneurs?

(And don’t get me started on the wage-theft lawsuits. Right now I am focusing just on death-and-disease swamps, not on possible wage theft. Take a look at https://casetext.com/case/dinh-v-weruntexas-llc and at https://www.leagle.com/decision/infdco20191122763)

“[H]onestly, no one is being held accountable for how badly this pandemic has been handled”, says contributor Est[Aaspeeping with reference to Kamp Houston and Bow Wow. Well yes, everyone involved — Governor Abbot, Messrs Reitzell and Martins, the patrons who foolishly think they will be living forever and who, amorally, don’t care who all they infect, all the reviewers who say nothing about the damage being done to the African American community, that whiny Rapper Bow Wow who accuses Mayor Turner of not liking him, the smug and despicable teenage parking attendants — all need to be held accountable and exposed.

Or, to state this a bit more concretely, may they all go to hell.

J’accuse — yet again.


Kamp Houston And COVID19 Enforcement

The TABC has made a start in shutting down joints that flagrantly violate COVID-19 restrictions.

https://www.houstonchronicle.com/entertainment/restaurants-bars/article/Nightclubs-Spire-and-Cle-among-Houston-liquor-15882542.php.

Now if they would only get to Kamp Houston, which, as was noted in a review, cited in a previous post, lets its staff openly thumb their nose at those restrictions. As the second wave of COVID-19 deaths becomes worse and worse, it is important to shut down all of these breeding grounds of disease and pollution.

I don’t see how the owners/managers of these establishments can look at themselves in the mirror, given their total disregard for the well-being and even the lives of others.

See as well: people not wearing masks in Kamp Houston.


You Plug Em; We Plant Them

Recently, a bar and club named Kamp Houston, owned or managed by Jonathan Reitzell and Mojeed Martins, opened up right next to my apartment complex.  The club creates a COVID-19 issue for two reasons. First, a number of people in my apartment complex are recovering from COVID-19. The impenetrable wall of noise emanating from Kamp Houston makes the situation of these people, already very bad, absolute hell. One might reasonably expect Messrs. Reitzell and Martins to know that placing a club continuously playing egregiously loud music until 2:30 am right next to an apartment complex will create a hellish situation not just for those recovering from COVID-19, but for everyone in that complex. But it would seem that these two just do not care. They are far more interested in squeezing as much loot from the club as possible as quickly as possible, the consequences for other people be damned.

Second, acquaintances of mine who have entered the premises tell me that people are not wearing masks, and are not observing physical distancing.  The patrons need to make a considerable effort to make themselves heard over the extremely loud music, vastly increasing the risk of spreading the infection through micro-droplets.  Although it is true that the risk of infection is less for patio dining than it is for indoor dining, even patio dining is a danger if the violations are flagrant enough.

And the violations are flagrant indeed. This is a place in which managers do not bother to wear masks, and people lower down the chain dare to tall a patron “You’ve come to the wrong place for that [reasonable measures to prevent the spread of COVID-19].”  https://blackgirlswhobrunch.com/2020/09/08/kamp-houston/. One is reminded of what the owner of a funeral home is alleged to have told a crime boss: “You plug them; we plant them.”

The owners of Kamp Houston, Jonathan Reitzell and Majeed Martins, have proven themselves to be so cavalier about violating COVID-19 measures that another club they own or manage, Mount Prospect, landed on Houston’s Accountability Wall aka Wall of Shame. Given the recent surge of new COVID-19 cases, it is especially important that Mr. Reitzell and Mr. Martins not be allowed to get away with the scofflaw attitudes that exist among the people doing work for them.  That Kamp Houston caters to the African American community, which has born the worst of the pandemic, makes it even more important that they not be allowed to get away with this. The city of Houston needs to shut Kamp Houston down.


NOISE, PESTILENCE, AND POSSIBLE WAGE THEFT

Wall Of Shame: One of the victims of Kamp Houston’s wall of noise and sickening bass is an elderly lady who has recently recovered from COVID-19. Already weakened by her experience with COVID-19 hell, she is now horribly stressed out by the fresh new hell of a nonstop blast of sound emanating from Kamp Houston. These typically continue until 2:30 am. Other victims include everyone in the path of that solid wall of sound who cannot relax at home after a hard days work and cannot get a decent night’s sleep. If any people contract COVID-19 because of what some regard as excessively lax measures on the part of the managers to contain the spread of the disease, those people too will be victims. Finally, whatever the legal complexities, those employees who have filed lawsuits against the managers and owners for nonpayment of wages will doubtlessly see themselves as victims as well.

Kamp Houston is a “bar and restaurant” (located in Houston, Texas, naturally) that recently opened up in a residential area, blaring LOUD — I mean LOUD — noise and the sickening THUMP THUMP THUMP of bass music nonstop until 2:30 am directly into an apartment complex right across the fence from them. Its managers, Jonathan Reitzell and Mojeed Martins, also own a joint called “Prospect Park” that landed on Houston Mayor Turner’s Wall of Shame aka Accountability Wall for laxness in preventing the spread of COVID-19. (see https://www.houstontx.gov/wallofshame/)

Reitzell says Kamp [Houston] will follow all recommended guidelines for limiting the spread of COVID-19. Staff will be wearing masks, hand sanitizer stations are located throughout the property, and they’ll be taking temperatures at the door. Prospect Park landed on Mayor Sylvester Turner’s Wall of Shame Accountability Wall….

https://houston.culturemap.com/…/08-05-20-kamp-new-bar…/

“You’ve come to the wrong place for that”: Although Reitzell tries to produce one impression of how seriously Kamp Houston takes COVID-19, the author of the web site Black Girls Who Brunch presents a rather different picture. When she confronted a parking attendant with the fact he was not wearing a mask, the attendant, in the presence of his manager, said: “You’ve come to the wrong place for that.” The wrong place, that is, if one were expecting an enterprise that took seriously inhibiting the spread of COVID-19.

What I WILL say though, is many of the parking attendants were not wearing masks! I know there is a divide about wearing masks. I personally subscribe to team #MaskUp particularly when you are out in public. When I rolled up, the valet stopped me to valet my car or to charge for self-park. Andddd he ain’t have a mask on. I leaned back in my car and said excuse me where is your mask?! He then summoned the manager to take my card for self-park. He also was not wearing a mask! Me being me, I also asked where was HIS mask! The first attendant said “You’ve come to the wrong place for that.” Well, that’s certainly not something I think a valet should say to any customer.

https://blackgirlswhobrunch.com/2020/09/08/kamp-houston/

Given the recent spike in COVID-19 cases and deaths in Houston and in Texas generally that threaten to overwhelm Texan hospitals, this cavalier attitude towards COVID-19 is reprehensible. It is true that this attitude was expressed by a valet (albeit with the apparent approval of his manager), but it is also true that the fish rots from the head down.

Unpaid Wages: Aside from issues of noise and pestilence, Reitzell and Martins have attracted two lawsuits so far regarding nonpayment of wages aka wage theft. I present the links to these lawsuits here so that the reader may draw their own conclusions.

https://casetext.com/case/dinh-v-weruntexas-llc

https://www.leagle.com/decision/infdco20191122763


Epistemically Accessible Possible Worlds, Compatibility, Failure Of Bivalence, And Inconsistent Situations

Caravaggio Card Sharps Kimbell
Caravaggio’s painting the CARDSHARPS nicely encapsulates the structure of a situation, and illustrates the three-place relation Rstu. Situations and their structure I will be discussing extensively in this essay in order to arrive at a satisfactory statement of the truth conditions for negation. This statement will be needed to resolve the paradoxes of Classical Logic’s Material Implication, paradoxes which Strict Implication does not completely resolve. Rstu I will be discussing in a different essay

I start by attempting to define situations (as opposed to possible worlds) in terms of parts of possible worlds that are epistemically accessible to me from my situation in the actual world. This will let me show how A v ~A can be false for a situation. In other words, both A and ~ A are false for that situation, though not for a possible world. The situation therefore counts as non-bivalent. I will show this by way of a set of truth conditions for negation that rely on a concept of a compatibility relation between situations that relies on possible worlds that are epistemically accessible from the actual world for a sentient being S.

I will then add ‘ostensible objects’ to my account of situations. This will let me show how ‘A and not A‘ can be true for a situation, a situation that would therefore count as inconsistent. I will show this employing a concept of an incompatibility relation between situations that relies on (impossible?) worlds that are epistemically inaccessible from the actual world for a sentient being S.

Both non-bivalent and inconsistent situations are needed for Relevant Logic, a paraconsistent logic, in order to eliminate countless irrelevant implication propositions that would otherwise be true.

I am willing to ‘go there’, so to speak, because I will do practically anything (even becoming one of those squeegee car-window washers waiting to pounce on cars at intersections in the hopes of gaining a quarter) to avoid making the following true:

If Cliff lives in Houston, then the earth has at least one moon

If Paris, Texas is the capital of France, then Calypso music originated in Wisconsin

If I vote for Hillary Clinton, we will end up with a criminal president who is under investigation from day one

All of the above statements are true in Classical Logic but false in Relevant Logic.

Let me start, then.

Nota Bene: in what follows, I will be enclosing the names of words and phrases in double quotes, and the names of concepts, relations, and propositions within single quotes. I will use | to mean “alternatively”. The first occurrence of an important technical term will be in bolded italic.

Although the contents of this paragraph will probably seem a bit opaque to a reader who is not already familiar with these issues, I will list out anyway the points I will be making here. We can analyze ‘compatibility’/’incompatibility’ in terms of (parts of) epistemic possible worlds. We do not need to leave these concepts as primitives. Since, as it will turn out, situations have everything to do with knowledge/information, it should not surprise us that the concept ‘epistemic possible world’, as well as related epistemic concepts, should be useful for analyzing them. The method I employ in the following will itself also rely heavily on the concept of epistemic possible worlds. All of the above will be used to analyze a truth condition for negation that will allow for the existence of situations that fail to bivalent and that fail to be consistent. And ultimately, of course (though I will not be discussing this in detail here), the aim of doing that is to show how the above implications can be regarded as false.

Here is the crumb-trail for this disquisition. First I will be discussing possible worlds in general, then possible worlds that are epistemically accessible for an agent S from another possible world (especially the actual world). I will then discuss situations, which discussion will branch off into three streams. In one stream, I will attempt to cash out the concept of exposure aka unconcealedness aka unhiddenness. (I use these three terms interchangeably to name the same concept. I will usually be using “exposure”, but I will sometimes use “unconcealedness” and “unhiddeness” when I am in a more Heideggerian mood. Although this concept is taken from Heidegger, I have the distinct feeling Heidegger would not be happy with my treatment of them.) In a second stream, I discuss what in a situation (as opposed to a possible world) is truth-making for a sentence. (So yeah, I am keeping my aims modest — just knowledge and truth. Hahahahahaha.) In the third stream, I will discuss the binary compatible/incompatible relation among situations. These three streams will converge in a statement of the truth condition for negation, which is (spoiler alert) as follows:

A situation makes ~A true if and only if every situation compatible with it fails to make A true

RL p. 75

This truth condition for negation will then let me show how situations can fail to be bivalent and fail to be consistent. The discussion of inconsistent situations will include a discussion of ostensible objects.

But to get to this truth condition, I will need to discuss what it means to “make” a sentence true, and what it means to say one situation is compatible/incompatible with another. Articulating what it is to make a sentence true will require a certain amount of verbiage (hopefully not too baroque).

But I can give a bare-bones account of compatibility/incompatibility right now. Compatibility/incompatibility are binary relations between situations:

Two situations are compatible if and only if they can hold at the same time in the same possible world

And:

Two situations are incompatible if they cannot hold at the same time in the same possible world.

These two definitions employ the modal concepts ‘can’ and ‘cannot’ respectively. It will therefore be necessary, in order to dig deeper into the compatibility | incompatibility relations, to discuss the foundation of modal concepts, i.e. possible worlds. I need to discuss possible worlds anyway because the relata of these binary relations, situations, are also to be explicated in terms of possible worlds. Situations are parts of possible worlds. It will therefore be necessary to discuss possible worlds first.

Here are the topics I will be discussing, in order: Possible Worlds Spawned-From-The-Known Possible Worlds Spawned-From-The-Unknown Possible Worlds Possible Worlds That Are Epistemically Accessible To Me From The Actual World Situations Epistemic Possibility Epistemic Truth Compatibility/Incompatibility Situations Drawn From Spawned-From-The-Unknown Possible Worlds Situations Drawn From Spawned-From-The-Known Possible Worlds Bivalent and Inconsistent Situations Making A True

Possible Worlds

At least for now — until I am forced to change — I will take a possible world to be defined by a set of natural-language descriptions [but what if those descriptions contain vague concepts, such as “hill” or “yellow”? would that not make them violate the requirement that possible worlds be complete?], each one of which corresponds | fails to correspond to a state of affairs which, because it obtains | fails to obtain at a time t, is (to follow Chisholm) identical with a proposition. There is therefore a one-to-one relationship between a state of affairs and a proposition that obtains | fails to obtain at t. There is, of course, a many-to-one relationship between natural-language descriptions and a proposition aka state of affairs at t. “Umuulan” uttered in Manila as one holds an umbrella and “It is raining” also uttered in Manila while holding an umbrella are natural-language descriptions in Tagalog and English respectively which both express the proposition named (in English) by ‘it is raining’.

A sufficient condition for a state of affairs’ obtaining is its having a set of objects located in space-time and bearing the relevant relations to one another. For example, the state of affairs expressed by the sentence “Our Unix SA is standing to Genghis Khan’s right; and my brother Dan is standing to Leon Trotsky’s left who in turn is standing to Genghis Khan’s left” obtains if our Unix SA, Genghis Khan, Dan, and Leon Trotsky have a location in space-time at t and are spatially related to one another in the way just described.

The description that expresses the proposition are sentences in a natural language that are used to perform a speech act of describing. If my cat Tiger is now sitting on the mat in my apartment, that state of affairs obtains, and the description performed by uttering the English sentence “My cat Tiger is now sitting on the mat” expresses a proposition that is true because it corresponds to this state of affairs. In a derivative way, the description/sentence also corresponds to this state of affairs and is also true. If Tiger is not now sitting on this mat, the aforementioned state of affairs does not now obtain, and the aforementioned proposition does not correspond to anything in my apartment that would make it true. The proposition is false, as is the sentence expressing that proposition whose utterance performs the speech act of making a false description.

I will leave ‘state of affairs’ as an unanalyzed primitive, explicating it only by providing examples. ‘Corresponds’ I will also not say much about, except to say that it is a relation between a proposition and a state of affairs, and the relation might be, as Chisholm thinks, identity at a time t.

As one possible world among others (if something is actual, it is also possible), the actual world comprises that set of descriptions, each one of which expresses a proposition that corresponds to a state of affairs that obtains. In the actual world, the color of the walls in my apartment is a nice, subtle portobello mushroom. The description “my apartment has portobello-mushroom colored walls” corresponds to this particular state of affairs, this particular piece of the actual world. It is a member of the set of descriptions that defines the actual world. I will say that the description maps to the state of affairs. I conceive of states of affairs that obtain as akin to bricks building up the actual world.

In the actual world the color of the walls in my apartment is not a wild fuchsia. The description “fuchsia-colored walls” does not correspond to this particular piece of the actual world. That this state of affairs fails to obtain (i.e., my apartment walls being wild fuchsia) means that it is not part of the actual world. The actual world contains just the one portobello mushroom brick, so to speak, and not a fuchsia brick.

Spawned-from-the-known possible worlds. Through a kind of wave of the hand, I can specify a possible world distinct from the actual world by saying “everything is the same as in the actual world, except the color of the walls of my apartment is a wild fuchsia.” In doing this, I have just spawned, so to speak, or “accessed” a possible world (which, henceforth, I will call the “fuchsia-wall possible world”) by taking a description of a state of affairs I know to obtain in the actual world (“the walls of my apartment are a nice subtle portobello mushroom”), a state of affairs that is exposed to me, so to speak, and substituting for it a different description (“the walls of my apartment are a wild fuchsia”), a description which fails to map to any obtaining state of affairs in the actual world. I will call possible worlds accessed this way “spawned-from-the-known possible worlds.”

One may feel that the hand-wave needed to specify/spawn/access the fuchsia-wall possible world surely constitutes a defect in the specification of that possible world. The specification is serviceable, let’s say, rather than ideal. It lets us talk about the fuchsia-wall possible world, but surely only a specification, a listing-out, of every state of affairs comprised by the possible world would be perfect (made without defect). But only a mind as capacious as God’s would be capable of doing this. God exists or she/he/they does not exist; but the concept ‘possible world’ (at least when regarded as a set of descriptions) needs at least the idea of God’s mind in order to be completely intelligible. For, as I will consider later, a possible world has to be complete — that is to say, it has to answer every question.

These possible worlds are defined by sets of descriptions some of which map to the states of affairs that “build up” so to speak the actual world and others which do not map to or correspond to any states of affairs obtaining in the actual world. When a description does correspond to a state of affairs obtaining at t in the actual world, I will say that the description is satisfied by the state of affairs.

A state of affairs is actual when the objects it comprises have a location in space time. For all I know, there may be more than one space-times. Here, however, I will assume there is just one, and that there is, therefore, just one actual world comprising all actual states of affairs. The actual world is one possible world among others, but it is the only one in which every description in the set of descriptions that defines it maps to the corresponding state of affairs which obtains.

If I may be allowed to indulge in wild metaphor for the moment, I will say that the fuchsia-wall possible world is composed of the same bricks as the actual world, with the exception that the portobello mushroom brick has been taken out and replaced with a written note saying “this is a fuchsia brick”.

I will call phrases such as “fuchsia walls” “key descriptions”, since these are the descriptions that, with the aid of the “everything else is the same” hand wave, are key to defining the fuchsia-wall possible world and opening up so to speak that world to me. It will be seen shortly that key descriptions are not limited to generating or “accessing” spawned-from-the-known possible worlds. When a key description is not satisfied by a state of affairs in the actual world, I will say that the content of that description is merely “posited“.

A positing may be actually realized by a person performing it, or it could be something potentially realized. An hour ago, for example, I had not posited a butterfly with black and white wings fluttering about in the Amazon at GPS location xyz, but I am now. An hour ago this particular possible world was just a potential one, contemplated perhaps by an infinite mind but by no one else. Compare this notion with that of a line in geometry that, potentially, is infinitely divisible, but each of whose segments is known by an infinite mind.

While I am still here, let me “access” (henceforth I will not be placing scare quotes around the word “access”) a couple more spawned-from-the-known possible worlds. I can say “everything is the same (even the color of my apartment walls) as in the actual world mutatis mutandis, except that water flows uphill.” Again, I have “generated” or accessed a possible world from a known fact in the actual world, namely, that water flows downhill. Or: “everything is the same as in the actual world, except that donkeys talk”. I have accessed a possible world by using a known fact in the actual world namely, that donkeys don’t talk. Naturally, the “mutatis mutandis” (would very much else really be the same if donkeys talked or water ran uphill?) makes me a bit uncomfortable, but I won’t try to deal here with the issues it may raise.

Spawned-from-the-unknown possible worlds. I can access a possible world, though not one necessarily distinct from the actual world, by using as my raw material a piece of the actual world about which I do not have knowledge. Suppose, for example, that, in the Pilsen neighborhood of Chicago (that somber city), near Western Avenue, Elizarraraz (from whom I was renting living quarters and studio space for a while … “Elizarraraz” is Ladino, the Iberian Sephardic counterpart to the Ashkenazim Yiddish, for “poor king”; many people of Jewish descent managed (in spite of the efforts of the Spanish Inquisition) to make their way to Mexico, from which country Elizarraraz’ paternal ancestors hail, in order to place as much distance as possible between themselves and the Inquisition … but I digress) . . . as I was saying, suppose that Elizarraraz has set up a shell game comprising three shells under one of which lies a peanut. The shells are set up on a table in an upstairs room into which a beautiful morning light is shining — the game is being played in the full, plain light of day. I do not know, of course, under which shell the peanut lies hidden.

Might this be the infamous rogue peanut?

I can generate three possible worlds from these three unknowns by filling in the “holes”, so to speak, with key descriptions taking the form “the peanut lies under shell #x”. In one possible world, the peanut lies under shell #1 and everything else is the same as in the actual world; in the other it lies under shell #2 and everything else is the same as in the actual world; in the third it lies under shell #3 and everything else is the same as in the actual world.

Possible Worlds That Are Epistemically Accessible To Me From The Actual World: I do not know anything that would rule out the identity of any of these possible worlds with the actual world. Following the literature, I will say that these are possible worlds that are epistemically accessible for me from my location in the actual world.

We can talk about the relation of espistemic [sic] accessibility. A world w0 is epistemically accessible from w for an agent S (in w) iff S knows nothing that would rule out the hypothesis that w0 = w. Then, p is epistemically necessary (for S) iff p is true at all possible worlds that are epistemically accessible from w (for S).

http://fitelson.org/125/accessibility.pdf

I modify the above to the following:

A world w0 is epistemically accessible from w for an agent S (in w) iff nothing in the body of knowledge possessed by S would rule out the hypothesis that w0 = w.

If one is beginning to suspect on the basis of the shell game example that there is a close tie between the concept ‘epistemically accessible possible world’ and “subjective” probability, one’s suspicions would be correct. Probability can also be interpreted in epistemic terms. ‘Epistemically accessible possible worlds’ lend themselves not just to an elucidation of one kind of possibility | necessity, but also to ‘probability’ seen as a epistemic/logical concept. And I want to discuss probability because I want to explain the concept ‘situation’ in terms of the concept ‘exposure’ (aka ‘unhiddenness’ aka ‘unconcealment’), and I want to explain ‘exposure’ in terms of probabilities of 1. ‘Situation’ then leads to the truth conditions for negation suitable for Relevant Logic.

[[[ Probably delete this paragraph. Want to segue directly into probabilities of 1. The sentences to which I will be ascribing a probability of 1 will include not just sentences like “two plus two equals four” (which, I take it are true in all possible worlds in which the laws of deductive logic are the same as those in the actual world), but will also include sentences like “the peanut is under shell #1” and “the walls of my apartment are portobello mushroom,” or “there is a goldfinch at my window.” It is often said that nothing is 100%, but these cases are perfectly common and everyday, existing in the plain light of day. I will, however, grant the force of this saying by pointing out that no finite mind can guarantee that these plain light of day situations will always stay 100%. ]]]

‘Probability’ seen as a epistemic/logical concept. According to Henry E. Kyburg’s account of probability, which I find useful, a probability is always asserted relative to a body of knowledge or evidence:

My own conception of probability is, like Keynes’s and Carnap’s, a logical one. Probability statements are logically true, if they are true at all. A probability is asserted always relative to a body of evidence; relative to different bodies of evidence different probability statements will be true. [Begin this section grayed out now but I need to deal with it later] This need cause us no concern, however, for as scientists we are all willing to share information with each other, and it is no real stretching of terms to speak of the body of general evidence in an entire field as the body of evidence relative to which we shall make our probability statements. [End this section grayed out now but I need to deal with it later]. I do not want to regard this body of knowledge as fixed in any absolute sense; over a period of time, however brief it changes. But in order to clarify the process of inference we introduce the logician’s standard idealization and regard the inference as taking place at a timeless moment. In this moment there are statements are open to question and statements that are not open to question — though in another moment, or from another point of view, they could of course be questioned. …

Let us refer to this body of general evidence as G. Formally, I shall regard G as a set of statements, and I shall suppose that G includes not only “observation statements” and the like, but also statistical statements and scientific laws and theories that are so probable (relative to other statements in G) as to be practically certain.

Henry E. Kyburg Jr., EPISTEMOLOGY AND INFERENCE (Minneapolis, University of Minnesota Press, 1983), p. 138

Kyburg seems to be using “knowledge” and “evidence” interchangeably. We deploy the known, i.e., evidence, against the unknown — in this case the area of darkness under each of the three shells brought into the actual world by our three epistemically accessible possible worlds.

What I know lets me deal in a disciplined way with what I don’t know, namely, these three possible worlds generated by my ignorance regarding under which shell the peanut lies. For starters, let’s say that I know that there is indeed a peanut under one of the shells. If I wanted to be extra-careful about the possibility of cheating, I might reasonably want to make the statement “there is a peanut under one of the shells” open to question, so that it needs to be verified. But for now let’s say both that I do indeed know that there is a peanut (and only one peanut) under one of the three shells, and that I trust Elizarraraz enough to not open this knowledge to question.

Let’s say also that I know that Elizarraraz has used a randomizer of some sort to decide which shell to place the peanut under. Finally, let us say that I know that Elizarraraz has used this randomizer in the past ten million iterations of his game, and that the peanut has turned out to be under shell #1 for a number of times approaching as a limit exactly 1/3 of the total number of iterations, and ditto for shells #2 and #3. In other words, the randomizer works.

For reasons that I will not go into here, randomness, though very much tangled up with ‘probability’ is not identical with it. So what we have just tested is the randomness of Elizarraraz’ selection of the shell under which to place the peanut, not the probability of finding the peanut under this shell or that.

Consequently, I know that, in the current iteration of the game, the peanut is equally likely to be under any one of the three shells. Given all these things I know, I assert a probability of 1 in 3 that when I lift any one of the shells, I will find the peanut there. Given all the evidence I have, this assertion would be powerfully intuitive. It is the only number one could assert, given that particular body of evidence. Relative to that body of evidence, there is just one probability to be asserted. But I am not sure I can say anything to support this claim other than ‘anything else (say, 1 in 4) cannot pass the laugh test’. We rely on our intuitions here.

A less complete body of knowledge — one without the test of randomness, for example — will have one venturing a guess that the probability is 1 in 3, and less a confident assertion that it is. If the asserted probability does not have a body of knowledge behind it at all, it is not a real assertion of a probability. It is just an acoustic blast.

Relative to Elizarraraz’ body of knowledge, however, the probability is 1 that the peanut is under shell #1, assuming that he knows which shell he placed the peanut under and assuming this is shell #1. “…relative to different bodies of evidence different probability statements will be true.”

There are of course other circumstances in which a particular body of knowledge yields a probability of 1. Assuming I do in fact know that there is one and only one peanut under the three shells, I would assert a probability of 1 that the peanut is under shell #1 should Elizarraraz turn over shells #2 and #3, revealing both to be empty. I will venture that this p(1), like the p(1/3) mentioned above, is a logical truth. The relation between it and the corresponding body of knowledge is a logical relation yielding just one correct answer. Force.

And should Elizarraraz lifts shell #1 and to expose the peanut before my gaze, I would assert a probability of 1 that the peanut was under shell #1.

Now at this point countless epistemic possibilities, i.e. key descriptions for possible worlds that are epistemically accessible for me from my location in the actual world, are trying to push their way into my imagination. Assertions of certainty, i.e., assertions of p(1), have a way of attracting these shades, much as the blood from the ewe and ram sacrificed by Odysseus on Kirke’s advice drew throngs of shades from Hades. Or again, much as zombies are attracted to the smell of brainz. Or again, much as endless hordes of desperate database-dependent employees suddenly materialize when they sense that a DBA has come online. I could go on. But you get the idea.

In the case in which Elizarraraz has turned over shells #2 and #3, revealing them to be empty, one can generate a possible world in peanuts sometimes behave the way electrons do as described to me by my undergraduate chemistry TA a while back. Chances are the electron is well-behaved, he said, and is orbiting close to a nucleus. However, there is a non-zero probability that the electron could abruptly find itself on the nose of the Mona Lisa. One does not know exactly where the electron is. In fact, the electron could be (nomic “could”) anywhere.

We have seen that a state of affairs in a possible world is nomically possible, i.e., is a nomic possibility, if it does not violate the laws of nature. That is to say, it is a state of affairs in a possible world that is nomically accessible from the actual world. If my chemistry TA was correct, then it is a nomic possibility that this or that electron (choose one) finds itself the next moment on the nose of the Mona Lisa. Its finding itself there could (nomic “could”) happen. All the places where the electron could find itself the next moment form a sample space against which, employing whatever theories and whatever wave functions (I don’t pretend to have anything except the foggiest idea what these are), we assert various probabilities. I don’t think I would be going too far out on a a limb if I suppose that the probability the electron will find itself on the next highest or next lowest energy level is considerably higher than the probability the electron will find itself on the nose of the Mona Lisa. I will assume this latter probability is extremely, extremely low. If the electron actually does find itself in these various places at the frequency predicted by the theory, we can think of our theory as having been confirmed to one degree or another. (I won’t be venturing here what a ‘degree of confirmation’ might be.) It is not just a theory, by something that is beginning to look like a body of knowledge We can have a greater confidence that the probabilities we assert relative to this body of knowledge (are logically drawn from this body) actually do let us cope with the unknown — these dark spaces in the actual — in a disciplined way so that, even lacking a deterministic chain of causal events, this bloody atom around which the electron is orbiting does not plunge us too deeply into the Twilight Zone.

Let’s say that given conditions x, y, and z, the probability that the electron will gain | lose energy and ascend | descend to level l0 is (to choose what I am sure are ridiculous figures) 1 in 10, and the chances it will land on the nose of the Mona Lisa is 1 in 1,000,000,000,000. If I am not mistaken, a non-standard view in quantum mechanics is that there is an unidentified factor w (or a set of unidentified factors) such that, along with x, y, and z, w increases those chances to 1. For example, the set of factors {w, x, y, z} result in a probability of 1 that the electron will land on the nose of the Mona Lisa. The laws of nature would be deterministic even at the level of the electron, and we could make predictions — or, as Kyburg would say, statements, or as I would say, sentences — that would be certain, that is to say, relative to our body of knowledge, would have a probability of 1. Since this is, I think, the prediction that would satisfy us most, this would be what I will call a “non-defective” prediction. Whatever is happening, there is no possibility of happening otherwise. We would cope with uncertainty — with the unknown — by obliterating it

But the standard view is correct, there is no such set of hidden factors (“hidden variables”). So the best predictive sentences we could make relative to our body of knowledge would assert probabilities not of 1, but of 1 in 1,000,000,000,000, or 1 in 10, and so on. While these would not make as satisfying a conquest of the unknown as p(1), they are perhaps serviceable as predictions. Jean Dixon may do worse.

These nomic possibilities, these uncertainties, are also epistemic possibilities. If I am concerned with where this particular electron orbiting around this particular atomic nucleus is, I know nothing that would rule out the identity with the actual world one nanosecond from now of the possible world in which the electron is on the nose of the Mona Lisa (or in the next higher-energy orbit, or in the next lower-energy orbit, and so on). Just as I know nothing that would rule out the identity with the actual world of the possible world in which the peanut is under shell #1 | shell #2 | shell #3. The difference between the electron and the peanut is that in the latter case we know there is a hidden variable w, namely Elizarraraz, who chose under which shell to hide the peanut. It is just that I am ignorant of w. In the case of the electron, according to the standard view, there is no hidden variable w to be ignorant of.

Trying to cope with a section of the world. Therefore a body of knowledge. Therefore assertions of probabilities. No assertion of probability can be made against a body of knowledge that has not yet been collected, motivated by a need to cope. Open up possible worlds by assembling sets of descriptions with key descriptions.. Sets of knowledge items.

Were the peanut hidden under one of the shells on Elizarraraz’ table to turn rogue and behave like my TA’s electron, the probability that it is under shell #1 would be less than 1. For the sample space would not be limited to the three shells on the table, but would also include the nose of the Mona Lisa in the Louvre in Paris, France, or some other strange location far from Chicago, much less Pilsen or Western Avenue. — That is to say, if the nose of the Mona Lisa were an epistemically possible location of the peanut.

But of course we know that objects as large as peanuts do not behave this way in the actual world. So I know something that would rule out the identity with the actual world of the possible world in which the peanut is on the nose of the Mona Lisa. That possible world is not epistemically accessible for anyone who knows this from the actual world. That location is not an epistemic possibility.

Or do we know this? I propose the following thought experiment. …drags down the probability. I would know this is a place where the electron could be. Though problem of two different kinds of possibility getting mixed. Say the Junior High student figures out a probability that this proton in the peanut will … ping! … land on the nose of the Mona Lisa, then at the same time that neutron lands in the same place …. until they arrive at an incredibly, incredibly low probability that the peanut will find itself the next nanosecond on the nose of the Mona Lisa or at some other strange place far from Western Avenue in the Pilsen neighborhood of Chicago. Maybe the length of time required for something like this to happen anyplace in the universe would be the entire age of the universe starting from the big bang to the final heat death of the universe. Maybe we need several such universe life-times. Nonetheless, it would be a nomic possibility. Not. Or rather, not necessarily.

Well, no. At least it would not be a known nomic possibility. At least not a nomic possibility known by me. My ignorance of the laws of nature generally and of the laws of physics in particular is of course vast. So although I take my TA’s word for it that an electron revolving around some nucleus in the peanut in Elizarraraz’ shell game could (nomic could) end up on the nose of the Mona Lisa, I have no idea if a slow and lumbering proton in that nucleus could be as quirky. Were I to bet, I would say that the peanut’s ending up on the nose of the Mona Lisa would be a nomic impossibility. That is to say, it is (epistemically) possible that this happening is nomically impossible. Only an omniscient being, I would think, that has the capacity to survey all possible worlds nomically accessible from the actual world to see if a particular event is nomically possible, i.e., if there is a possible world in which this event happens. No finite being knows all the laws of physics. [if a law is nomically possible it is also nomically necessary] So I have no idea if a proton in the peanut in question could find itself on the nose of the Mona Lisa, even as a once-in-the-lifetime of the universe possibility.

Persistence is deeply taken for granted but even ‘taken for granted’s is too mentalistic– possibly something one has never thought of before, like the solidity of the concrete floor. It is the table top that lets us make inferences, for example, that the peanut is under shell #1. Lets us know things. The background against which. It is just there. Not represented. Not just another item of knowledge. Not so much a “I assume the peanut persists in its current location’ as in ‘I am in contact with the persisting world’ — to take one piece out of it would mean I have lost contact with the world, would enter the rabbit hole — the same feeling one may get when dealing with the quantum world. Turn this tabletop over and everything is a mess. The persistence of everything is the non-wavy concrete floor I walk upon. Not easy to justify, at least directly. Easier to justify indirectly (cf doubting the world itself presupposes the world). If I may indulge for a moment it is the non-conceptual relation I have to the world.

Indirect argument in favor of persistence: there is nothing special about not being observed , at least on the larger-than-quantum world. Since we never seem to observe things just disappearing, there is no reason to think the peanut just disappears. This just never happens — at least not for those who haven’t been thrown into a mental institution. But as the Oracle guru Tom Kyte says, you cannot prove a negative. Maybe there were reports in the past. Maybe this will happen in the future. A kind of faith similar to the “perceptual faith” discussed by Merleau-Ponty. But as in the case of the perceptual faith, the “coulds” are empty wraiths. Not real possibilities. Spooks that are the product of the imagination only. The subset of my set of knowledges that comprises these skeptical possibilities is empty. Peanuts do not suddenly turn rogue: never do, never have, never will.

05/08/2021

Does the perspectivalism of probability mean that one body of knowledge spits out a 1 and another spits out something less than 1? Just as one body of knowledge spits out a 1/3 while another spits out a 1/2? If determinism is true on the peanut level, then the nomic probabilities are all either 0 or 1. Infinite mind would surely defeat any randomizer, so this would hold true across iterations of the game.

hhhhhh

The three shells are on the table. Shells #2 and #3. One item in my body of knowledge is my knowing that Elizarraraz has placed one peanut under one of the three shells. Plus I know that neither he, no anyone else, has removed the peanut by sleight of hand. How I know this is not important: what is important is the fact that I do know this. I will leave it as an exercise or the reader to come up with a way of ensuring that no sleight of hand was involved, and that, even in the absence of any such, the peanut did not suddenly disappear. I, however, do not have any observation of the presence of the peanut.

Now I can imagine that the peanut simply disappeared — that it turned rogue and suddenly found itself on the nose of the Mona Lisa. I then make this the key description of a possible world. Everything else is the same as in the actual world — except the peanut has disappeared from shell #1. Is this a possible world that is epistemically accessible for me from my location in the actual world? Is there anything in my body of knowledge that would rule out the identity of this possible world with the actual world?

One might think at first there clearly is such an item in my body of knowledge. We know that peanuts do not behave this way in the actual world, although if my TA is correct electrons do. Peanuts do not just disappear from under shells with out someone removing them. This is not how peanut-sized objects in the world behave. We never see things of that size just disappear. To be sure, the peanut under shell #1 is not currently observed, but there is no reason why this fact about it should make it different from observed peanuts.

What, however, about one nanosecond from now? I am about to lift shell #1 to confirm that the peanut is in fact under it. It remains at lesat a logical possibility that the peanut might, at that very nanosecond, relocate itself to the nose of the Mona LIsa. In which case the proabably that is its under shell #1 would be less than 1.

Well, no, it is hard to see how that would figure into my calculation of the probability. To add to the sample space, would need a nomically accessible possible world. It would have to be nomically possible for the peanut to arrive at this location in the Louvre. That is to say, its doiung so could not violate the laws of physics. Such a violation would mean the transpostiion would be omically ipossle. There would be no possible world noimically accessible from the actual world in which the peaut ends up on the nose of the Mona Lisa.

But, of cocurse, I don’t know all the laws of physcias. Nor does any other finite mind, I assume. For all I or anyone knoes, there is some physical law that would let the peanut do this under certain circumstances. Maybe some One Two THree Infinity thung with all the air in the room rushing to a single corner just by chance.

05/09/2021

Suppose now I state as a key description the sentence “the peanut finds itself on the nose of the Mona Lisa or some other strange place”. I do not think one would encounter much opposition were they to assert that peanuts do not behave this way in the actual world. But what if one asserted, not just that peanuts generally or normally (even defining “normally” to some extreme number of sigmas) behave this way, but that peanuts never turn rogue, or that in no possible world nomically accessible from the actual world do any rogue peanuts exist? I think one would be hard-put to say these things with certainty. For one does not know all the physical laws holding in the actual world, and never will. Something could (epistemic “could”) seem nomically impossible but in fact be nomically possible because of some currently unknown law of nature. One does not know. This ‘not knowing’ creates room for the epistemic possibility that the peanut could do something wildly unexpected such as land on the nose of the Mona Lisa, even if the probability is is so low that it one cannot hope to see it happen except once during the lifetime of the universe.

But a mere epistemic possibility that ~p needs to be guarded against in order to know that p. A mere epistemic possibility won’t do it — the epistemic possibility needs to tie in with a different sort of possibility, for example, a nomic possibility. Epistemic versus nomic possibility lets us see how impotent — well, wraith-like — epistemic possibility is.

In different situations, different criteria for what is to count as knowing. In the ordinary context of interacting with people, socializing, playing games, playing billiards, worrying about getting caught cheating at cards, being in the thick of things and people, the world impinging on one and forcing its weight on one, one might go so far as to question, motivated by Elizarraraz’ skill at sleight-of-hand whether there really is one and only one peanut among the three shells. One might insist on putting everything on video so that one can review the tape for any irregularities. On the ordinary-life standard, this or similar measures would be enough to satisfy the truth conditions for “there is indeed just one peanut among the shells”. But on this standard, one would be acting bizarrely if they tried to verify that throughout the game the peanut did not suddenly disappear, maybe zapped by aliens or deciding on its own accord to attach itself to the nose of the Mona Lisa. That, in the absence of any sleight-of-hand shenanigans, the peanut might not persist in its location where Elizarraraz placed it is so taken-for-granted that the thought it might very likely never occurred to one outside of a philosophy seminar, just as the idea that a concrete floor might oscillate up and down like a water wave probably never occurred to one until one experiences a low-intensity earthquake. Later knowledge of the circumstances in which concrete can behave like a pond into the middle of which one has thrown a pebble might lead to regarding this as a serious (nomic) possibility; but no knowledge exists currently that would motivate guarding against the possibility that the peanut might turn rogue. No need to emulate those ghost-hunting shows in which sounds are recorded all night and infrared images captured on video in the hopes of catching a ghost or poltergeist in the act. See! Thepeanut suddenly disappeared, then returned! Sleight of hand is Wittgenstein’s grains of sand; persistence is his stream bed. Taken for granted background against which items can become knowledge.

So when the ordinary everyday standard of knowledge is in play, I do know that the peanut is under shell #1 when Elizarraraz turns over shells #2 and #3 and reveals them to be empty. I know this because I know that there is just a single peanut among the three shells. Given this body of knowledge, the probability that the peanut is under shell #1 is 1. Therefore, given this body of knowledge, the possible world in which the peanut is not under shell #1 is not epidemically accessible for me from my location in the actual world.

Might the concept of a situation be useful here?

Knowledge is basic, and I am basically taking knowledge as a primitive.

Epistemically possible that nomically possible. Can’t prove it directly — just indirectly. Wittgenstein’s background.

[The things that have been bugging me are almost certainly resolved by the perspectival character of probability.] [Do I know anything that would make the probability less than 1? It would be less than 1 if I knew that the peanut could transpose itself from shell to shell, or onto the nose of the Mona Lisa. Or if I know I am hallucinating, or that I am a brain in a vat. But I am lacking that knowledge. So no intuitive transfer to less than 1. Nothing that “forces” one to say less than 1.

Sleight of hand. So what? Either I know these things or I do not. If I do, the probability is 1. If I do not, the probability is less than 1 or null, that is to say, “not applicable.”

05/08/2021

Elizarraraz, after all, knows where he placed the peanut, and he knows it will still be there. (Or does he?) Peanuts, after all, have a way of persisting where one has placed them. The peanut is not going to spontaneously translocate to another shell, or suddenly appear on the nose of the Mona Lisa or some other unlikely place, or sublimate into thin air, or get zapped by aliens and made to disappear into some quanta of energy that have dissipated by the time one lifts the peanut. That the peanut is under the shell Elizarraraz placed it under is not reasonably open to question. For now.

Later, however, we could (epistemic “could”) acquire new knowledge, new evidence that may motivate us to place in question the persistence of the peanut under shell #1. There is nothing in my body of knowledge, for example, ;that would rule out the identity of a possible world 5001 CE with the actual world 5001 CE in which it has come to the attention of humanity that a fleet of flying saucers is hovering just outside earth. (Say, the space aliens are no longer doing their mist thing ala American Cosmic (see Rick Riordan’s Percy Jackson novels) and now let us actually see them). In this epistemically accessible possible world, the space aliens take a perverse delight in messing up shell games and zapping the peanuts in the game. Given this new knowledge, the probability that the peanut is under shell #1, given that this is where Elizarraraz has placed it, would no longer be 1. What was once not open to question is now open to question.

Or again, it is epistemically possible that it is nomically possible that the peanut could suddenly show up on the nose of the Mona Lisa (or some other unusual place). To see how this is (epistemically) possible, consider what my chemistry TA told ;me some eons ago. Chance determines where the electron of a given atom is, he said. The electron is more than likely to be orbiting the atom’s nucleus in one of its usual paths. But the possibilities are endless. That electron, he said, could suddenly appear the next moment on the nose of the Mona Lisa. Its appearing there is a nomic possibility, since it is allowed for by the laws of nature or even predicted — in a way — by these laws.

Predicted in a way … let’s say that given conditions x, y, and z, the probability that the electron will gain | lose energy and ascend | descend to level l0 is (to choose what I am sure are ridiculous figures) 1 in 10, and the chances it will land on the nose of the Mona Lisa is 1 in 1,000,000. If I am not mistaken, a non-standard view in quantum mechanics is that there is some set of currently unidentified factors such that, along with x, y, and z, increase those chances to 1. For example, the set of factors {w, x, y, z} result in a probability of 1 that the electron will land on the nose of the Mona Lisa. The laws of nature would be deterministic even at the level of the electron, and we could make predictions — or, as Kyburg would say, statements, or as I would say, sentences — that would be certain, that is to say, relative to our body of knowledge, would have a probability of 1. Since this is, I think, the prediction that would satisfy us most, this would be what I will call a “non-defective” prediction. Whatever is happening, there is no possibility of happening otherwise. There may seem to be nomic possibilities, but in fact these, like ghosts, demons, and poltergeists, evaporate with the increase of knowledge.

But if there is no such set of hidden factors (“hidden variables”), the best predictive sentences we could make relative to our body of knowledge would assert probabilities not of 1, but of 1 in 1,000,000, or 1 in 10, and so on. While these would not make as satisfying a conquest of the unknown as p(1), they are perhaps serviceable as predictions. Jean Dixon may do worse.

Now I know nothing that would rule out the identity with the actual world of the possible world in which some physicist calculates a probability not of some isolated electron in the peanut, but the entire peanut itself, suddenly showing up on the nose of the Mona Lisa or in some other euqlly unlikely place. . have a If what was happening with the electron were deterministic, we could say that Theseset of laws are at that level stochastic. The chances of the electron jumping (up or down) to a different energy level are 1/n. At the moment we can’t say anything more than that; we are unable to provide a chain of deterministic causes of the jump that would render its probability 1. That is to say, given such and such conditions, we know that the probability

If there were then the 1/n number would lend itself to an interpretation solely in terms of epistemically accessible possible worlds. In one of these possible worlds the electron remains at its current energy level and orbit the next moment; in the other it jumps to a different level when certain conditions are present. In neither case do I know anything that would rule out the identity of the possible world with the with the actual world as it will be the next moment. Here all possibility [modify this] is epistemic, based on my ignorance. Were some sufficiently capacious mind to acquire all knowledge about the electron, the possibilities would disappear. There would be just one possibility: the way the electron is now.

of that possible world One interpretation of this stochastic character is that

[Nomic probabilities less than 1: not knowing factor w, (there being no factor w to know) not even God would not know anything that would rule out the identity with the actual world of the possible world in which the electron finds itself on the nose of the Mona Lisa. This wold be an epistemically accessible possible world even for God. So nomic possibility would reduce to epistemic possibility. It is epistemically accessible possible worlds all the way down.]

[ “And the bank of that river consists partly of hard rock, subject to no alteration or only to an imperceptible one, partly of sand, which now in one place now in another gets washed away, or deposited. On Certainty, p. 15e. ]

When trying to account for where the electgron of a given atom is, aliens seem thingThe three epistemically-accessible possible worlds whose key descriptions are given by “the peanut is under hell #1 and everything else is the same as in the actual world | the peanut is under shell #2 … | the peanut is under Butshell #3….” provide a sample space to which I can Elizarraraz’ shell game here. [Live possibility determined by what I know and how it relates to my/our practical interests.]

What is included in the set are the “background truths” on the basis of which all other truths rest. It is certainly epistemically possible that I am awake, not hallucinating, not a brain in a vat, am in contact with a tangible world. If I am so, then it is epistemically impossible that there is no tangible world that I am in contact with. For the identity with the actual world of any possible world in which I am not in contact with the the (an) actual tangible world is ruled out by my ‘knowing’ that there is a tangible world impinging upon me every moment I am awake. ‘Know’ meaning too basic to show directly, but any attempt to show that I do not know undercuts itself. An indirect proof. Background. Basic. But also some justification.]

Adding to this account the claim that one does not necessarily know or even believe they know something that the they actually do know will save me a fair amount of agony and grief. A skeptic, for example might persuade me that I do not know that I am awake and not dreaming when in fact I do know that I am awake and not dreaming. Someone may be told by someone who completely convinces them for a moment “Who are you going to believe: me or your lying eyes?” [[It is possible to hold conflicting beliefs at the same time.]]

The actual world is, of course, a possible world that is epistemically accessible for me and to everyone existing in it because I, along with everyone else, know nothing that would rule out the identity of the actual world with the actual world. Since the actual world is my primary concern here, I will assume that the possible world w that S is located in and from which they access other possible worlds, is the actual world. I will sometimes replace ‘S knows nothing that would rule out the hypothesis that’ with ‘so far as S knows’ or ‘to the extent of S‘s knowledge’.

Not every spawned-from-the-unknown possible world is a possible world epistemically accessible to me from my location in the actual world. I could, for example, also generate a possible world from the three unknowns just mentioned by positing a peanut that is always, of its own accord, switching between shells and sometimes even finding itself on the nose of the Mona Lisa, mimicking thereby the possible behavior of a rogue electron as described by a chemistry TA I once had as an undergraduate. But we know things (I think … I hope) that rule out the identity with the actual world of the possible world in which peanuts behave this way: namely, that peanuts do not behave this way in the actual world. Although electrons may behave this way (if I can trust my memory of what my undergraduate chemistry TA told me), peanuts do not jump from shell to shell and they never find themselves of their own accord on the nose of the Mona Lisa. This possible world is not epistemically accessible for me from my location in the actual world.

No peanut here — so far

Possible worlds spawned from unknown pieces of the actual world, then, fall into two categories: those that are epistemically accessible for a knower S from S‘s location in the actual world (every now and then I will be referring to these just as “epistemically accessible possible worlds”), and those that are not.

The possible world w0 in which Bigfoot is roaming the forests of western Washington state is epistemically accessible for me because I know nothing that would absolutely rule out the identity of this possible world with the actual world. Likewise, the possible world w1 in which Bigfoot is not roaming the forests of western Washington state is also epistemically accessible for me because I know nothing that would rule out the identity with the actual world of this possible world. I think the chances are greater than 50% that Bigfoot is not roaming these forests, but that is not the same as my knowing this.

These two possible worlds are incompatible; they cannot be the same possible world. The one world precludes the other. One makes ‘Bigfoot is roaming…’ (A) true; the other makes ‘Bigfoot is not roaming…’ (~A) true. A possible world answers every question: for any given possible world, either Bigfoot is roaming in the possible world or she is not. One must be true but not the other. Both cannot be true. So in all possible worlds A ^ ~A is false. A possible world cannot be inconsistent.

(At least for now, I won’t try to deal with possible counter-examples to this assertion. One such possible counterexample is Graham Priest’s contention that a person walking out of a room is, for one moment, both inside the room and outside the room when the center of their gravity aligns with the center of the door space. I am tempted to think that ‘inside the room’ and ‘outside the room’ are two different situations which have a common boundary, with the result that the description “outside the room” is not always the negation of “inside the room”. But I won’t try to expand on this now. At the moment I will simply assume that in all possible worlds A ^ ~A is false.)

Which possible world we are talking about hinges on how it answers the Bigfoot question (A or not A?). The identities of w0 and w1 depend upon this answer. The identity of possible world w0 depends upon that world’s not being possible world w1. If I exist in a possible world in which A is true at a time t then all of a sudden per impossibile I am existing in a possible world in which A is not true at this same time t, then I have been transported to a different possible world. (Maybe Scottie beamed me into it.)

And one of them (at any given time), A or not A, must hold in w0 and w1. In neither world can neither ‘Bigfoot is roaming the forests of Western Washington State’ nor ‘Bigfoot is not roaming the forests of Western Washington State’ be true. The worlds must be bivalent. One or the other — at least one and at most one — A or not A, must be true for these possible worlds to be the possible worlds — mutually exclusive worlds — they are. To remove A from w0 would be to strip that world of its identity; likewise, to remove not A from w1 would be to strip that world of its identity. Neither w0 nor w1 can be a non-bivalent world. In all possible worlds, ‘A v not A‘ is true. ‘A v not A‘ is necessarily true, which means that ‘If A then A‘ is also necessarily true.

So the falsity of ‘A ^ ~A‘ and the truth of ‘A v ~A‘ stems from the criteria for the identity of possible worlds. Possible worlds have to be complete, answering every question (Is there, or is there not, a butterfly with violet wings fluttering about in the Amazon at GPS point xyz?). They have to be consistent. They must be bivalent. They would undergo serious ‘criteria of identity’ crises were these conditions not fulfilled.

To sum up this discussion of possible worlds: possible worlds fall into two categories: those possible worlds that are spawned from the known and those that are spawned from the unknown. In turn, spawned-from-the unknown possible worlds fall into two categories: possible worlds that are epistemically accessible to a sentient being S and those that are not so accessible. Unlike situations, to which I am about to turn, possible worlds must be complete (must answer every question, including what is happening at GPS point xyz in the Amazon), must be consistent, and must be bivalent.

I now turn to a discussion of situations and their compatibility/incompatibility. I will be discussing almost exclusively what I will call informational or epistemic situations, which, naturally, will be analyzed in terms of information and as parts of epistemic possible worlds. Unlike possible worlds, situations can be incomplete, inconsistent, and non-bivalent.

Situations

I now relate the concept of epistemically accessible possible worlds to the concept of a situation. A situation is a part of a possible world and comprises one or more states of affairs. A situation is not necessarily a proper part of a possible world; for I count each possible world, including especially the actual world, as a situation. Nonetheless, when I talk about situations, I will have mainly in mind situations that are proper parts of possible worlds.

Among those situations that are proper parts of a possible world are those whose states of affairs they comprise correspond to the key descriptions defining possible worlds. As we have seen, the key description “the walls of my apartment are fuchsia” defines, along with the hand-wave “and every other state of affairs is the same as in the actual world” the possible world in which the walls of my apartment are fuchsia instead of portobello mushroom. This state of affairs, had it obtained, would have had the aforementioned key description corresponding to it. I will call the situation which comprises this state of affairs a “key-description situation”.

A situation that comprises just a single state of affairs I will call a “singleton situation”. There is a many-to-one relationship between single states of affairs and the set of objects existing (actually or possibly) in whatever relationships among one another and having whatever properties. The state of affairs named by 788UIOYOIYTYTIURRRBBBB4yt76876%^%$##DYCbHGFUIYTDTFJvDIYOBOvo ‘Tiger is now sitting on the keyboard of my laptop’ FI^T%$^%DXGDIGVHLOUFC:”}{PVTDXERhjkakb sdkdvsdwlebwhcjhsasssdff is a single state affairs obtaining at t; the state of affairs named by ‘Tiger’s color is silver’ also obtains at t and is a distinct single state of affairs. There are therefore at least two singleton states of affairs here mapping to the set comprising my cat Tiger at t.

Situations that are proper parts of possible worlds are limited in some way. They are finite in one way or another. A major cause of finitude of course, is being born. One’s (merely possible or actual — but from now on I will assume ‘actual’ unless otherwise noted) entry into a (merely possible or actual — but see the previous parenthesis) world results in their getting plunged into a world which has them as one center (among countless others, not totally unlike Nicholas of Cusa’s description of space as infinite and having infinite centers) and a horizon that extends only so far. One exists in the thick of a mileau with which they must constantly cope. A certain portion of the actual world gets exposed, or unconcealed (I try to define “exposure” below) to one, starting at birth and continuing through one’s lifetime. That is to say, one acquires and has available to them information. I will be leaving the term “information” undefined, except to accept Dretske’s claim that information can be either conceptual (information grasped intellectually or in terms of categories) or non-conceptual (information not grasped intellectually, for example information felt, as Nelson Goodman put it in his LANGUAGES OF ART, in the bones and in the muscles). I use the term “exposure” partly to avoid the implication that what I am talking about is necessarily conceptual in character. It is thoroughly obvious that any being that is not omniscient will have only a limited portion of the actual world exposed to them. Like being born, not being omniscient is a major cause of finitude.

Caravaggio’s painting THE CARDSHARPS very nicely illustrates, I think, four typical features of situations. First the boundaries of the information that is available to one form the boundaries of a situation. Second, to be in a situation is to be placed in the thick of things: one is grappling with the exigencies of a situation. Third, the information might be information grasped not by the mind but felt by the bones and muscles, emotionally. Fourth, there can be a conduit of information from one situation to another.

Caravaggio,, THE CARDSHARPS
 

Caravaggio’s painting depicts three situations — four, if one includes the situation of the person observing the scene.. One situation comprises the situation of the callow young man, apparently of some wealth and status and vulnerable to being considered as a mark, who is pondering his cards. Exposed to him are one side of the cards, the table, and the front of the worldly-wise teenage cardsharp. Although he is directly looking at just the cards at the moment, I think it is safe to assume that in the very recent past he has acquired information about and has available to him information about the teenager and about the middle-age-ish man behind him. The young man, the mark, is a center of a situation within which a certain amount is exposed and from which much is hidden. The cards nicely serve as a visual symbol of the fact that his situation has boundaries shaped by a perspective and a point of view.

The teenage cardsharp of course has his own perspective, his own point of view, on the scene. What he is exposed to includes the back of the mark’s cards, the table, the cards he feels with his hands as he draws them from his back, the knife’s-edge tension he feels arising from the fact he has to accomplish his move perfectly, the feeling of danger arising from the fact the scene could very easily explode into violence — fists or swords — if he is not smooth enough. His own vulnerability, the fragility of his enterprise and its danger he cognizes in the bones and the muscles. Included in his situation is a kind of very broad present perfect. He has been shaped by a larger world which — if I remember my European economic history correctly — that has been suffering from harder times for a while now; and this card game is where he is now. All of this is his situation.

Oh, and yes — I almost forgot — part of the cardsharp’s situation includes a view of his confederate signalling to him the content of the mark’s cards. The confederate is in the thick of his own situation and of course he feels the knifes’s edge tension and danger, the fragility of their endeavor and the not at all improbable chance it could go wrong. These aspects of his situation are exposed to him, just as they are to his younger confederate. This situation serves as a conduit of information linking the mark’s situation with the teenager’s.

If I may be permitted to foreshadow what belongs to another post, we have here the 3-place accessibility relation between situations Rstu, where s is the signaler’s situation, t the teenager’s situation — a situation that includes a view of the signalling — and u is the mark’s situation. But more of that later, in a different post.

Any key or potential description that opens up a possible world maps to a situation. The key description ‘the walls of my apartment are fuchsia’ opens up, along with the phrase ‘and everything else is the same as in the actual world’ for me that possible world. The key description maps to the key situation that is part of this possible world, namely, the situation in which the walls of my apartment are fuchsia. I will say that situations hold in a possible world, including the actual world. That the walls of my apartment are portobello mushroom is a situation that holds in that possible world which happens to be identical with the actual world.

A situation comprises one or more state of affairs that obtains or could obtain. I use “comprise” for its suggestion that a situation surrounds, encloses, includes the states of affairs. The situation of my apartment in the actual world, for example, comprises the states of affairs ‘my cat Tiger is sleeping at my feet’ and ‘the walls of my apartment are portobello mushroom’, both of which obtain. Each of these states of affairs can be splintered off to comprise a distinct situation by itself.

“Known” aka “exposed to” aka “unconcealed” counts as a key description. That part of the actual world which I actually know, i.e., actually have information about, am cognitively exposed to, comprises my comprehensive actual situation. Everything that Smith has information about, everything that Morgenstern has information about, everything that Elizarraraz has information about, everything that an omniscient being has information about, comprises the comprehensive actual situation of Smith, Morgenstern, Elizarraraz and the omniscient being respectively. I will dub situations carved out this way from a possible world (including and primarily the actual world, of course) “informational” or “epistemic situations”; henceforth I will be using “situation” to refer to epistemic situations only, unless otherwise noted. A sentient being exists in an informational situation; this being is in the thick of things which press upon them and with which they must cope. That situation is defined by the information that is available to this being.

My own informational situation, the situation I am in, includes everything I am familiar in my apartment, as well as the view of the courtyard outside. It includes my knowledge that Houston is in Texas, Seattle is in Washington state, and St. George and Salt Lake City are in Utah. It includes all my old haunts in downtown Chicago and in that city’s Rogers Park, Near West, and Pilsen neighborhoods. Taken together, all this knowledge, all this information — both knowledge that and in-the-bones-and-muscles knowledge, comprises, along with the objects the information is about, what I will call my comprehensive actual situation.

My comprehensive actual situation includes numerous sub-situations — my cat Tiger’s sitting on a mat, the doorbell’s ringing inside my apartment. I will say that one is in a comprehensive actual situation or sub-situation; sometimes I will say that a situation — especially a sub-situation — holds for one. Sometimes, to emphasize the fact that the things within one’s situation are, typically, things with which they must cope, I will say one is grappling with and in the thick of a situation.

A bit later, when I discuss ostensible objects, I will be dropping the word “actual” and talk only about my “comprehensive situation.”

Now anything which blocks information from me … distance, shells, the practical difficulties (including getting the needed funding) of searching for probably-mythical creatures … will create a space for a possible world epistemically accessible for me from the actual world in which I exist. All that is required for the generation of a possible world that is epistemically accessible for me from my location in the actual world is that what I posit to “fill in” these spaces (a peanut in either shell #1 or shell #2 or shell #3; a Bigfoot | alternatively an absence of a Bigfoot roaming the forests of western Washington state; the sea-glass green or Venetian red or goldenrod yellow or periwinkle blue color of my neighbor’s walls) not be ruled out by what I know about the actual world.

The range of information available to me is obviously limited. It does not include enough information to absolutely rule out the identity of w0 (Bigfoot is roaming the forests of western Washington state) with the actual world, nor the identity of w1 (no Bigfoot is roaming the forests of western Washington state) with the actual world. It will not include enough information to rule out the identity of any other possible world that is epistemically accessible for me from the actual world — for example, the possible world in which the peanut lies under shell #1, the possible world in which it lies under shell #2, or the possible world in which it lies under shell #3. Nor does my comprehensive actual situation tell us whether, for any given GPS point in the Amazon, a butterfly is flapping its wings there, and if one is, whether its wings are purple or chartreuse. Nor does it tell us whether the walls of my neighbor’s apartment are colored sea-glass (viridian) green or Venetian red, a brick wall blocking this information from me, and my not having any other source of information that would tell me what the color is.

So unlike a possible world (including the actual world) which is “dense” in the sense that it answers every question, a situation has “holes” in it in the sense that it does not answer every question. It is littered with pockets of missing information. (Is the peanut under shell #3 or is it not?) The situation comprises the actual world minus all the holes in which epistemically accessible possible worlds can be generated by any positing whose content does not rule out, given what I know about the actual world, its being a component of the that world. If a possible world is dense like a slab of most cheeses, a situation possesses many “holes” — pockets of missing information that can be filled in by positings consistent with what I know about the actual world — and is in that regard like a slab of Swiss cheese.

Or, to switch metaphors, my comprehensive actual situation is like a mesa (comprising all the knowledge/information I have) in southern Utah surrounded by a fog-covered desert plain. Lurking within within this fog are countless possible worlds that are epistemically accessible for me from my location on this mesa in the actual world.

Delicate Arch in winter, near Moab, Utah

Since my comprehensive actual situation could be (in a sense of “could” that I will be clarifying shortly) identical with the Bigfoot possible world, or with the non-Bigfoot possible world, or with the ‘my neighbor’s walls are wine red’ possible world, and so on, my comprehensive actual situation could exist in more than one possible world. One is constantly finding out which possible world their comprehensive actual situation belongs to (and therefore which possible world the actual world belongs to). Is this the possible world the one in which the peanut is lying under shell #1 or the one in which shell #1 hides nothing except a piece of table top? Is this the world in which Bigfoot is roaming the forests of western Washington state, or the one in which no such creature is roaming those forests? Is this the world in which my neighbor’s walls are wine red, or the world in which they are some other color?

The key descriptions of these (epistemically accessible for me from my location in the actual world) possible worlds define circumscribed situations within those worlds. These descriptions might or might not be satisfied by the actual world. On the table in the Pilsen neighborhood of Chicago (that somber city) on which Elizarraraz has set up a shell game, the peanut may or may not be under shell #1. In the forests of western Washington state, Bigfoot might or might not be roaming. I will call these situations “derived from epistemically accessible possible worlds situations”, or “epistemic situations”. These are situations which the various epistemically accessible possible worlds that lurk in the holes in the swiss cheese, or in the fog surrounding the mesa, comprise.

This concludes my discussion of possible worlds and situations. I now turn to the “three streams” mentioned above, which will converge into a discussion of the truth condition for negation needed by Relevant Logic.

Truth And Possibility

[Possibility (modal) to probability back to necessity (modal).]

Just after Delicate Arch surrounded by fog.

The truth condition for negation is, as my reader will remember, the following:

A situation makes ~A true if and only if every situation compatible with it fails to make A true

But what is it for a situation to make a sentence true? Having just discussed possible worlds and situations (in the course of which I foreshadowed the concept ‘exposure’), I will now turn to what it means for a sentence to make a sentence true. A situation makes a sentence true when the state of affairs to which that sentence corresponds forms part of that situation by virtue of lying exposed within it. I explicate exposure (unhiddenness, unconcealedness) in terms of probabilities equal to 1, and hiddenness (failure to be exposed) in terms of probabilities of less than 1.

Exposure. Above, I have said that the situations I am concerned with are those parts of possible worlds to which one is or has been exposed, or unhidden. The concept ‘unhidden’ cries out to be explicated in terms of the concept ‘hidden’. I will explicate hiddenness in terms of probabilities that are less than 1. I have never entered my neighbor’s apartment, so I have never seen the color of his walls. As I type this, that color is hidden from me by a brick wall. There are any number of epistemically possible colors his walls could be. I do not know what that number n is, but whatever it is, 1 divided by that number is the probability that any given color is the color of his walls, assuming that we treat each color as equally likely.

Now should I walk into his apartment and see his walls (and see that their color is wine red), that part of the actual world ceases to be hidden from me. It has become exposed, revealed, made manifest to me. And the probability that my neighbor’s walls are wine-red is no longer 1/n, but 1. For if epistemic probabilities less than 1 require ignorance, a hiddenness of some kind, something that has prevented the flow of information (e.g., a brick wall, a lack of funding), it follows that getting exposed, de-ignoranced, made manifest, unhidden, revealed makes for a probability of 1.

But wait! In talking about the color of my neighbor’s wall, I am talking about perception. One may wonder if any perceptual situation, at least, could (which accessibility condition?) have a probability of 1. Surely that probability cannot ever be 1! And now, having just used the modal words”could” and “cannot”, I need to spell out (method) what species of possibility this particular use involves. What is the relevant accessibility condition here?

There are any number of epistemically accessible possible worlds in which I seem to see that my neighbor’s walls are wine red but while in fact they are not wine red. In each of these possible worlds, there is nothing in my body of knowledge that would rule out the identity with the actual world of the given possible world. In the absence of any indication that I may be hallucinating, I suffer a vivid hallucination of wine red when in fact the color of my neighbor’s wall is sea-glass green. Or the lighting and whatever other conditions in my neighbor’s apartment might have been so cleverly manipulated that, in the absence of any knowledge or suspicion of this manipulation, I identify the the color as wine red. Or, unaware that I am dreaming, I merely dream that I was in my neighbor’s apartment and saw that the color of his walls were wine-red. In each of these circumstances, it would seem that my visual experience fails to be a signal that increases to 1 the probability that the walls of my neighbor’s apartment are wine red. It would seem I will never be in a position to absolutely rule out the identity with the actual world of any of these possible worlds. I am therefore in the same position with respect to them as I am with respect to the possible world in which the peanut lies under shell #1 | shell #2 | shell #3. In neither case am I in a position to assert a probability of 1. My body of knowledge will not allow it.

So it would seem that epistemic (im)possibility is what is being talked about in the use of “cannot” above. My body of knowledge is so impoverished, it would seem, that I cannot rule out the identity with the actual world any possible world I could conjure up in which I experience my neighbor’s walls as wine red even though they fail to be wine red. In no possible world epistemically accessible to me is the probability equal to 1 that, when I experience the walls as wine red, they are wine red.

Don’t I need to rule out each of these (epistemic) posI cannot rule out the identity with the actual world of any possiblesibilities before the sentence “the walls of my neighbor’s apartment are wine red” can be assigned, relative to what I know, a probability of 1?

Spoiler alert: no.

Outline: I will discuss three situations which include a situation s. My seeing the wine-red color of my neighbor’s walls. The doorbell apparatus. The pressure gauge. In each case, it is intuitive to claim that there is a nomic necessity when s holds. The flow doesn’t suddenly stop for no reason. To get into this more deeply would need to appeal to an infinite mind that surveys all those possible worlds whose laws of nature are the same as those of this actual world.

Situation s will include an indefinite number of negative facts. No poltergeist is producing the doorbell sound. (Though things can sometimes get a bit spooky when one has been under quarantine for too long.) Aliens are hovering above zapping the doorbell apparatus just as Channing Tatum is pressing the button and generating the doorbell sound through a causal sequence that bypasses him. No mad scientist has cut off my connection to the external world — has stopped the flow — and has substituted inputs generated by an algorithm. All these examples have substitution as a common theme — Dretske’s Herman example is another such. That the flow of information not be impeded is all that is required. Its “intended” function, with “intended” put under scare quotes. The concept ‘functionality’ is important here — thunk of these particular channels of information or information links to be devices with an “intended” function — where either the intention is real as in the case of the doorbell apparatus or the pressure monitor, or even where it is merely useful in a ‘medical illustration of the nerves and blood vessels sort of way to think of of some designer being who had the intention. That the flow happen normally. “Normal” means intersection of intention and statistical normality.

Nomic/functional necessity/probability is a species of nomic necessity. Take nomically-accessible possible worlds and filter out some, most of which will be non-normal. Ultimately appeal to a mind with knowledge — if only as a guiding idea or useful fiction. Natural processes plus randomness to give us lack of knowledge (I don’t know where the next raindrop will fall on the pavement stone.) Epistemic necessity/probability is a different creature altogether. Include the background perceptual faith in the set of knowledge items that make sense of an assertion of a probability.

Ultimately the ‘I might be a brain in a vat’ (epistemic “might’) scenario is incoherent if it is attempting to show that I can be wrong about everything. I would need to show I am not a brain in a vat only if there were some evidence making this a serious possibility. Doubtful if is a nomic possibility (not contradicted by a law of nature). An epistemic possibility only.

Situation s ensures that A)100% of the time, when the doorbell rings, someone or something is depressing the button outside, and B) 100% of the time, when someone or something is depressing the button outside, the doorbell inside is ringing. We can construct situations in which A is true and B is not true, but I will not try to do that here. Situation s ensures that, 100% of the time when the dial points to 7, the pressure in the boiler is 7 units. Grounding this 100% of the time is nomically necessity. In all possible worlds in which the laws of nature are the same as in this actual world, this is what happens. An infinite mind could survey all of these possible worlds and verify this — or reveal it to be false. The infinite mind would know all the laws of physics. We do not. If this doesn’t happen, that would surely mean that the laws of nature had stopped working.

Now think of my perceptual/cognitive system as similar to the doorbell apparatus and to the pressure gauge. Oriented towards world as.a whole, though, not to particular objects. Also has awareness of its own condition, its own status as having a world impinging upon it. It is possible for it to tell veridical experiences apart from illusory or hallucinatory.

There is nothing in my body of knowledge that would rule out the identity with the actual world of the possible world in which given s it is nomically/functionally necessary that someone or something be pressing the button outside when the doorbell rings, or that the pressure in the boiler be 7 units when the dial points to 7, or that my neighbor’s walls be wine red when I see that his walls are wine red. In other words, it is epistemically possible that these events be nomically necessary given s. As for myself, I am willing to go out on a limb and say they are nomically necessary. I rather doubt that it is within the aegis of the laws of nature to come to a screeching halt at some point in the future, but that may be just me. Therefore, it is epistemically possible that the nomic probability in each of these cases be 1. Take any similar event in the actual world, 100% of the time when the doorbell rings etc. Take any similar event in any possible world nomically accessible from the actual world, 100% of the time….and so on. Ironically, this is a kind of frequency, except the element of randomness is taken out. And relies on knowledge — the knowledge of the possibly/probably fictional omniscient entity who serves as a ‘guiding concept.

Austin’s tree. The place where skeptical doubts go to die. The plain light of day that shrivels all skeptical doubts. Something is ruling out the epistemic alternatives. Just being awake rules it out. But maybe should call this ‘perceptual faith’ rather than knowledge. Like Wittgenstein’s ‘the world didn’t pop into existence three months ago’, this forms the background against which we have knowledge. More than an item of knowledge itself. I will no more try to resolve the brain-in-a-vat issue than I will try to resolve the ‘did the universe pop into existence three months ago’ issue.

p(1) — no chance otherwise — if s is in play.

If something has a probability of 1, it is a logical truth. But wait, what does probability have to do with flipping a coin? explain. I must explain this. I am discussion probability because I want to explicate exposure | unhiddenness bzw hiddenness in terms of probability.

There is something defective about having to do the handwave in specifying a possible world. Really need to appeal to an omniscient being, if only as a useful fiction. Likewise something defective about random truth, truth as just correspondence.

If s holds. Cannot directly refute the various background considerations — I might be a brain in a vat, and so on. But the idea that I can be wrong about everything is incoherent.

But can justify shunting to the side, because so far in the cases in which … one can tell the difference. And were there ever a case in which one cannot tell the difference, that may not show much.

So now I have defended the idea that a perceptual truth can have a probability of 1.

04/18/2021

All of these are, I assert, epistemic possibilities. — Or they are if it indeed the case I know nothing that would rule them out as being parts of the actual world — and this real or alleged ‘inability to tell’ because one can always stipulate a not-caused-by-the-external-world sensation in place of what is caused by the external world. Might I not have, when I am awake, a direct awareness that I am in a direct relation to the external world? [Very clumsily put, but I don’t want to lose sight of this point]. Its c

By considering a possible situation s, as well as some insights to be gleaned from the disjunctivist theories of perception, we will see that yes, perception situations can have a probability of 1.

Situation s. Negative facts. Seeing is an information link like the doorbell apparatus. Except here the apparatus knows that it is awake, i.e., knows it is in contact with the concrete, tangible world. It can be mistaken abut particular items in that world — the spot of sunlight that at first seems like a stone (technically an illusion), the “snow” that at first seems like a fine misty rain outside on Fannin Street (technically a hallucination). But I can’t be mistaken about the whole shebang. If you think differently, please give me more than just an epistemic possibility. Give me anomic possibility before I will take you seriously. Not a serious possibility.

That I may know this is definitely an epistemic possibility. Now it may seem that it is an epistemic impossibility, since it is an epistemic possibility that I may be a brain in a vat. That I may be a brain in a vat may or may not be a nomic possibility, but at least it is an epistemic possibility. — Or is it? It is true that in the brain in the vat scenario my experience remains exactly the same. So I can’t tell just from what I experience that I am not a brain in a vat. But this is mistaken. No separate signal tells me that my situation s is in order. My knowledge is inherent in the original signal and it is difficult to isolate out or individuate what it is in the signal that places me in the truth. The steadiness of its impinging on me, its being impossible to escape, its flow. A lack of steadiness after all would be one thing that would persuade me that I am a brain in a vat — the algorithm has be absolutely unfailing. It is not a Dretskian I need a monitor to monitor the monitor and so on ad infinitum. Now suppose my being in the truth is the actual world. s does hold — nothinjg is interrfreing with my perceoptual /cognitivei system — nothing is subsituting for the signal coming in from the world — as if the guy with radio waves subtitutes for the signal from the button. As long as s holds, the probability is 1. Given s, the probababililty is 1. The signal has a proabgility of , and I corectly interpreent it — just as the dial’s point to 7 rendss p(1) the porboability that the pressure is 7 units, and I correctly interet it meaning this. .

Disjunctivism as seen througth the eyes of a Merleau-Ponty scholar. gshdfshgdwrecNe

[[[Insert aria about all the could be’s. In the situations in which I am actually seeing the object, there are not true epistemic could be’s. ]]]

I am about to show, however, that a disjunctivist theory of perception will give us what we need. There are indeed perceptual situations for which the probability of certain sentences is 1. So if you will bear with me, dear reader, I am about to launch into a discussion of disjunctivism that, in spite of its length, will only just barely graze the surface. Worry not, however — we will be returning to the surface for air eventually.

04/07/2021

Epistemic Possibility. If I know nothing that rules out the identity with the actual world of the possible world which has as its key description ‘the peanut is under shell #1’, there is one possible world epistemically accessible for me from my location in the actual world in which the peanut is under shell #1. It is therefore possible — epistemically possible — that the peanut is under shell #1. That the peanut is under shell #1 is a possibility. As part of the possible world that has this as its key description, the peanut’s being under shell #1 could be a situation that is part of the actual world and therefore could become part of my comprehensive exposed actual situation. It’s being so, if I may be permitted to risk wearing out the word, is a definite possibility. Possibility defined in terms of what I do not know — my ignorance. This is the sense of “could” that is operative when, before the shell is turned over, I can truthfully and non-misleadingly say that the peanut could be under the shell, but then can no longer truthfully say this once the shell is turned over and turns out to be hiding nothing but empty air and a patch of table surface. This is a sense of “possible” that requires ignorance, not knowing. [See P.Z. Myers.] I will call possibility understood this way “epistemic possibility”.

But what I do know (along with what I do not know) lets me come up with a number, or at least an interval that expresses the probability that the peanut is under shell #1 | alternatively under …. I know that there ks just one peanut at issue, and that the it lurks underneath one of the shells, currently unspecified.. I won’t be elaborating exactly how I know these things; I shall take it as a given that I do. These particular items in my body of knowledge, along with my failing to know under which shell the peanut lies, lead rather intuitively to my asserting “1 in 3” as the probability that the peanut lies under shell #1 (alternatively …).

If we construe this body of knowledge as a set of sentences, we can construe the knowledge items I don’t possess as a failure of certain sentences to appear in that set. None of the following sentences appear in this set: “the peanut is under shell #1”; “the peanut is under shell #2”; “the peanut is under shell #3”. The absence of these sentences from my body of knowledge — these dark gaps in my otherwise pearly-white set of teeth — expresses my ignorance of which shell the peanut lies under. As regards the positive elements of this set, what I do know, actually elaborating this set would of course be a practically impossible task, not just impracticable because of the vast number of things I know (“there is a porcelain tea cup sitting on my dba-work notebook”) but also the difficulty in specifying what would be salient enough to play a role in specifying the number that is the probability given this subset of my knowledge. My knowledge that Timbuktu was the capital of the ancient African Kingdom of Mali is probably not salient at all. Other items are more salient. The most obviously salient item would be the knowledge that out of 200 shell games played with the same shells and the same peanut the peanut turned out to be under shell #1 67 times. I would need to include the knowledge expressed by the sentence “peanuts tend to stay put under the shell they were placed under and do not behave like rogue electrons”. I would also need to include my knowledge that Elizarraraz does not try to play cute psychological tricks with the peanuts, and God knows what else. Included in the subset — I assume this is a proper subset — of things I know are items more salient or less salient to the probability of the peanut’s being under shell #1. My asserting a probability of 1 in 3 is relative to this subset of knowledge.

Making an asserted probability relative to a body of knowledge or subset thereof renders that probability perspectival in nature. Add an item of knowledge gained by turning over shell #2 — say, that shell #2 hides nothing except a small expanse of table — changes the probability that the peanut is under shell #1 from 1 in 3 to 1 in 2. Adding yet one more item of knowledge by turning over a peanut-less shell #3 changes the probability that the peanut is under shell #1 from 1 in 2 to 1.

The same probability of 1 would have been achieved by turning over shell #1 to expose the peanut to my sight. I can count as seeing the peanut, after all, only if the peanut is actually there. If the peanut is not there, I do not see the peanut. By placing radical demands on my assertions that I know that p, I might hesitate to say I know that I see the peanut. But the doubts are not relevant to whether I see the peanut. Either I do see the peanut or I do not; and if I do, the probability is 1 that the peanut is there. Were an infinite mind to check off all the cases in the actual world which I am in fact seeing a peanut (not hallucinating one, not dreaming one), and all such cases in every possible world in which this thing we call ‘seeing’ exists and peanuts exist, in each such world the peanut is there. [Stating this so that it doesn’t get lost in the woodwork: my assertion that I see the peanut, or that the boiler pressure is 7 units, may have a probability less than 1. Nonetheless, this doesn’t mean that in situation s I don’t see the peanut | know the peanut is there or that, again, in situation s, the arrow pointing to 7 doesn’t generate a probability of 1 that the boiler pressure is 7]. Linkage between probability of 1, necessity, and all possible worlds accessible thus and so. — But wait — probability is tied to knowledge. I in fact know even if there are standards of knowledge I subscribe to that prevent me from asserting I know. My assertion that I know that p may have a probability less than 1. But one cannot conclude from that that knowing that p isn’t an item in my body of knowledge. ]

In situation s, my assertion that the peanut is there has a probability of 1. That part of my nervous system — eyes, retina, brain, everything connected with my responding appropriately to what is there is working perfectly. But what about my assertion that I do see a peanut there, that I know there is a peanut there? Must I first be able to discount all the skeptical possibilities before I can legitimately make this assertion? Suppose there are different standards for knowing that I see, knowing that I know? Suppose I can be said to know I know only given the lowest, most commonsensical standards of knowing?

[Move from my observing the boiler monitoring devise and my being the device. When I am the device the massive flow of information definitely impinges upon me to give me the J.L. Austin situation or the ‘self-validating situation. I am the channel of information experienced from the inside. ]

[Important: s will include negative facts. Rasmussen.]

In a course on epistemology given by Barry Stroud in one of my previous lives, Stroud related a story about J.L. Austin that is apropos here. Austin was walking with a colleague on campus, discussing the usual arguments for skepticism. “I don’t really know there is a tree there”, said the colleague. “I might be dreaming or hallucinating.” So Austin walked his colleague over to the tree, obtaining thereby what Merleau-Ponty would call a “maximal grip” on the tree and letting (to continue using the Merleau-Pontyian language) their bodies “gear into” the tree. For example — although this would probably not have been a part of their experience they would have been likely to have remarked upon — their bodies were “set” to move around the tree to see aspects of it that were hidden a moment ago, prepared to touch something with a texture of bark, something that would have been hard had it been kicked, and so on. (Maybe they did kick it ala Doctor Johnson.) All this time — to depart from Merleau-Ponty language — the tree would have been continually causing (by reflecting light, by providing resistance to their bodies) in a droning, steadfast, continuous way their experiencing the tree, an experiencing that is, correspondingly, steadfast and completely steady. The tree was there in its bodily presence, relating to these other two bodies in at least a causal way and probably in other ways as well. This sheer bodily presence would have ;made any skeptical imaginings they may have had previously seem like unreal will-o-wisps of the imagination,. “Now tell me,” Austin said: “What could possibly be doubtful about this tree?’ There is nothing wraith-like, thin, or flickering about its existence. It is easier of course to entertain skeptical doubts alone and from the calcium tower of one’s skull, but here were two people together experiencing the same tree, bodily walking around it, perhaps touching its bark, perhaps kicking it — far from the artificial circumstance and ethereal heights of any ivory or even any calcium tower. To experience the tree this way is to have it in its bodily, physical presence — it is to enjoy/suffer a presentation coming together through several senses at once (mainly sight and touch). The presentation possesses a strong warrant for the actual presence of the tree — it is strong — nay, indefeasible, to use McDowell’s term — evidence that the tree is actually there and could, if one of its limbs fell (sudden snap!), crack one’s skull. The presentation is self-validating. In his letters to Descartes, Hobbes asserted that when one is awake, one knows that they are awake. To be awake is to be open to the presencing of the various sensed physical objects around one. It is to be in a state in which one is not closed off from one’s surrounding environment and the various objects in it, in their bodily presence. To know one is awake is to know one is in this state. If one is in fact dreaming or hallucinating, their faculties may or may not be so clouded as not to be aware of this. But if one is awake and one’s faculties are sufficiently clear, one knows one is awake. The steady sensory presence of the object is a signal that closes off all the other epistemic possibilities.

varI will briefly discuss JL Austin’s moving around the tree with the skeptic. Disjunctivism. Powerful warrant. Different criteria for knowledge suitable for different contexts. Merleau-Ponty’s ‘I can’t [modality?] be wrong about everything. Because probability is tied to knowledge/evidence, all of this leads to a probability of 1 when my body is properly geared into the scene. I will be just sketching these things out, then moving on. The concept of exposure.

End this part of MAIN

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[[[Probability, certainty, and necessity form a kind of trinity here: that in all the possible worlds just described the peanut is under shell #1 means that there is no possibility the peanut could be under one of the other two shells and not under shell #1; this possibility is excluded or ruled out by my knowledge of items a and b (where have we seen that phrased “ruled out” before?) and is therefore not part of a sample space of equally-likely possibilities; which means in turn the that the probability is 1. Since we are talking about knowledge here, it makes sense to call this probability of 1 “certainty”. Polya distinguishes between probability used to deal with “random mass phenomena” (frequency) and probability as credence. Remaining within the realm of probability as credence, let me go out on a limb and assert that I know that p if and only if p has, given my body of knowledge, a credence of 1. Again, let me go out on a limb and assert that every case of epistemic necessity that p is also a case of my certainty that p; a case of p having a probability of 1, and therefore a case of my knowing that p.]]]

[[[So when Elizarraraz turns over the two shells, either I know that they are peanutless, or I do not. Either the probability that the peanut is not there is 1, or it is less than 1. But, of course, there are possible worlds in which this probability is less than 1. I might have been hallucinating empty tabletop, after all, when shells #2 and #3 were turned over. That is to say, there are epistemically accessible possible worlds in which I am hallucinating this. There is nothing in my body of knowledge that would rule out the identity with the actual world of the possible world in which I am hallucinating this. Or some clever scientist might have found a way to create a kind of stealth-fighter peanut invisible to any kind of electro-magnetic radiation. Or a visual psychologist might have devised the perfect camouflage for the peanut so that I mistakenly think I am not seeing a peanut. Or I might have some temporary brain spasm that prevents me from recognizing peanuts that I do in fact see. Or someone comes up with some weird gorilla not seen among all the basketball players trick, but applied to peanuts. Or I might be a brain in a vat with accurate information regarding everything except for my (non-existent) hands and the state of shells #2 and #3.. All of these are, I assert, epistemic possibilities. — Or they are if it indeed the case I know nothing that would rule them out as being parts of the actual world — and this real or alleged ‘inability to tell’ because one can always stipulate a not-caused-by-the-external-world sensation in place of what is caused by the external world. Might I not have, when I am awake, a direct awareness that I am in a direct relation to the external world? [Very clumsily put, but I don’t want to lose sight of this point].]]]

[[[[Outside Interference: If somehow a causal event inside the doorbell apparatus instigates, independently of and somewhere past the button, the causal flow leading to the production of the doorbell sound, the production of that sound obviously does not imply that something or someone is depressing the button outside. For example, if a resident poltergeist started up of its own accord a stream of electrons heading towards the sound-production part of the system; or if a freak bolt of lightning somehow sent energy to the apparatus, accomplishing the same thing; or if someone rigged up a complicated apparatus triggering a burst of energy past the button using radio waves or whatever; or if, bizarrely, the causal flow simply started by itself midstream (i.e., past the button) without any one at all causing it or triggering it, but a billions perhaps of distinct causes affecting each electron in such a way that we in our ignorance say the event “happens by chance”. This would be an event similar to the possible but still incredibly unlikely event described in the ONE, TWO, THREE INFINITY type books in which each molecule of air in the room “decides” to abscond to the corner of the room all of sudden. Or God in their trinitarian wisdom decides just to initiate a new causal flow midstream past the button. In all these cases except perhaps the penultimate one, something outside, that is to say , distinct from, the system comprising the doorbell apparatus renders the button outside otiose in the production of the doorbell sound. And if one thinks about it, even the penultimate case is one in which God-knows-how-many billions of little causes outside the apparatus are impinging upon it midstream. Perhaps we can protect that apparatus from poltergeist by wrapping it in tin foil, and from bolts of lightening or radio waves by sheathing it in a mile of lead … or, in a less labor-intensive way, we can isolate the system conceptually from any such outside interference and simply say “In all those situations in which the doorbell apparatus is free of outside- or distinct-from-the-system interference, the doorbell sound implies that someone or something is pressing the button outside”. A bit like the medical drawings of the circulatory or nervous system in which the distinct colors designed to lift them from the rest of the entangling muck of the body functions as a kind of idealization. The system considered by itself — apart.

If there is an “outside”, there is an “inside”. ]]]

[[[That I know this implies that nothing is impeding the flow of information from the peanut into my sensory/cognitive system. No gross defects in the retina or brain; no dream state or hallucination arising from a complete or partial cutting-off of this flow of information. Since no such particular impedances exist in my case, my body of knowledge does not include the knowledge of their existence. Only such impedances would result in my not knowing the peanut is there. Something that had disrupted the normal reliability of my sensory/cognitive system, made it no longer an actual channel of information. In not knowing any such impedance, there is nothing in my body of knowledge that would rule out the identity of the possible world in which this peanut is staring at me in the face with the actual world in which the peanut is staring at me in the face. So in all possible worlds in which my body of knowledge includes the knowledge that the peanut is there (e.g. w0 in which my neighbor’s walls are wine red; w1 in which his walls are seaglass green, where I do not know what the color of his wall is), I know nothing, there is nothing in my body of knowledge, which rules out the identity of that world with the actual world. The knowledge that I see the peanut means that I see the peanut in all possible worlds epistemically accessible for me from my location in the actual world. It is epistemically necessary that I see the peanut, and that, therefore, the peanut is there. ]]]

[[[So much would follow from the meaning of the words “know” and “see”]]]

[[[So if we base our notion of possibility/necessity on those possible worlds that are epistemically accessible for me from my location in the actual world, the presence in my body of knowledge the knowledge that I see the peanut does indeed render as 1 the probability that I see the peanut. Note that this is not the claim that I must know that there is no impedance in my sensory/cognitive system. That is different from there not being in my body of knowledge knowledge of a defect in my retina, a tumor in the visual center of my brain, knowledge that I am dreaming or hallucination, and so on. The former means I do not know that I know. The doorbell apparatus might be a perfectly good channel of information without my knowing a year later that it is in fact in good condition, nothing impeding.]]]

Were I suffering an actual hallucination or merely dreaming that the peanut was there, my body of knowledge would not include that the peanut is there as one of its items (henceforth the “peanut item”). For if I know that p, p must be true. If I know that the peanut is there, the peanut must be there. But if I am merely hNeallucinating or dreaming the peanut, the peanut is not there. Clearly, then, the peanut item would not be a part of my body of knowledge. No surprise here.

Therefore the I argue, however, that the possibility I may be hallucinating or suffering from other sensory/cognitive defects does not suffice to render less than one the probability there is a peanut there, in the circumstance just described. An actual hallucination (or similar defect) yes; a merely possible hallucination no. Concomitant with this probability of 1 is a sense of “necessary” which I will model partly as epistemic necessity, but with one more component. I will call this necessity the “necessity of absolute reliability”, a species of nomic necessity. [[[Adding depth to the meaning of “see” is that what is seen exists/existed]]]. In the course of my argument, I will introduce a concept of the background.

As for the sentence “once I overturn shell #1 to expose the peanut the probability that there is a peanut there becomes 1”, this sentence nicely illustrates Kyburg’s contention that:

My own conception of probability is, like Keynes’s and Carnap’s, a logical one. Probability statements are logically true, it they are true at all.

Kyburg, EPISTEMOLOGY AND INFERENCE, p. 138

In this case, I assert the numerical probability of 1 relative to my background knowledge that 1) the peanut is not under the other shells and against my background knowledge that 2) there are no rogue peanuts, that is to say, the probability that this peanut in Elizarraraz’ shell game may end up on the nose of the Mona Lisa is 0. There may be other items included in the set comprising my background that contribute to this value of 1; there may be non-propositional/non-conceptual items as well. My attempt to scan what I know may fail to turn up anything else — but there was a time when this scan would have failed to turn up the rogue peanut consideration either. At any rate, it seems safe to say that, given at least items 1) and 2), plus zero or more other items, the probability is 1 that the peanut is/was just a moment ago under shell #1.

***** Important to emphasize that the hidden is the primary example of the epistemically accessihble. *****8

[[[ The possible-world analysis of this 1.]]]] At the moment, at the time of this writing, in my vast ignorance, I know nothing that, given 1) and 2), would rule out the presence of the peanut under shell #1. In every possible world epistemically accessible for me from my location in the actual world (for example, the possible world in which Bigfoot is roaming the forests of Western Washington state, or the world in which aliens did leave debris behind on a visit to the New Mexican portion of the Colorado Plateau ala AMERICAN COSMIC (my priors for this are about 1 in 20)), nothing rules out, given 1), the identity with the actual world of the world in which the peanut is under shell #1. It is therefore epistemically necessary that the peanut be under shell #1 in the the shell game set up by Elizarraraz in the Pilsen neighborhood of Chicago, given that I know the peanut is under one of the three shells but not under the other two shells. This epistemic necessity fits very nicely with the probabilistic necessity of 1.

[[[Use the concept of epistemic necessity to rule out the absolute bizarre counter-examples.]]]]]

[[[Were I somehow to have the knowledge that I am hallucinating. That what is coming in IS information is what anchors this, even if I may not be able to establish this to a certainty of 1.]]]

The interesting thing about the concepts of necessity/possibility is that they are employed by two domains, possible worlds and probability, which, while obviously related to one another, are not identical. Something is necessary (to use Steinhart’s idiom) if it is true in all possible worlds accessible from a given world. By fiddling around with what “accessible” means, one gets different, stronger or weaker, concepts of necessity. Going from stronger to weaker, logical necessity, nomic necessity, epistemic necessity each requires a different concept of accessibility. Each such concept will come with a complementing concept of possibility. Somewhere in this essay, I will | have already attempted to define a concept of epistemic possibility complementing the concept of epistemic necessity.

When I know that the peanut is under shell #1 — either because I have just turned that shell over, or because I can deduce this with certainty on the basis of other things I know (e.g., there is a peanut under one of the three shells, the other shells are empty, there are no rogue peanuts, peanuts do not sublimate as a gas into thin air, or just vanish entirely, leaving no material trace at all in any state of matter). That the peanut is under shell #1 is an item in my body of knowledge, or it is not. If it is an item in my body of knowledge, there is nothing in my body of knowledge that would rule out the hypothesis that the peanut is indeed under shell #1.

Various conditions are of course notorious for disrupting the (assumed) reliability of the senses which normally leads one to think that if they see a peanut after turning over shell #1, then shell #1 was hiding the peanut just a moment ago. One might be hallucinating the peanut. Or the whole shell game might be transpiring inside a dream and there never were these three shells one of which is hiding a peanut. Both dream and hallucination are possibilities, at least in some sense of “possibility”. These possibilities are sometimes thought to mean that the probability cannot be 1 that the peanut was under the newly-turned-over shell #1. Originally the probability was 1/3 * the probability I am dreaming or crazy; now the probability is 1 /the probability I am dreaming or crazy.

In the possible worlds in which I am not dreaming, hallucinating, not a brain in a vat, etc., I obviously do not know that I am dreaming etc. For if I know that p, p must be true. If p is not true, I do not know that p. So in all possible worlds in which nothing disrupts my sensory/cognitive apparatus, nothing prevents it from functioning the way it is “supposed to”, and in which Elizarraraz has set up the shell game in the manner described above, the peanut does get exposed when I turn the shell over. I will say that these possible worlds are epistemically and functionally accessible for me from my location in the actual world. Nothing in my body of knowledge rules out the identity with the actual world of the possible world in which the peanut that had been lurking under shell #1 is now staring at me in the face. It is therefore epistemically and functionally necessary that

Given that the possibility, that, the moment before I turned over shell #1, the peanut had just landed from its previous position on the nose of the Mona Lisa, or that it had been intermittently vanishing or materializing … given that these possibilies would rule out the hypotheseis

12/07/2020

[[Briefly discuss the background]]]

That probability statements are logically true, if they are true at all, of course challenges Steinhart’s assertion that something with a probability of 1 is a logical truth. I take Steinhart also to mean that if something does not have a probability of 1, it is not a logical truth. But of course the statement that the probability the peanut is under shell #2 is 1 in 3 (a true statement given a relation to a certain background of knowledge) is also a logical statement true relative to a body of evidence/knowledge. The point is that something can have a probability of 1 and not be a logical truth in the way that q –> q is a logical truth, that is to say, something that is true in all possible worlds in which the laws of logic are the same as in the actual world.

Before that, when I observed just a shell, the credence to assign to there being a shell there is 1. Likewise, when I first observed the color of my apartment walls, the credence to assign to that color’s being portobello mushroom is also 1. This credence, or “probability”, is assigned relative to a body of knowledge that includes such propositions as those expressed by “I am not dreaming at the moment” and “I am not hallucinating at the moment”. I might be wrong about what propositions are to be included in this reference body of knowledge — for example, notoriously, I might believe that I am awake when in fact I am dreaming — but we should not automatically assume that having a false belief about what is included in my body of knowledge means that I do not know that thing. Also, I might not necessarily be able to express in a natural language (or in a formal language, for that matter) a proposition that is in fact part of my body of knowledge. [[[Present pluperfect]]]

[[[Talk about evidence instead.]]]

]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]

Return to the Main body. 03/15/2021.

An epistemic probability of 1 means that all other possible worlds are ruled out by one or several items in my body of knowledge. Once both shells #2 and #3 have been turned over, the epistemic probability is 1 that the peanut is under shell #1 given that the rogue peanut possible world has already been ruled out by virtue of not being epistemically accessible for me (assuming it is not) and given my knowledge (gained from Elizarraraz) that there is only one peanut lurking among the three shells and that shells #2 and #3 are empty. The probability the peanut is under shell #1 has to be 1. That probability must (epistemic “must”) be 1. Necessarily, given what is in the body of knowledge that has found a home in me, the peanut must be in shell #1.

One may try to apply skeptical arguments to try to show that the probability must be less than 1. Do I really know that rogue peanuts do not exist? That the peanut did not sublimate into a gas, so I will find nothing when I uncover shell #1? That I might be hallucinating the three shells? That I might be dreaming them? Any one of these eventualities would mean a probability of less than one — or, in the case of the hallucinating or dreaming cases, where there are no three shells, something other than a probability, much less a probability of 1.

Remember, however, that a probability is a logical relation between a statement and a body of knowledge/evidence. What is in my body of knowledge [need to discuss why I talk this way] rules out the identity with the actual world of these various hallucinatory shells or rogue peanut worlds. Either I know that there are three shells on Elizarraraz’ table, or I do not. Either I know that rogue peanuts do not exist, or I do not. Either I know that the peanut has not sublimated into thin air, or I do not. If I do know these things (and all the things that an infinite intelligence might bring up) then the probability that the peanut is under shell #1 is 1. [Kyburg’s statements not open to question.]

Now one may think that unless I can, for example, completely rule out the possibility that the peanut has, for example, sublimated into thin air, I do not in fact know that it hasn’t. But there is a certain steadfast, normal, boring regularity to the world that, I dare say, licenses in most circumstances neglect in clearing out the most bizarre possibilities.

Knowledge, which so far I have not said much about. Take Dretske’s boiler example. Suppose that, when the apparatus is in perfect condition and nothing interferes, it is nomically necessary that when the pressure is 7 whatever units, the dial points to 7. To be nomically possible is to avoid violating the laws of physics as they are found here, and to comprise that state of affairs in a possible world surveyed by our infinite intelligence. To be nomically necessary is for the state of affairs to obtain in all the nomically accessible possible worlds surveyed by our infinite intelligence. It is epistemically possible that the above is nomically necessary. Now I also know, as a materials engineer with 25 years of experience, that physical conditions take time to become less than perfect. What is more, I have just inspected the apparatus and I know (remember, either I do know this or I do not) that the apparatus, now that I have it open, is in perfect condition. Given these two items of knowledge, I also know that the apparatus remains in perfect condition one second after I have closed it up. Reality has a certain inertia. The aforementioned two items justify this third item and let it count as knowledge. (Notice the Russian-doll character of this). Add in the ‘wisdom of the wise’ element. So there would be an item in my body of knowledge that would rule out any other epistemic possibility other than the pressure in the boiler is 7 whatevers. Assuming this really is an item in my body of knowledge. But of course I am not in a position such that, were the physical condition of the channel to deteriorate, I would know immediately. Even if the wrapping were transparent my own physical equipment, my nervous system, could deteriorate without my knowing it.

If I do know this about the inertia of the real, and if the apparatus is in perfect condition, and if nothing interferes (no alien spaceship is hovering nearby to zap the apparatus in a manner unbeknownst to us), then one second later the dial’s pointing to 7 rules out the epistemic possibility that the pressure in the boiler is anything other than 7 whatever units. My knowledge about the inertia of the real, if indeed I do have this knowledge, which then lets me know that the apparatus is in perfect condition, ….

Let’s say that Hobbes was correct in claiming (at least according to Stephen Priest) that when I am awake, I both can be and am aware that I am awake and in actual contact with actual objects. There is something “self announcing” about the reality of this encounter.

I know something that rules out the identity with the actual world of any possible world in which a mass is not also a wave. Namely, I know that a mass is also a wave. So in one fell swoop, I can refer to all such possible worlds. It is epistemically impossible for it to be nomically possible for a mass not to be a wave. Likewise, it is epistemically impossible for it to be nomically possible for the dial to point at 7 and the pressure in the boiler not to be 7 whatever units, given that the physical condition of the monitoring apparatus is perfect and that there is no outside interference (no alien spaceship hovering nearby sending down a beam to disrupt the normal causal flow from water pressure to position of the dial). I know that no possible world in which, given these conditions, one 7 happens but the other does not can be identical with the actual world. There is the causal flow just as water flows downhill. In all epistemically accessible possible worlds, worlds that could be identical with the actual world (I know nothing that would rule out the identity), the one 7 does not happen without the other given the aforementioned conditions. It is epistemically necessary this (the one 7 with the other 7) be nomically necessary. A law-governed causal link such that the one 7 cannot fail to happen (given the aforementioned conditions) provided the other 7 happens. All other possible worlds are ruled out. That is to say, all other possibilities are ruled out. This is the “surely there must be some kind of necessity” I was looking for.

03/19/2021

And no, I do not need to discount all of these possibilities in order to count as knowing these things. Dretske and the boiler pressure. Urgency. e

[Problem: I will never know, I daresay, that I have identified all of the exigencies. Have to rely on the concept of an infinite intelligence at least as a guiding concept. ] But let me back up a moment. Suppose I think I know all these things, but when I turn it over, shell #1 turns out to be empty. I am then forced to conclude that there is something I thought I know which I in fact did not know. Maybe I did not know that there was a single peanut among the three shells. Maybe rogue peanuts exist after all (so the rogue peanut possible world should not have been automatically eliminated, being an epistemically accessible possible world after all). Maybe there is some other item in my body of ostensible knowledge, currently unidentified, that turned out not to have been true.

RETURN TO MAIN

We have seen that, contra Steinhart, it is possible for something not to be a logical truth (that is to say, something true in all possible worlds tout court) and still have a probability of 1 given a particular concept of accessibility. Let me say, then, that a state of affairs is exposed, unconcealed, unhidden, or revealed (I will use these terms interchangeably; I will be using “unconcealed” when I am in a more Heideggerian mood), in a situation when, given the body of knowledge possessed by the sentient being whose situation it is, that body of knowledge would license an assertion of 1 as the probability of that state of affairs. When that probability is less than 1, that state of affairs counts as hidden or concealed.

Since my comprehensive actual situation is that part of the actual world that is exposed for me, every state of affairs in it is an exposed state of affairs. If a state of affairs is hidden, it is not part of my comprehensive actual situation.

Epistemic Truth: Correspondence is the truth-making factor, whether the state of affairs lies within a possible world or within a situation. But a sentence can correspond to a state of affairs with in a situation only if that state of affairs has been exposed within that situation: a situation comprises exposed states of affairs only. So when I utter a sentence that is true because it corresponds to a state of affairs within my situation, for example:

The walls of my apartment are portobello mushroom

it corresponds to an exposed state of affairs. All sentences that are true because they correspond to a state of affairs in my situation will be corresponding to an exposed, an unconcealed state of affairs.

Let me say that a sentence is true in a situation when it corresponds to a state of affairs within that situation. (For the best defense of the correspondence theory of truth that I have seen so far, see Joshua Rasmussen, Defending The Correspondence Theory Of Truth, Cambridge, Cambridge University Press, 2014). Let me also say that a situation makes the sentence true when a state of affairs within that situation corresponds to that sentence. Since a state of affairs is not comprised by a situation unless it is exposed within that situation. Exposure, unconcealment, is a necessary condition for a situation’s making the sentence true. A situation cannot make true a sentence that corresponds to a hidden state of affairs, since that state of affairs cannot count as within or being a part of, that situation.

So if any of the following sentences is true, my comprehensive actual situation does not make them so. The states of affairs that would make them true are states of affairs in different situations.

1) The butterfly fluttering about in the Amazon at GPS point xyz has chartreuse wings

2) Shell #1 is hiding the peanut

3) The walls of my neighbor’s apartment are wine red

4) Bigfoot is roaming the forests of western Washington state

The first sentence, 1), might be generated by my laptop which I have programmed to spit out sentences of that form. Relative to my situation, it is an epistemic possibility: the situation that comprises that state of affairs could be drawn from a possible world whose identify with the actual world cannot be ruled out by anything in my body of knowledge. The number of variants of this situation is humongous, so the credence/probability to be assigned to 1) is extremely low, provided it makes sense, given my lack of knowledge, to assign any precise number at all to this provability. The probability to be assigned to 2) is 1/2, given everything I know (if I know it). The credence to be assigned to 3 is 1 divided by the number of paint colors out there. My own Bayesian priors for 4) is about 1 in 100. (I know, I know — I have just lost any credibility any reasonable person might have been willing to grant me.)

Sentences 1 through 4 may or may not be made true by states of affairs exposed in other situations. For example, they may be made true by the comprehensive actual situation of an omniscient being to whom every state of affairs in the actual world is exposed, and for whom there are no brick walls, no funding difficulties blocking off the flow of information — a situation to which I will apply the label ‘worldly situation’. But none of them is made true by my comprehensive actual situation. Nor, as we will see, does my situation make true the sentences formed by prefixing “It is not the case that” to each one. The worldly situation does make at least one of A or ~A true in each case, so one would be justified in exclaiming “but surely A v ~A is true for each of these!” Yes — but it isn’t my comprehensive actual situation that makes them true.

Were however a conduit of some sort to link the situations relevant to 1 through 4 to my situation, either each sentence or its negation would be made true by my situation and in my situation. If my neighbor is reliable and he tells me that the walls of his apartment are wine red, he would have provided a conduit linking his comprehensive actual situation to mine and exposing in my situation the wine-red color of his walls. This state of affairs would then become part of my situation, having a probability of 1. My situation comprises what has an epistemic probability of 1 for me (that is to say, relative to the body of knowledge that has found a home in me). It comprises what is epistemically certain. [[[Need to discuss how something can fail to be a logical truth and still have a probability of 1.]]] Likewise, I might employ something like Google Earth to zoom in on that particular spot in the Amazon and discover there is indeed a butterfly with chartreuse wings fluttering about there. A sonar peanut detector might reveal to me that shell #1 is hiding the peanut, a conduit that perhaps is not quite totally kosher, like the one depicted in Caravaggio’s CARDSHARPS. [Exposure: removing what had prevented our knowing. Epistemic possibility requires our ignorance. Epistemic probability does as well. Remove the ignorance, get a probability of 1. As for only logical truths can reach p(1), either I know the peanut is there or I do not. Probability depends upon the particular body of knowledge that has found a home in me. Different accessibility conditions, different types of probability.

And a cryptozoologist with impeccable credentials might inform me that she was able to ascertain beyond a shadow of a doubt that the Bigfoot-like creature gallivanting around the various campsites in western Washington state impishly waving hello to campers and clearly enjoying their reaction, really is Bigfoot and not, as I had at first assumed it would have to be, my DFH friend Shaggy.

In each of these cases, an epistemic possibility — the ‘could’ generated by my ignorance — gets converted to an exposed actuality, a cannot-be-other-than. Something that has an location in space-time gets unconcealed, unhidden. Something gets made true in my situation by the exposure of a previously hidden state of affairs in a different, merely possible situation. A probability of less-than-one gets turned into a probability of 1. To get exposed or to have been exposed is to have a probability of 1, where that probability is relative to one’s body of knowledge.

Knowledge has as one necessary component truth. I do not know that p unless p is true. Epistemic truth would reverse this relationship; p is not true in a situation (made true in that situation) unless p is known, exposed unconcealed — unless information, conceptual or non-conceptual, is available about it.

Here then, is the main take-away from this section: a situation cannot make true a sentence that corresponds to a hidden state of affairs. As a complete possible world, the actual world has sufficient resources, so to speak, to make true any sentence that corresponds to any state of affairs, hidden or exposed, within that world. But a situation does not have these resources. It is unable to expose every truth, and no sentence is true in a situation unless it has been exposed. Just as one does not go to Judge Judy to expose the truth in the murder trial of the century, I do not use my (current) comprehensive actual situation to expose the truth regarding whether there is a butterfly fluttering about at GPS location xyz in the Amazon, and, if so, what color its wings are.

Judge Judy trying to expose the truth of the Amazonian Chartreuse Butterfly Sentence

So much for truth. Let me turn now to compatibility/incompatibility. I will then combine these two separate discussion streams into a discussion of the truth condition for negation that will leave room for relevant implication.

Compatibility/Incompatibility

Compatibility and Incompatibility are binary relations holding between situations. Mares takes these relations to be primitives, but I think they can be explicated in terms of possible worlds. I discuss these relations as they hold between situations drawn from spawned-from-the-unknown possible worlds and spawned from the known possible worlds respectively. I give a nod to the concept of defeasibility.

Situations Drawn From Spawned-From-The-Unknown Possible Worlds: The possible world in which the walls of my neighbor’s apartment are Venetian red is epistemically accessible to me because nothing in my body of knowledge rules out the identity with the actual world of this possible world. This possible world has “my neighbor’s walls are Venetian red” as its key description. The hand-wave “and everything else is the same as in the actual world” accomplishes the rest of this definition of the possible world. This world could (epistemic “could”) be identical with the actual world, and, upon the exposure to me of my neighbor’s walls as in fact being Venetian red, that particular situation (a singleton comprising just one state of affairs) drawn from this possible world would become part of my comprehensive actual situation.

Epistemic Compatibility: When a key-description situation s1 is drawn this way from a possible world that is epistemically accessible for me from my location in the actual world (remember, I will sometimes refer to these simply as “epistemically possible worlds” to save breath) and would therefore become part of my comprehensive actual situation s0 upon exposure, I will say that s1 is epistemically compatible with s0. Every situation s1 defined this way will be epistemically compatible with s0; this manner of definition provides a sufficient condition for epistemic compatibility.

So the key descriptions of all the epistemically accessible possible worlds lurking within the fog surrounding the mesa, all those ghost-worlds haunting all those holes in the lump of swiss cheese … all of these key descriptions define situations that are epistemically compatible with my comprehensive actual situation. No epistemically possible world will have a situation-defining key description that is incompatible with my comprehensive actual situation.

If I may be allowed to go out on a limb for a moment, compatibility is to be analyzed in terms of possibility, which in turn is to be analyzed in terms of possible worlds. As I will show shortly, different accessibility relations will allow some pairs of compatible situations and disallow others.

[[[A little reflection will show that every situation mapping to a key description of a possible world that is epistemically accessible for me from my location in the actual world will be epistemically compatible with my comprehensive actual situation. For any given key description, were there anything in my body of information and knowledge that ruled out its being part of the actual world, it would not be a key description for a possible world that is epistemically accessible for me. It therefore would not map to — really, be — a situation within an epistemically accessible world. It is not the case that it could be a part of the actual world; a fortiori, it is not the case that it is could be part of the actual world known to me or about which I have information. That is to say, it is not the case that it could be part of my comprehensive actual situation. Therefore all epistemic situations [define these above] are epistemically compatible with my comprehensive actual situation.]]]

Two situations can be epistemically compatible but incompatible in other ways. It is not completely inconceivable that, were I completely omniscient, or at least close to it, I might discover that the following two situations are nomically incompatible: the walls of my apartment are portobello mushroom, and the walls of my neighbor’s apartment are primrose pink. For suppose the universe is deterministic, at least on the post-quantum level. An incredibly complicated chain of events starting from the big bang, knowable only by an omniscient being, has resulted in the color of my apartment being portobello mushroom. This situation holds in all possible worlds that are a) nomically accessible from this world — i.e., the same laws of physics hold as in this actual world; and b) have the same initial conditions. Conceivably, there is just one such world, the actual world.

Another incredibly complicated chain of events starting from the big bang with the same initial conditions, also knowable only by an omniscient being, has resulted in my neighbor’s walls being chicory-flower blue (a beautifully paled even somewhat chalky ultramarine with a hint perhaps of violet). This situation also holds in all possible worlds nomically accessible from this world which have the same initial conditions. There might be just one such world, but it would still be true that in all possible worlds accessible from the actual world in the way described my walls are portobello mushroom and my neighbor’s walls are chicory-flower blue.

Necessarily, then, (nomically-plus-initial conditions necessary), my neighbors’ walls cannot be primrose pink at the same time my walls are portobello mushroom. The two situations preclude one another. They are incompatible.

To talk about two situations existing in the binary relation ‘incompatible’ is to talk about their necessarily not holding at the same time in the same possible world. In one sense or another of “cannot”, they cannot hold at the same time in the same possible world. Here the sense of the modal “cannot” is nomic-and-initial-conditions necessity. There is no possible world accessed this way from the actual world in which my walls are portobello mushroom and my neighbor’s walls are primrose pink.

Which sense of “cannot” is in play, which situations get included in the incompatibility relation will depend upon which accessibility relation one chooses. ‘Portobello mushroom in my apartment’ precludes and is incompatible with ‘primrose pink next door’ if the accessibility relation is ‘nomic and same initial conditions’, but not if the accessibility relation is ‘nothing in my body of knowledge rules out the identity with the actual world of the possible world in which my walls are portobello mushroom and my neighbor’s walls are primrose pink’. Because I am definitely not omniscient, my knowledge being limited and my ignorance vast, the two situations remain epistemically compatible. The latter epistemic accessibility relation renders the two situations compatible — epistemically compatible.

The situation described above whose corresponding description forms the key description for the rogue peanut world is not epistemically compatible with my comprehensive actual situation or with any of its sub-situations. For that situation would have to be part of the actual world; yet in the actual world peanuts do not jump around from shell to shell and never end up on the nose of the Mona Lisa. This is true of any world for which this is the key description: for example, the world in which Elizarraraz has painted the exterior of the building he owns across the street goldenrod yellow instead of its very bright viridian green but the peanuts in his shell games went rogue; or the possible world in which the peanuts have also gone rogue but the sunflower in front is ever so slightly to the left … and so on ad infinitum. If I may be permitted a slight leap, then, I will assert that in all possible worlds in which peanuts have gone rogue, the key situation is epistemically incompatible with my comprehensive actual situation or any of its sub-situations. My situation (and each of its sub-situations) precludes any of the key situations, which means that never in any world shall the twain hold together at the same time.

Looking at situations drawn from spawned-from-the-known possible worlds will illuminate two dimensions of the epistemic incompatibility relation: the idea of difference, and the defeasibility of the aforementioned “cannot”.

Above, we saw that two situations are incompatible if they cannot hold at the same time. This “cannot” can be unpacked in different ways. An infinite mind might determine that there is no possible world nomically/initial-conditions-are-the-same-ly accessible from the actual world in the walls of my apartment are portobello mushroom and the walls of my neighbor’s apartment are sea-glass green. These two situations would be nomically/initial-conditions-are-the-same-ly incompatible. But, of course, it may perhaps be a bit awkward to appeal to an infinite mind for the truth conditions of negation. Maybe it would make sense for Infinite-Mind-ese, but less so for English.

Above, I explicated possible worlds in terms of descriptions, descriptions carried out both explicitly (“the possible world in which the walls of my apartment are a wild fuchsia”) in a handwave (“and everything else is the same as in the actual world”). A description is a sentence in a natural language (English, Tagalog, Spanish, French, Russian, Italian, Thai, Mandarin, Hopi, Cherokee, Navajo….) which has truth conditions. Were I to get a physics undergraduate to tutor me, I am reasonably confident that, before too much time passed, I could add to my body of knowledge and acquire the necessary skills to understand the truth conditions of “this brick is, at one and the same time, an entity with mass and a wave.” I might demonstrate this understanding by, say, listing out the relevant equations, all describing the same brick though perhaps not in ways totally obvious to my prescientific understanding of bricks.

Let me take as a “raw material” situation the brick my eyes light on in front of me as I write this. Were I to generate a spawned from the known possible world by substituting for this description the description “the wave active in front of me as I type this”, I would have thought at one time, had this made any sense to me at all (in fact, it is not making much sense to me now), that I had formulated a key description for a situation in a possible world a possible world different from the actual world. I would have thought that the brick situation and the wave situation could not hold together at the same time in the same possible world. The two situations, I would have thought, had to be incompatible. But apparently I would have been wrong. The “two” situations are the same situation, describable by a single description which might start out outlining the properties of a mass but end up delineating the properties of a wave.

What makes me think then that I am gaining access to a different possible world when I specify ‘everything is the same except the walls of my apartment are fuchsia instead of portobello mushroom”? What makes me so sure that the situation comprising ‘portobello mushroom walls’ is incompatible with the situation comprising ‘fuchsia walls’? All I can say (with reasonable confidence) is that I know nothing — there is nothing in my body of knowledge, and no cognitive skills — that would let me understand the truth conditions of the description “the walls of my apartment are portobello mushroom and fuchsia at the same time and in the same expanses”. My ignorance in this regard goes deeper than a mere inability to imagine. The inability to grasp the truth conditions means that I cannot enter such a possible world because I can provide (or eventually come to acquire) no key description for it. That a thing may have two different colors at the same time is not a possibility for me. Indeed, it is an impossibility for me.

Just as there is nothing in the body of knowledge possessed by me that would rule out the identity with the actual world of the possible world in which my neighbor’s walls are fuchsia, so making that possible world epistemically accessible for me from my location in the actual world, there is currently in my body of knowledge nothing that would rule out the non-identity with the actual world of the world in which my walls are both fuchsia and portobello mushroom at the same time and in the same expanses. [Just to state the possibilities: the epistemically accessible world in which my neighbors’ walls are wine red; the non-epistemically accessible world in which the peanut in Chicago finds itself on the nose of the Mona Lisa — a possible world that, though not epistemically accessible for me, is still semantically accessible for me because I can still articulate the truth conditions; finally, the semantically inaccessible — a lack grounded in my cognitive limits — world in which an object is two colors at the same time.]

)whose At one time, had the though ever occurred to me, I am sure I would have regarded the singleton situation comprising the state of affairs ck at tMy his location’ to be incompatible with ‘wave

For there is (I venture) in the body of knowledge possessed by me (intentional use of passive voice) this item: I have, so far, not encountered an object that is, in the same expanse, fuchsia and portobello mushroom at the same time. What is more, I will venture that in no possible world in which things have colors does an object exist that is, in the same expanse, two different colors at the same time. [Discuss qualifications and dismiss possible counterexamples someplace.] To be a color c1 different from a color c0 is to “displace” c0 so to speak should an object change color from c0 to c1. Necessarily, an object cannot be two different colors at the same time in the same expanse. The object cannot be two different colors (at the same time and in the same expanse). If this actually is an item in the body of knowledge possessed by me, this piece of knowledge rules out the identity with the actual world of any possible world (namely the fuchsia apartment wall world) for which s1 is the key description. Epistemically, the fuchsia apartment wall possible world cannot be identical with the actual world. So s0 and s1 cannot hold in the same world; s1 must hold in a different world. The necessity pertaining to this “cannot” and “must” is that of possible worlds epistemically accessible for me from my location in the actual world and given the body of knowledge possessed by me. Since s0 and s1 cannot hold in the same world, they are incompatible.

Situations Drawn From Spawned-From-The-Known Possible Worlds: All the sub-situations within my comprehensive actual situation are, of course compatible with one another. That they are all holding at the same time is proof of their compatibility. Clearly, they do not preclude one another.

It will be worth keeping in mind (if only for the sake of clarity) that among these compatible situations are singleton situations mapping to a set comprising the same objects. For example, the situation that maps to the state of affairs named by ‘Tiger is sitting on my keyboard’ is clearly compatible with the numerically distinct situation named by ‘Tiger’s color is silver and the color of the Chromebook keyboard he is sitting on is Payne’s grey with a slight greenish undertone’. Clearly, ‘Tiger is sitting on my keyboard’ is compatible with ‘Tiger’s color is silver and the color of the Chromebook keyboard he is sitting on is Payne’s grey with a slight greenish undertone’

One would normally expect key situations defining spawned-from-the known possible worlds to be incompatible within the same possible world with the situation serving as its “raw material” so to speak. If I access a possible world by taking the description “portobello mushroom walls” (the “raw material situation”) and substituting for it the description “fuchsia walls”, the portobello mushroom wall situation and the fuchsia wall situations surely must be in different possible worlds. (Warning — this “must” is about to be caveated to death.) I am not, after all, trying to land in the same possible world I started with! I am trying to imagine what the effect would be if the color of the walls were different from what they are now.

And surely my walls — at least not in the same expanses — cannot be fuchsia and portobello mushroom at the same time in the same possible world. This I am willing to bet my paint brushes on. Unable to hold at the same time in the actual world — or in any other possible world — the two situations are incompatible. The one precludes the other from holding. If one holds in a possible world, the other cannot hold in that same world.

Let me analyze this “cannot” in terms of possible worlds. Among all the possible worlds in which colors and walls work the way they do in the actual world, in not one of them is there a wall — or any other colored object — that is at once fuchsia and portobello mushroom (or any other pair of colors) in the same expanse. That is the sense of “cannot”. Yet it may be worthwhile asking what lets us determine that there are no chromatically accessible possible worlds in which an expanse can be at once fuchsia and portobello mushroom.

Going through them one by one.

Or I can say “I am unable to posit a chromatically accessible possible world in which the same expanse is at once two distinct colors, fuchsia and portobello mushroom or any other pair of distinct colors”. I could, of course, simply cobble together two key descriptions and ascribe them to my wall in a possible world different from the actual one, as in “the walls of my apartment are at once fuchsia and portobello mushroom in the same expanses” (henceforth the “fuchsia/portobello mushroom sentence”).

But I would not know the meaning of the sentence purporting to be that description, just as I would not know the meaning of “this idea is green”. At least I would not know the meaning of either sentence if we take one to understand the meaning of a sentence if they know what would be the case were the sentence true. Having no conception of what would be true were the fuchsia/portobello mushroom sentence true, I cannot be said to know what would be true given the truth of the sentence. Therefore, I do not know the truth conditions of the sentence. I do not know what the sentence means. And if we take a possible world to be a set of descriptions taking the form of meaningful sentences, I have not succeeded in positing a possible world.

One way to have a conception of something is to imagine it visually. If I picture a square resting on the ground on one of its sides, then moving so that one of its vertices is now touching the ground, I have succeeded in picturing a square “turning into” a diamond. I have a conception, implemented by way of the visual imagination, of what it is to be a diamond. This would suffice, I claim, to give conception of a diamond shape.

Of course, as Leibniz points out in his NEW ESSAYS, one can still be said to have a conception of something even when the lack the ability to picture that thing imaginatively. I cannot really imagine a icosahedron with its 20 equal faces. But I can conceive of one by forming a description in the mathematical language of geometry. This mathematical description provides another sufficient condition for having a conception of something. But I do rather doubt that there is a corresponding mathematical description of my walls being fuchsia and portobello mushroom at the same time that anyone could give, no matter how mathematically proficient.

So, provided I am not mistaken about such a mathematical conception existing for colors, there is no person (currently) who grasps the truth conditions for “wall that is at once fuchsia and portobello mushroom in the same expanse.” There is no person who is able to conceive what this would be. The description has no meaning. There is therefore (unless I am mistaken) no person who is able to posit a state of affairs corresponding to this description as a key situation for a possible world.

Therefore, even if the Most Proficient Knower somehow transferred all of their mathematical, physical, and conceptual skills to me, I would still be unable to posit a possible world in which colors and walls behave the way they do in the actual world but expanses could be at once fuchsia and portobello mushroom. Relative to my body of knowledge, there is no such world. For all I know, there may be for an omniscient being. But no such possible world exists for me.

So with one wave of the hand, I can say that among all the possible worlds I am able to posit given my body of knowledge and the conceptual resources this body affords me, there is not a single one in which an expanse exists that is at once fuchsia and portobello mushroom. I (at least the idealized knower me who, after the requisite mind-melds, has attained the honor of belonging to the set of Currently Most Proficient Knowers — henceforth CMPK) need not go through each possible world one by one to see if I can find one in which an expanse is simultaneously fuchsia and portobello mushroom. I no more need to do this than I need to keep adding three peanuts to a set of three peanuts to see if I always end up with six peanuts. I don’t face the ‘I just might discover an elephant-sized royal-blue swan’ problem.

So in all the possible worlds which I can posit, there is not a one in which the fuchsia wall situation holds at the same time as the portobello mushroom situation. These two situations cannot hold at the same time in the same world. They must hold in different worlds. This “cannot” and this “must” of course, is relative to my body of knowledge and the cognitive resources available to me as a CMPK.

So far as I know (I am ignorant of anything that would say otherwise), even an omniscient being would also be unable to posit a possible world in which the two situations hold at the same time. Even as CMPK, I cannot conceive of anything that allowed even an omniscient being to grasp the truth conditions of the fuchsia/portobello mushroom sentence. (This assertion is about to be caveated to death). My failure to imagine plus my failure to conceive in any other way, seems to place the odds against me in attempting to give an omniscient being the ability to grasp this truth condition.

[[[all of them displace the two colors this way.]]]

[What it is for two descriptions to be different. Some different descriptions involving the same object are prima facie perfectly compatible. Ultimate versus non-ultimate incompatibility. Defeasibility. Epistemic because relative to a body of knowledge/cognition. Therefore relative to a situation. ]]]

Let me say, then, that two situations are incompatible with one another when they cannot exist in the same possible world at the same time. This “cannot” is to be interpreted epistemically, relative to a body of knowledge/set of cognitive skills. If this body of knowledge belongs to an omniscient being, I will say the incompatibility is ultimate, or non-defeasible. If the body of knowledge belongs to a finite, situated being — even so best to think in terms of a CMPK –, the incompatibility is defeasible. I know nothing that would preclude the defeasible incompatibility from being identical with the indefeasible.

Another example will highlight the defeasible nature of incompatibility when the body of knowledge does not belong to an omniscient being.

[[[[September 30, 2020: explain the cannot. I range through all the possible worlds I can spawn from the known actual world. In none of them do the two colors exist at the same time. Like ranging through each case of 1 + 1. In fact, I cannot come up with the truth conditions for a description ascribing both colors to the same wall in the same world. So in all worlds in which colors and walls work the way they do in the actual world, all of them displace the two colors this way. My inability to conceive captures all of them. The incompatibility stems from my inability to conceive.]]]

In positing a different possible world, one needs a feature, after all, that is, well, different from the raw material feature one is using. Without a difference in the key descriptions, one does not access a possible world different from the actual world. This leaves open the possibility that while one thinks there is a difference in key descriptions, there is in fact no difference.

What does count as a difference in the key descriptions? If we take color as our guide, we can, I think, confidently say that the fact my apartment walls are portobello mushroom means that the same expanse of wall cannot be fuchsia, periwinkle yellow, cornflower blue, or any other color at the same time it is portobello mushroom. The sub-situation within my comprehensive actual situation that is defined by ‘my walls are portobello mushroom’ cannot be identical with any situation defined by ‘my walls are x‘, where for x one can substitute any color name except “portobello mushroom”. Again, I am willing to bet my paint brushes on this. I mean, I certainly have never seen any wall that is both (in the same expanse) portobello mushroom and some other color. Nor can I imagine this. I will go so far as to say I cannot conceive this — not in this actual world nor in any other possible world. Necessarily, a wall cannot be portobello mushroom and some other color at the same time and in the same expanse.

But why should one think this? Knowing that two situations hold at the same time in the actual world if dispositive for their being compatible. But what is dispositive for the incompatibility of two situations within the same possible world? Look as hard as I may in the actual world for a wall that is both fuchsia and portobello mushroom in the same expanses at the same time, I will surely never find one. But isn’t a search like this a bit like searching for an elephant-sized swan? I may never find one — but that is not an absolute guarantee I never will! As Tom Kyte, the database guru likes to remark, you can’t prove a negative such as “no swans the size of an elephant exist”.

Certainly I am unable to imagine a wall that is both of the aforementioned colors at the same time. It would seem, then that I cannot conceive of these two situations holding at the same time in the actual world, right?. (Spoiler alert: no.) And isn’t the inability even to conceive this co-holding evidence that the concept of their compatibility is incoherent?

It is also true, however, that I cannot imagine a mass being at the same time a wave. Yet on my layman’s Wikipedia-level understanding of physics, every mass is also a wave. The situation to which corresponds the description “humongous lumbering mass furiously scribbling away on a Chromebook” exists at the same time as the situation corresponds to the description “tiny petite wave furiously scribbling away (more precisely, keyboarding away) on a Chromebook”. So the two situations must be compatible. How can that be?

The apparent incompatibility can be resolved, I think, if we heed Leibniz when he tells us that imagining is not necessarily conceiving. I cannot really imagine a icosahedron with its 20 equal faces. But I can conceive of one by forming a description in the mathematical language of geometry. I suggest, then, that while one may not be able to imagine the situations “humongous lumbering mass” and “tiny petite wave” holding for the same entity at the same time, one may be able to conceive this using the mathematical language of physics.

Certainly I cannot conceive this — my conceptual resources are too limited. But I am willing to bet that the physicist, as they delve into the properties of this mass in an ever-more sophisticated way, will end up ascribing properties to this mass that are also properties of a wave. For all I know, I have wave-properties such that, were the wave (per impossibile) long enough, I would be able to pass through two separated doors at the same time and form a diffraction pattern on the other side (but what would that be?), just as, if I am not mistaken, an electron is able to pass through two separated slits at the same time and form a diffraction pattern on the other side.

Let us suppose that there is a long series of mathematical equations that describe the behavior of masses that are also waves. The conception ‘mass that is also a wave’ would comprise this series; that is to say, the conception is one large description. Let’s say I hire a physics undergraduate to come up with this description for this particular humongous lumbering mass/petite tiny wave that is identical with me. We have seen that a single state of affairs at t maps to the propositional content of a description. Therefore the singleton situation comprising that state of affairs also maps to that propositional content. Given this single description the physics undergraduate has arrived at, the singleton situation named by “Cliff is a humongous lumbering mass” is identical with the situation named by “Cliff is a tiny petite wave”. The identity of the “two” situations is, of course, a sufficient condition for their compatibility.

Identity is a two place relation, with one singleton situation bearing one name related to the same singleton situation bearing a different name. The “two” situations are numerically one, comprising the same proposition aka state of affairs at t. Other propositions/states of affairs might comprise the same objects, but be comprised by different situations. The same lumbering mass/petite tiny wave may be part of the state of affairs named by ‘lives in Houston’ and also part of a different state affairs named by ‘studied philosophy in Chicago at Loyola University’, with the result that it is involved in three numerically distinct situations each comprising a different state of affairs.

Let’s say that at time t I was completely innocent of even the popularizations of quantum mechanics, especially of the notion that every mass is also a wave. I now hire the physics undergraduate to give me enough knowledge to let me construct a conception of a mass that is also a wave. After endless agony, the physics major finally succeeds at t0 in imparting to me enough knowledge to do just this. At t, I knew nothing that would have ruled out the hypothesis that, among all the worlds that obey the laws of physics of the actual world (i.e., are nomically accessible from the actual world), in none of them are masses identical with waves. Lacking the needed conceptual resources, I would not have been able specify the truth conditions for any sentence of hte form ‘

In other words, there is nothing in my body of knowledge that would rule out the hypothesis that, among all the possible worlds in which a wall can be some color and in which what it is to be a color (however that may be articulated) is the same as it is in the actual world, there is no world in which the same expanse of wall is both fuchsia and portobello mushroom at the same time. So far as I know there is no possible world in which ‘fuchsia-wall’ and ‘portobello-mushroom wall’ are two names for the identical situation. The necessity, and therefore the incompatibility, are epistemic, grounded in my lack of knowledge, my ignorance. The necessity and the incompatibility are defeasible.

I continue. I have never encountered a wall that is both fuchsia and portobello mushroom in the same expanse and at the same time — just as I have never encountered a large mass that in any obvious way is also a wave. I am unable to picture imaginatively a wall that is both colors at the same time — just as I am unable (at present) to picture imaginatively a large mass that is also a wave. I am lacking a non-pictorial conception of a wall that is both colors (henceforth “at the same time and in the same expanse” will be understood) — and until I have such a conception, I will continue to regard the two wall-color situations as incompatible. In no possible world in which walls (or anything for that matter) have colors are the walls of my apartment both fuchsia and portobello mushroom. As parts of states-of-affairs-comprised-by-situations-that-are-parts-of-possible-worlds these two situations must be parts of possible worlds. To put the matter a bit more simply, the walls cannot be these colors without being in different possible worlds. I am in the same position with regard to the wall colors as one would have been with regard to mass/wave situations before our knowledge of physics expanded enough to give us a conception of the fact that a lumbering mass is also a wave.

For all I know, we may eventually broaden our knowledge enough to allow us to conceive an identity in the same possible world of the fuchsia wall situation and the portobello mushroom situation. Or maybe an infinite or at least extremely large intelligence already has such a conception. I am not willing to bet my paint brushes, however, on anyone arriving at such a conception in my lifetime, or ever. Nor am I able to ground the assertion that this conception will never arrive, no more than I can ground the assertion that we will never discover an elephant-sized swan. Someone in 1801 might have made the same assertion regarding large masses and tiny waves. All I can say is “so far as I know, the same expanse of wall cannot be, in the same world, at the same time, and in the same expanse both fuchsia and portobello mushroom.

In other words, there is nothing in my body of knowledge that would rule out the hypothesis that, among all the possible worlds in which a wall can be some color and in which what it is to be a color (however that may be articulated) is the same as it is in the actual world, there is no world in which the same expanse of wall is both fuchsia and portobello mushroom at the same time. So far as I know there is no possible world in which ‘fuchsia-wall’ and ‘portobello-mushroom wall’ are two names for the identical situation. The necessity, and therefore the incompatibility, are epistemic, grounded in my lack of knowledge, my ignorance. The necessity and the incompatibility are defeasible.

Side note for the sake of clarity: I have moved, then, from discussing individual worlds that are epistemically accessible for a sentient being S (the possible world in which Bigfoot does indeed roam the forests of western Washington state; the possible world in which the walls of my neighbor on the other side of the brick wall I am facing as I write this are wine-red) to sets of possible worlds that ground epistemic necessity (there is nothing in my body of knowledge that would rule out the hypothesis that, in the set of possible worlds that are accessible in such and such a way from the actual world, none comprise situation s).

Strictly speaking, epistemic necessity is compatible with, does not preclude epistemic contingency (there is nothing in my body of knowledge that would rule out the hypothesis that, in the set of possible worlds that are accessible in such and such a way from the actual world, there is at least one that comprises situation s). This is perhaps a bit like saying “all unicorns (all zero of them) are yellow ocher” and “all unicorns (all zero of them) are rainbow-colored”, where the particular set of rainbow colors in question excludes yellow ocher. Unlike the usual uses of “necessary” and “possible” “epistemic necessity” cannot be defined as “not epistemically possible” and vice versa.

Nonetheless I do think there is a certain asymmetry between epistemic necessity and epistemic contingency. Reviewing possible worlds to try to find one in which the walls in it are (at the same time and in the same expanses) both fuchsia and portobello mushroom is rather pointless given that one does not know what it means for a wall to be both these colors at once. And one does not know what this means because one does not have access to the truth conditions for “this wall is fuchsia and portobello mushroom at the same time”. (Henceforth I will call this the the “fuchsia/portobello mushroom wall sentence”.) Currently, one lacks the means for getting these truth conditions. Imagination would have been one means. My imagining Tiger sitting on my Navajo mat suffices to give me the truth conditions for the English sentence “Tiger is sitting on my Navajo mat”. I know the meaning of that English sentence because, via the imagination, I know what would be the case if the sentence were true. But imagination certainly does not give me a way to get at the (quite possibly non-existent) truth conditions for the fuchsia/portobello mushroom wall sentence. My imagination can fail me in giving me the truth conditions for the English sentence “this humongous lumbering mass is also a tiny petite wave”, but someone (I am confident) has a conception stated in the mathematical language of physics of precisely this. (Maybe, in honor of Hilary Putnam’s division of semantic labor which relegates to certain experts the distinction between a beech and an elm, I will ask a physics undergraduate to write this down for me.) But no such mathematically-expressed conception seems to exist to give us the truth conditions for the fuchsia/portobello mushroom wall sentence. That is to say, so far as I know no such conception exists.

At the time of this writing, I can state confidently that I do not have a conception for the fuchsia/portobello mushroom wall situation that would give me access to the truth conditions for the fuchsia/portobello mushroom wall sentence. I also lack a conception for the humongous lumbering mass/petite tiny wave sentence (I will need to make sure above that I have named this sentence). But I am fairly confident that I can appeal to someone in my linguistic community (some physics undergraduate, for example) who does have a conception ghat gives them access to the relevant truth conditions, just as Hilary Putnam in his MEANING OF MEANING can appeal to a tree expert for the truth conditions of ‘is an elm’ versus ‘is a beech’ even though he lacks access to those truth conditions by himself. The access is distributed across members of a linguistic community unlike epistemic accessibility, which — at least given how the concept has been defined so far — is restricted to individual sentient beings. Let me define, then, what I will call semantic accessibility in the following way:

A world w0 is semantically accessible from w for an speaker S (in w) in linguistic community L to which S belongs iff S is able to consult with speakers in the linguistic community L to which S belongs who have a conception giving them access to the truth conditions of the key description of w0.

Then, p is semantically necessary (for S in L in w) iff p is true in all possible worlds that are semantically accessible from w (for S in L in w). And p is semantically possible (for S in L in w) iff p is true in at least one possible world that is semantically accessible from w (for S in L in w).

I am call this accessibility relation “semantic” of course because it is concerned with truth conditions. A “conception” that gives one access to a particular set of truth conditions is whatever resources one possesses that lets one know what it would be for the sentence “snow is white” to be true (namely, that snow is white). Since semantics is concerned with language — the meanings of words — and language is a communal enterprise, it is natural that the definition of semantic accessibility should include a reference to a linguistic community.

I started my discussion of possible worlds by asserting them to be identical with sets of descriptions, some of which are satisfied by states of affairs in the actual world (a “brick”, to speak metaphorically), and others which are left unsatisfied (a “written description” is in place where the brick should be). Without access to the truth conditions of a description, one has no access to what the description means. One therefore has no access to the possible world the key description is meant to open up. If, say, an omniscient mind knows the truth conditions, that mind has access to that possible world. For us more limited creatures, however, we may not necessarily know if there is a possible world out there we can ever hope to gain access to in the first place. As time goes on and — as in the case of humongous lumbering masses/tiny petite waves worlds — we may gain a conception which gives us access to the world and opens it up to us. I can no more definitively say this won’t happen for the fuchsia/portobello mushroom wall world any more than I can say that I will never encounter an elephant-sized swan. I am willing to bet that the communal body of knowledge — the resources available to members of the linguistic community to form the needed conception — will never expand so as enable anyone to access the truth conditions for the fuchsia/portobello world, but….

So we can divide worlds — the sets of descriptions, satisfied or unsatisfied, real or merely purported [[expand on this — difference between nonsense such as “trd4r3e3bbubijvbhjihyiurhtrg” and words that are intended to be used to describe but fail in that function because the truth conditions are lacking) into those worlds regarding which there is nothing in the communal body of knowledge that would rule out (preclude) their belonging to the set of possible worlds, i.e., the set of worlds, that is to say, the set of descriptions whose truth conditions one has access to. If a world is not a possible world, it is an impossible world, a status that it may (epistemic “may”) or may not have permanently.

[[[Let me note parenthetically that the entities I have defined with reference to a personal or communal body of knowledge — epistemically accessible possible worlds, epistemic probability, semantically accessible possible worlds rather paradoxically depend for their definition precisely on what is not in the body of knowledge. For probability part of the relevant body of knowledge consists in knowing what one doesn’t know — I don’t know under which shell the peanut lies, though I know that there is one peanut and that it lies under one of the shells.]]]

[[[Explain this a bit more. Compare with probability as a number relative to a body of knowledge.]]]

To continue: I propose, then that every key situation to which corresponds a key description generating a spawned-from-the-known possible world be regarded at first as (epistemically) incompatible with the situation in the actual world that formed the raw material of this key description. As far as one knows — that is to say, unless and until one’s body of knowledge has expanded sufficiently — the possible situation has to be seen as belonging to a possible world different from the actual world and as numerically distinct from the situation that forms its raw material.

Epistemic incompatibility, then, is the converse of epistemic accessibility. A possible world is epistemically accessible for me from my location in the actual world if there is nothing in my body of knowledge that would rule out its identity with the actual world; and a situation within that possible world could (epistemic “could”) be part of the actual world. For example, there is nothing in my body of knowledge that would rule out the identity with the actual world of the possible world in which my neighbor’s walls are wine red; and the situation named by ‘my neighbor’s walls are wine red’ could be a situation within the actual world. Correlatively, there is nothing in my body of knowledge that would give me the conceptual resources to conceive of my neighbor’s walls being both wine red and sea glass green in the same possible world; or of my own walls as being both fuchsia and portobello mushroom in the same actual world; or any wall in any possible world in which there are things called “walls” that have colors having two distinct colors at the same time and in the same expanses. There is nothing in my body of knowledge that would rule out the non-identity with the actual world of the possible world in which my apartment walls are of a different color. More generally:

A world w0 is epistemically distinct from w for an agent S (in w) iff there is nothing in S‘s body of knowledge that would rule out the hypothesis that w0 != w.

And:

A key description d0 is epistemically incompatible with a key description d for an agent S in world w for whose definition d is key iff every world w0 accessible for S by way of a key description d0 is epistemically distinct from w.

[[[[Two descriptions d0 and d1 are epistemically incompatible for an agent S (in w) iff, given the body of knowledge possessed by S, d0 and d1 together fail to provide a key description giving S access to a possible world.]]]]]

And:

Two situations s and s0 are epistemically incompatible iff the key descriptions to which they correspond are epistemically incompatible.

That two situations are incompatible is defeasible. [[Need a similar definition of compatibility.]]

To sum up this discussion of epistemic compatibility/incompatibility: Key description situations drawn from spawned-from-the-unknown possible worlds are epistemically compatible with the corresponding situation in the actual world when they are epistemically accessible from the actual world. Otherwise they are incompatible. Key description situations drawn from spawned-from-the-known possible worlds may at first be assumed to be epistemically incompatible with their “raw material” situations in the exposed part of the actual world, but then may become epistemically compatible as our knowledge grows. I dare say, however, that it is rarely — if ever — the case that one should bet the ranch — much less one’s paint brushes — on the incompatibility between two situations ever morphing into compatibility.

[[[[Lumberoom: Imagination, then is not an absolutely reliable guide to incompatibility. The mere inability to imagine two situations as being the same situation is not exactly an absolutely reliable guide to their being incompatible and therefore forever doomed to non-identity. My mere inability to imagine that the walls of my apartment, in the same expanses, are at once fuchsia and portobello mushroom does not suffice to guarantee that they cannot be. At the same time, I do not know what it would be for the walls (in the same expanses — henceforth this will be understood) of my apartment to be both portobello mushroom and fuchsia at the same time. I do not know — I haven’t the faintest idea — what would be the case if the sentence “the walls of my apartment are both fuchsia and portobello mushroom at the same time” were true. The truth conditions for that sentence are lacking for me — I don’t have access to these truth conditions. I am therefore unable to posit a possible world which has this sentence as its key description.]]]]

[[[[But I do have access to the truth condition for the possible world in which the walls of my apartment are fuchsia, not portobello mushroom. I know what would be the case if the sentence “the walls of my apartment are fuchsia” were true. I have the knowledge expressed by the sentence “this is fuchsia” and the knowledge of what it is to paint walls a certain color and whatever other knowledge is required to give me the conceptual resources to know this truth condition. I am therefore able to posit the fuchsia apartment wall possible world.

At one time, no one would have had the conceptual resources to know the truth conditions for the possible worlds (one of which which happens to be the actual world) in which “lumbering mass at work on its laptop scribbling away” is describes the same situation as does “petite tiny wave at work on its laptop scribbling away”. I am not sure I have the conceptual resources to know these truth conditions. I am confident, however, that a competent physicist would. Perhaps even they would not be able to imagine these truth conditions pictorially; but perhaps the ability to produce a series of equations describing the situation would count as knowing the truth conditions. At one point in time (t0) no sentient being S had the conceptual resources afforded by the needed body of knowledge; then at another point in time (t1) some agents do. At t0 the prudent thing to say would have been “so far as I know, ‘is a wave’ and ‘is a particle with mass’ are incompatible descriptions of the identical situation (namely, this person scribbling away)”; at t1 one can now say they are indeed compatible descriptions of the same situation.

Now, I submit, at the time of this writing, the prudent thing to say is that so far as I know, ‘the walls of my apartment are fuchsia” and “the walls of my apartment are portobello mushroom” are incompatible descriptions of the identical situation (namely, the walls of my apartment being such and such a color). But obviously I have no guarantee that my current body of knowledge and the resulting conceptual resources available to me will always be the same. Perhaps these can change just as they did in the case of the mass that is also a wave. The only entity that could provide such a guarantee would be an omniscient being. My being finite — i.e., my being situated — means that the ability to provide such a guarantee is likely to be forever beyond my reach. So I have to rest content with the “so far as I know”.

Let’s say, then, that incompatibility is relative to a body of knowledge, just as epistemic accessibility and probability (at least according to Kyburg) are. The incompatibility of descriptions d0 and d1 is relative to the body of knowledge possessed by a (possibly fictional) omniscient being who knows (if they do know this) that the two can never describe the same situation at the same time. The epistemic incompatibility of d0 and d1 is relative to a body of knowledge that fails to provide the resources — a failure that quite possibly will never be remediated — to give one access to the truth conditions for a single situation’s holding for which both d0 and d1 serve as key descriptions at the same time. [[[To have access to the truth conditions is to have access to a possible world.]]] This incompatibility means that d0 and d1 can never, together, provide a key description giving one access to a possible world. ]]]]]

[[[[[[

Include someplace in the main discussion.

To gain access to a possible world is to have the ability, provided by one’s body of knowledge plus whatever other abilities, to conceive or represent the truth conditions of that world’s key description. If, given one’s body of knowledge and one’s cognitive abilities, one cannot cognize the truth conditions of the combination of d0 and d1, that combined description cannot open up or give one access to a possible world. The one description precludes the other. And there is no situation that they, in combination, correspond to. This absence of truth conditions is what provides the meaning of epistemic incompatibility.

Generally, one would expect that coming up with an ostensibly different key description (my walls are fuchsia, not portobello mushroom; Tiger is from planet XZDOIN#K deep in the Orion galaxy, not planet Earth) would result in pairs of incompatible descriptions and therefore incompatible situations which cannot hold at the same time in the same possible world (especially in the actual world). “Different” means “not identical”. Different description, different situation.

The one exception to different descriptions generating different situations would be when the descriptions are parts of a longer description whose individual sentences (perhaps in the forms of mathematical statements) cohere — maybe surprisingly –into a single description. The physicist starts with a mathematical description of a lumbering mass…and when they finish, end up with something that also describes a very small wave. They may still be unable to picture something’s being both a lumbering mass and a tiny petite wave at the same time — nonetheless, their long mathematical description constitutes a setting forth of the truth conditions. ]]]]]

[[[Need now to show how room is left for a situation not to be compatible with itself]]]

I now join these two streams: the discussion of truth, and the discussion of compatibility/incompatibility.

Non-Bivalent And Inconsistent Situations

Non-Bivalent Situations: The binary relations ‘compatibility’ | incompatibility holding between two situations give us a useful truth condition for negation that will let us see how situations can be both bivalent and inconsistent. The case for bivalent situations is perhaps a bit less … venturesome … than the case for inconsistency. We will see where I end up.

Let’s take a look at this truth conditions for negation, but modified so as to be talking about epistemic compatibility | incompatibility, not compatibility | incompatibility per se. The epistemic compatibility relation Cst holds between situations s and t if and only if s and t are not epistemically incompatible. s is epistemically incompatible with t for S from S’s location in the actual world if s is the key-description situation of a possible world that is not epistemically accessible for S from their location in the actual world. For example, the key-description situation in which Elizarraraz’ peanut has turned rogue and ended up on the nose of the Mona Lisa specifies a possible world that is not epistemically accessible for me from my location in the actual world because my body of knowledge includes the item ‘peanuts do not behave this way in the actual world.’ There is something in my body of knowledge that rules out, or precludes, the identity of the possible world of which this situation is a part with the actual world. This lack of epistemic accessibility means that the situation in which the rogue peanut has landed on the nose of the Mona Lisa is incompatible with the situation in which, at the time of this writing, the Mona Lisa is hanging inside the Louvre blissfully ignorant of possible misbehaving peanuts.

From the compatibility of s with t (and vice versa), it follows a fortiori that s is cognitively, truth-conditionally compatible with t (and vice versa). That is to say, one’s body of knowledge gives them the ability to posit s and t holding in the same world at the same time, either as two distinct situations or as the identical situation.

A situation makes ~A true if and only if every situation [epistemically] compatible with it fails to make A true.

RL, p. 75

Let’s take ~A to be the sentence: “it is not the case that the walls of my apartment are fuchsia”. So A is the sentence “the walls of my apartment are fuchsia. What situation might make ~A true? The situation s0 in which the walls of my apartment are currently portobello mushroom is a plausible start.

This situation s0 is (I venture) epistemically/semantically incompatible with the situation s1 in which the walls of my apartment are fuchsia. As we have seen, two situations are incompatible if they cannot hold at the same time in the same world. Here, the “cannot” is of the epistemic/semantic variety. Not only have I never encountered an object being two different colors at the same time in the same expanses; not only have am I completely confident that I never will encounter such; not only do I find myself unable to imagine this; but I have no cognition at all (the inability to cognize needing to be distinguished from the inability to imagine, as we saw above in the mass/wave case) of what would be true if an object were of two different colors at the same time in the same expanses. I don’t know what it would be for the actual world in which the walls of my apartment are a nice subtle portobello mushroom to be identical with the possible world in which those walls are a wild fuchsia.

Just as there is currently nothing in the body of knowledge possessed by me to rule out the hypothesis that the possible world in which the walls of my neighbor’s apartment are wine-red is identical with the actual world, there is currently nothing in this body of knowledge that would give me the capacity to even formulate the hypothesis that the the portobello mushroom world is the identical with the fuchsia possible world. s1 is epistemically/semantically incompatible with s0.

But s1 is the only situation that could make A true. We have seen that a necessary condition for a sentence to be true in a situation is that the sentence correspond to a state of affairs in the situation. Only a situation within my apartment which contains the state of affairs ‘the walls of my apartment are fuchsia” could provide the needed correspondee, so to speak, to the sentence “the walls of my apartment are fuchsia” acting as corresponder. But s1, the situation which comprises that state of affairs, is incompatible with s0, the situation that comprises the state of affairs in which the walls of my apartment are portobello mushroom. It follows then that no situation epistemically/semantically compatible with s0 makes A true. Therefore truth condition for negation stated above renders s0 a situation that makes ~A true. The situation in which the walls of my apartment are portobello mushroom makes the sentence “the walls of my apartment are fuchsia” false.

[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[ Epistemic Compatibility: As we have seen, every sub-situation within my comprehensive actual situation is epistemically compatible with every other such sub-situation and with my comprehensive situation itself. The fact that all these sub-situations hold at the same time in the actual world ices their all being compatible. [[[Be sure to reconcile this with the impossible cube. The impossible cube can never be actual.]]] Drawn from the actual world, these sub-situations are also epistemically compatible with any other situation drawn form the actual world by virtue of the fact that the actual world is epistemically accessible from the actual world. For any key description that is used to define the actual world, there is nothing in my body of knowledge that would rule out, i.e., preclude its being a part of the actual world.

All these actual situations are compatible with one another by virtue of the fact that that all situations drawn from possible worlds (one of which is the actual world) that are epistemically accessible for me from my location in the actual world are epistemically compatible with my comprehensive actual situation. And as we have seen, all possible situations — not just those possible situations that happen also to be actual — that are drawn from epistemically accessible possible worlds are epistemically compatible with my comprehensive actual situation. [[[Make sure I am not committing some part/whole fallacy.]]]

Negation: Negation works unproblematically for the dense parts of the lump of swiss cheese, for the mesa surrounded by the fog, for that part of the actual world which is exposed to S. Let’s take, for example, ~A to be the sentence “It is not the case that the walls of my apartment are fuchsia.” My comprehensive actual situation makes that sentence true. Let’s see how the two truth conditions for negation work for ~A.

Now we have seen that a sub-situation is compatible with the situation of which it is a part. So every sub-situation within my comprehensive actual situation s0 is epistemically compatible with s0. For no sub-situation within my comprehensive actual situation makes A (“It is the case that the walls of my apartment are fuchsia”) true. One of these sub-situations is, of course, the singleton situation comprising the state of affairs at t identical with the proposition expressed by “the walls of my apartment are portobello mushroom”, namely A. That situation especially fails to make A true. Tiger trying to get onto the keyboard as I write this; the doorbell ringing, the chalky Venetian red color of the cliffs in Southern Utah — list them all — each is epistemically compatible with s0 and each fails to make A true.

And surely every situation outside my comprehensive actual situation will also fail to make A true. [[[Discuss situations outside s0.]]] For example, whatever the color of my neighbor’s apartment walls may be, that is not a singleton situation what will make it true that the color of my apartment walls are fuchsia. I think it is fairly safe to go out on a limb, then, and say that every situation epistemically compatible with s0 fails to make “it is the case that the walls of my apartment are fuchsia” true. s0 therefore makes the sentence “it is not the case that the walls of my apartment are fuchsia” true.

Note that if nomic-and-initial conditions compatibility were in play, my neighbor’s walls being periwinkle yellow, say would make it true that my walls are fuchsia if the initial conditions at the big bang deterministically led up to these two causal lines. But I think it would violate our sense of what ‘not’ means if my neighbor’s walls being wine red made “it is not the case that my walls are fuchsia” true. This is why I think “compatible” should be taken to mean “epistemically compatible” in the truth condition for negation. ]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]

Negation works unproblematically for the dense parts of the lump of swiss cheese, for the mesa surrounded by the fog, for that part of the actual world which is exposed to S. But matters are different inside the holes in the lump of swiss cheese, or down in the depths of the fog surrounding the mesa. Consider the sentence “the walls of my neighbor’s apartment are wine red”.

Consider the situation in the possible world, epistemically accessible for me from my location in the actual world, that has as its key description “the walls of my neighbor’s apartment are wine red”. Within this possible world, the key situation (a singleton) would, if the state of affairs it comprises obtained in the actual world, make the sentence “It is the case that the walls of my neighbor’s apartment are wine red” true. Let this sentence be A at the moment.

As part of a possible world that is epistemically accessible for me, this key situation counts as an epistemic situation. As a situation that is hidden from me, as being attached to a probability less than 1 (but presumably greater than 0), it is not part of my comprehensive actual situation, which comprises only exposed states of affairs with a credence of 1. But being an epistemic situation, it is epistemically compatible with my comprehensive actual situation.

A mere probability does not make a sentence true. The probability that the peanut is under shell #1 is 1/2, as is the probability that the peanut is not under shell #1. But this probability does not make either “The peanut is under shell #1” or “The peanut is absent from shell #1” true. The probability is not the truth-making factor. The assertion “the probability is 1/2” does not answer the question “what makes it true that the peanut is under | is absent from shell #1?” What answers that question is rather the peanut’s presence under | absence from shell #1.

Likewise, the probability that my neighbor’s walls are wine red is something like 1/the number of wall paint colors that are out there. Let’s say the probability is 1/10000. The assertion “The probability is 1/10000” is not the answer to the question “Are my neighbor’s walls wine red?” (Henceforth the “wine red question”.) The proper answer to that question would be “My neighbor’s walls are wine red”. That the probability is 1/10000 gives one the possibility that my neighbor’s walls are wine red. But wine-red walls are what make the sentence true — if it is true — not the mere possibility of wine-red walls. The sentence “My neighbor’s walls are wine red” corresponds | fails to correspond to whatever state of affairs obtains as to the color of my neighbor’s walls, not to whatever state of affairs might obtain.

[[[To say that a sentence is “merely probable” is not yet to say that it is true, though of course it might also turn out to be true in the end. The mere probability that the peanut is under shell #1 is not a truth-maker.]]]

Every brick that composes this particular epistemically accessible possible world is present and is the same brick that composes the actual world, with the exception of one missing brick. In place of this brick is a piece of paper on which is written “The walls are wine red”. In order to be true, the wine-red sentence has to correspond, so to speak, to the brick, not to the inscription.

Nothing within my comprehensive actual situation makes the wine-red sentence true: not the portobello mushroom color of my walls, not Tiger’s sitting on the mat, not my doorbell’s ringing — no sub-situation in this situation comprising whatever states of affairs does. And as we have just seen, neither does the singleton situation that, outside my comprehensive actual situation, is part of the for-me epistemically accessible my-neighbor’s-walls-are-wine-red possible world. So according to the above truth condition for negation, it is false. A, that is to say, “It is the case that my neighbor’s walls are wine red” is false.

But if bivalence held for my comprehensive actual situation, [[[remember to distinguish between holding in and holding for a situatioun]]], then ~A would have to be true: “It is not the case that the walls of my neighbor’s apartment are wine red”. Then the following sentence would have to be true: “My neighbor’s walls are sea-glass green; or my neighbor’s walls are Navajo white; or my neighbor’s walls are goldenrod yellow; or my neighbor’s walls are Tiepolo pink; or my neighbor’s walls are cornflower blue; or my neighbor’s walls are ultramarine blue; or my neighbor’s walls are Venetian red….” and so on for every wall color except for wine-red.

But using the same reasoning as for wine red, each of these or’d sentences is false for my comprehensive actual situation. That is to say, no situation epistemically compatible with my comprehensive actual situation s0 — no sub-situation in or within s0, and no situation drawn from a possible world epistemically accessible for me from my location in the actual world — makes any of these or’d sentences true. So the entire sentence that comprises them is false. So for my comprehensive actual situation s0 and for all situations epistemically compatible with it, both “It is the case that my neighbor’s walls are wine red” and “It is not the case that my neighbor’s walls are wine red” are false.

Bivalence holds within an epistemic situation (i.e., states of affairs are exposed to a sentient being), in that way my comprehensive actual situation is like a possible world. But bivalence fails for my comprehensive actual situation i.e., when I reach outside that situation to consider situations that are hidden from one and sentences whose truth is merely probable. When considering the truth of A requires a reach into the fog surrounding the mesa, or into one of the holes in the lump of swiss cheese, both A and ~A are false. One’s comprehensive actual situation turns out to be not enough to render at least one of these sentences true. This in turn means that there exist situations for which, for certain sentences A (obviously not all), “If A then A” is false. In this way, Relevant Logic can avoid the Classical Logic paradox: “A –> (B v ~B)”, alternatively, “A –> (B –> B).

Complete, a possible world answers the wine-red question as well as the peanut question as well as the Bigfoot question as well as the Amazonian chartreuse butterfly question. Finite and fragmentary, a situation cannot. A situation is partial. Like Judge Judy’s courtroom being the wrong tribunal for answering the question who is the culprit in the murder of the century, a situation is the wrong tribunal for answering the wine-red and the peanut (is the peanut under shell #1 or under one of the other two shells?) questions.

Partial situations allowing for this can exist because situations are not complete. They do not answer every question. (Does a Bigfoot creature roam the woods of western Washington state or does it not? Is there a butterfly fluttering about in the Amazon at GPS location xyz or not; and if there is, are its wings chartreuse? Is the peanut under shell #1 or does that shell hide only a small expanse of table-top? Are the walls of my neighbor’s apartment wine red or some other color?) My comprehensive actual situation remains the same whichever happens to be the correct answer. The identity of this situation does not depend upon the answer. This sameness leaves room for non-bivalent situations. [[[[Expand on this]]]]

But as we saw above, the identity of a possible world does depend upon the answer. The Bigfoot possible world is not identical with the non-Bigfoot possible world. So possible worlds do not allow for the failure of bivalence. In any possible world, including the actual world, either a Bigfoot creature roams the woods of western Washington state or does it not. Unlike situations, which can be partial, a possible world must be complete. It must answer every question.

All of the above is my attempt to nail down, by putting in my own terms, Mares’ discussion of non-bivalent situations in his RELEVANT LOGIC: A Philosophical Interpretation. This is an exercise in writing to learn. In particular, this is my attempt to nail down the following passage from Mares:

Partiality is straightforward [ahem! Cough cough], so we will start with that. Consider the situation that consists of the information that is currently available to me. The includes what is going on in my study as I write this section of my book, and what I can see through my window. Nothing happening here makes it true that it is currently raining in Toronto (which is on the other side of the globe). But situations in which it is raining in Toronto are compatible with my current situation. So neither ‘It is raining in Toronto’ nor ‘It is not raining in Toronto’ is true in my current situation. Thus bivalence fails for this situation and the situation is partial.

RL, p. 75

Let me turn now to inconsistent situations.

Inconsistent Situations: Dealing with inconsistent situations is a bit more of a stretch. But let me venture (as I try to strengthen my shaking knees) the following attempt to use the concept of ostensible objects to allow for inconsistent situations. There are singleton situations, I claim, that are incompatible with themselves because they comprise impossible objects. ‘Compatible’ is not always a reflexive relation for a situation.

First, some words on the concept ‘incompatible’.

Compatibility Again: Situation s1 is compatible with situation s2 when s1 and s2 can hold at the same time. For example, the situation that corresponds to the description “Tiger is sitting on the mat” (where I have deposited him to keep him off my keyboard) holds at time t. The situation that corresponds to the description “The doorbell is also ringing in my apartment at t” also holds at t. [[[Need to say something about “corresponds” vs. “defines”]]] That the two situations hold at the same time clearly means they are compatible. Their co-holding is dispositive. And as two sub-situations within my comprehensive actual situation s0 (I will be reserving “s0” to name my comprehensive actual situation unless otherwise noted), one would of course expect them to be compatible, as are all sub-situations within s0.

In the actual world, my cat Tiger was born on earth and did not travel here from the planet XZDOIN#K deep within the Orion galaxy. But surely the situation whose description forms the key description of the possible world in which Tiger is from XZDOIN#K (with cats, those creatures of mystery, one always has one’s suspicions) is also compatible with the doorbell’s ringing and with many of the sub-situations within my comprehensive actual situation. Since this is a situation drawn from a spawned-from-the-known possible world, it is perhaps fairly safe — though as we have seen, not absolutely safe — to say that this situation is not compatible with the situation that formed its “raw material”, Tiger’s origins being the planet earth. Surely the situation defined by the situation “Tiger is from planet earth” cannot co-hold with the situation defined by “Tiger is from planet XZDOIN#K deep within the Orion galaxy”. The two situations are different. They cannot be identical situations. The two situations are not compatible. The one precludes the other.

However, the mere fact that two descriptions seem like they cannot be descriptions of one and the same situation does not mean that these two descriptions cannot correspond to the identical situation. What is more, one of the differing descriptions may be a key description of a spawned-from-the-known possible world and the other may be the “raw material” of this description. One may think they have accessed a possible world numerically distinct from the actual world, but end up landing in the same old actual world anyhow.

Above, I have said that two situations s and s0 are epistemically incompatible iff the key descriptions to which they correspond are epistemically incompatible. In turn, a key description d0 is epistemically incompatible with a key description d for an agent S in world w for whose definition d is key iff every world w0 accessible for S by way of a key description d0 is epistemically distinct from w. [[[[Two descriptions d0 and d1 are epistemically incompatible for an agent S (in w) iff, given the body of knowledge possessed by S, d0 and d1 together fail to provide a key description giving S epistemic access to a possible world.]]]]]

Ostensible Objects:

[[[This particular expanse of wall cannot be portobello mushroom or sea-glass green at once. The one situation precludes the other. The two situations are not compatible. And their inability to exist at the same time is dispositive for their being incompatible.

Likewise, the holding of two situations at the same time is dispositive for their being compatible, their not precluding one another. My cat Tiger’s being on the mat (where I have just deposited him to keep him from sitting on my keyboard) at the same time that the doorbell is ringing definitively shows that these two situations are compatible. ]]]

Now I will try to show that ‘compatible’ is not always a reflexive relation. A situation can be incompatible with itself. If a situation is incompatible with itself, it excludes itself. This is a funny position for a situation to be in, a bit like Mark Twain or Groucho Marx or whoever said he refuses to belong to any club whose standards are so low as to have him as a member. But there we are.

Take a look at a depiction of an impossible cube, inspired by the Dutch artist Maurits Cornelis Escher.

https://www.youtube.com/watch?v=UibfZnfNYyc

If you see the cube as if a bit from above, take a look at the vertical bar closest to you, and the bar that gets experienced as running horizontally behind that bar to connect to two lower vertices behind it. Were this an actual object existing in the physical world and you were requested to touch the horizontal bar behind, you would reach past the vertical bar just mentioned and move your fingers along the horizontal bar behind from one vertex to the other. I hypothesize that this potential touching informs your visual experience of the bar behind so that your visual experience is that of a ‘bar behind’. The horizontal bar looks ‘behind’ just as a paper shopping bag looks heavy when one knows it contains groceries and looks light when one knows it is empty. This, I take to be one example of Merleau-Ponty’s contention that the different senses fuse together (see his Phenomenology of Perception), a view not totally dissimilar to George Berkeley’s contention that sight and touch are “entangled” (see his A New Theory of Vision). Those willing to sign a waiver releasing the author from any liability for any resulting brain damage might also want to consult a certain Cliff Engle Wirt’s journal article The Concept of the Ecstasis.

But the (more or less) horizontal bar is also experienced as cutting in front of the vertical bar. If the experience ‘behind’ is salient enough, the eye just accepts this, even though there is no visual experience of the horizontal bar coming from behind to wrap itself in front of the vertical bar then back again on its journey to the other vertex. In the physical world, these two states of the horizontal bar exclude one another. The horizontal bar cannot, at the same time, be behind and in front of the vertical bar. The two situations are not compatible.

But the visual experience of ‘horizontal bar in front’ is compatible with the visual experience of ‘horizontal bar behind’. For the situation comprising the one experience can and does hold at the same time as the situation comprising the other experience. That the two situations should be compatible may seem strange at first, but really should not. For just as, as John Searle constantly points out, the visual experience of a blue object need not be itself blue, and the visual experience of a square object need not itself be square, the visual experience of ‘bar simultaneously in front and behind’ need not itself have the (impossible) property ‘simultaneously in front and behind’.

Now visual experiences are of ostensible objects which usually actually exist but sometimes do not. My visual experience of my cat tiger (with a mouse) at my left as I write this has as its ostensible object a cat that actually exist. Tiger, although he is, yes, an ostensible object of my vision, is not merely an ostensible object of my vision.

My visual experience of the periwinkle-pink rhinoceros grazing peacefully at my feet while I write this … er…. I mean, were I to have such a visual experience … is (or rather, would be) of an ostensible object that does not exist. There is in fact no purple rhinoceros grazing, peacefully or otherwise, at my feet. The purple rhinoceros is merely an ostensible object of my vision. Nonetheless, I can still talk about him and even give him a name (say, “Alfred”). I can even get upset if he seems miffed and refuses to show up for a few days.

Likewise, my visual experience of the impossible cube I “see” on my laptop screen is of an ostensible object that in fact does not exist. It is merely an ostensible object. It no more exists in the physical world than does my periwinkle-pink rhinoceros. Even so, it does seem to make sense to talk about impossible cubes. We talk about ‘this impossible cube’ among different, varying impossible cubes (say, some with differently colored bars). An ostensible object is an object, existing or not existing, actual or possible or impossible, that can be talked about

Now I propose that we regard one’s comprehensive actual situation and sub-situations as comprising at least those objects that one is involved with. From this it follows that my comprehensive actual situation and all sub-situations comprise ostensible objects, both merely ostensible objects and more-than-merely-ostensible objects. My involvement with my cat Tiger consists in my bond with him. My involvement with the impossible cube consists in my preoccupation with this object as a possible avenue to show how inconsistent situations can exist.

Now if we allow the situation ‘Cliff in his apartment typing away at the keyboard of his laptop to produce disreputable screeds’ to comprise the superset ‘ostensible objects of perception’, not just the proper subset comprising ‘physical objects existing in time and space’, that situation will contain, as a sub-situation, the impossible cube I visually experience on my screen. The situation comprising this impossible object is not compatible with itself. It is constantly excluding itself. In a way that sounds very Hegelian, it is incoherent, existing in contradiction.

One would expect such an object to be unstable, and this one in fact is. The horizontal bar behind is constantly threatening to become the horizontal bar in front of the vertical bar, with the result that the cube suddenly switches from being vied from above to being viewed from below.

Now let’s take s to be the singleton situation that comprises the impossible cube depicted on my laptop screen. Let A be the proposition expressed by the English sentence “The horizontal bar is behind the vertical bar”. (That this proposition is about the impossible cube is given.) I venture the claim that no situation compatible with s makes A true. For surely the only situation that could possibly (I will leave ‘could possibly’ undefined) make A true is s itself. But as we have just seen, s is not compatible with itself. And surely no situation that is compatible with s will make A true. For example, that Tiger is to my left is compatible with s (this situation holds at the same time as s), but clearly does not make A true. Nor can I think of any other situation apart from s that would make A true.

Therefore, ~A counts as true according to the truth condition for negation stated above. But it is also the case that no situation compatible with s makes ~A true. Only s could make ~A true. For example, that Tiger is lying to the left of me, always about to press his paw onto the keyboard, clearly does not make true ~A, ie., “The horizontal bar is not behind the vertical bar”. But s is not compatible with itself. So ~(~A) is true, which means of course that A is true. So the truth condition for negation gives us the result that a situation exists for which A ^ ~A is true. Inconsistent situations do exist.

This way we can avoid the Classical Logic paradox (A ^ ~A ) –> B. That is to say, from a contradiction every proposition follows — the Principle of Explosion. This principle would, of course, allow for multitudinous irrelevant implications and therefore cannot hold in Relevant Logic. We can avoid the principle of explosion if we maintain that situations comprise ostensible objects, which include not just actual objects, and not just possible objects, but also impossible objects.

Naturally, a possible world cannot contain impossible objects. (Duh.) Unlike situations, possible worlds must be consistent. So, as Mares notes, a possible world must be both complete and consistent:

First, whereas worlds are complete, situations can be incomplete. To use the terminology of Barwise and Perry … worlds decide every issue. That is, they tell us, for any proposition, whether that proposition is true or false. Situations, on the other hand, do not decide every issue. In some situations, the information whether a given proposition [e.g., “Bigfoot roams the forests of western Washington state”] is lacking. This property of situations is sometimes expressed by saying that at some situations ‘the principle of bivalence fails’. Second, situations need not be consistent. That is, there are some situations that make contradictions true. Possible worlds, on the other hand, are completely consistent.

Mares, RL, pl 27

I have tried to use the concept of possible worlds that are epistemically accessible to a knower S as a way of making sense of the concept ‘partial situation’, that is to say ‘non-bivalent situation’. Partial aka non-bivalent situations are ones in which A v ~A and A –> A may not be true. Trimming out all the possible worlds (that is, all the ones not identical with the actual world) that are epistemically accessible to me leaves me with that portion of the actual world about which I have information — Cliff’s comprehensive actual situation. Defining this situation this way already makes it relative to a knower, i.e., a person in a situation. A situation has a center — this person.

Likewise, I have tried to use the concept ‘ostensible object’ to make sense of the concept of an inconsistent situation. As the center of my comprehensive actual situation, my perceptual apparatus gives me the ability to experience ostensible objects that do not exist as well as ostensible objects that do exist. Some of the merely ostensible objects are possible objects (e.g., the purple rhinoceros gazing peacefully at my feet); others are impossible objects (e.g., the impossible cube inspired by Escher). A ^ ~A is true for at least some situations containing impossible objects.

So now Cliff’s comprehensive situation includes more than just the actual world. As a possible world, the actual world cannot contain impossible objects. Containing a surplus, so to speak, over and above the actual world, my comprehensive situation can no longer be described as just a restriction of the actual world. We need now to speak of just ‘Cliff’s comprehensive situation’, leaving out the ‘actual’.

The falsity of A ^ ~A and the truth of A –> A (aka A v ~ A) still hold for possible worlds. So aficionados of the law of the excluded middle and of the principle of non-contradiction need not freak out. These fail to hold only for situations. On the other hand, situations are better suited than possible worlds to account for natural language:

…the ubiquity of expressions that clearly depend on restricted parts of the world gives us reason to believe that natural language is built primarily to talk about restricted parts of the world and not talk about complete possible worlds.

Mares, RL, pl 40

The End: And here I will end this installment of my writing-to-learn project for Mares’ Relevant Logic A Philosophical Interpretation. My tiny fragile bark is already way out as it is in the open sea, trying, far from the safety of any shore, to cope with some huge and frightening waves. I do not need to go any further at the moment. I leave you, gentle reader, with Emil Nolde’s depiction of a person, in their finitude, in the midst of, in the thick of a situation they must grapple with.

Emil Nolde, The Sea I

Lumber Room:

Compatibility/Incompatibility:

What follows is a series of points that I will be trying to shoehorn into this essay as I revise it now that I have hammered it into at least an initial shape.

[[[Let me say that a situation such as the shell #1 situation is epistemically compatible with another situation — say, my comprehensive actual situation — if it is epistemically possible for it and that situation to combine so as to comprise a larger situation. The situation whose defining description forms the key description of the shell #1 possible world is a possible part of my comprehensive actual situation. It is therefore compatible with that situation, and that situation is compatible with it. ]]]

[[[Conversely, every situation that maps to a key description of a spawned-from-the unknown possible world that is not epistemically accessible for me is epistemically incompatible with my comprehensive actual situation. Above, I gave an example of a spawned-from-the unknown possible world in which there is always the possibility of a rogue peanut in one of Elizarraraz’ shell games, taking its cure from the behavior of electrons as described by my undergraduate chemistry TA, ending up on the nose of the Mona Lisa. Given our knowledge that peanuts (nor any other objects on the post-quantum level) do not behave this way in the actual world, we know something that rules out the identity of this possible world with the actual world. The rogue peanut world is not epistemically accessible for me from my location in the actual world, which means that the rogue peanut situation is not compatible with my comprehensive actual situation. To rule out is to exclude; to exclude is to render incompatible. Conversely, to fail to rule out is to fail to exclude; to fail to exclude is to render compatible.]]]

[End with drive towards inconsistent situations?]

. [[[This knowledge may or may not be knowledge that I can access immediately, or even knowledge that I know I have. ]]]

[[[[[[[That the peanut be under shell #1, for example, fits in with, does not conflict with, is not ruled out by the knowledge I have about the actual world. I make this claim rather confidently — in fact, I am willing to bet my paint brushes on its truth. Nonetheless, unless I can be said to both to know and to have at my fingertips everything I know, perhaps I cannot be absolutely certain that in the body of knowledge I possess, there is an item of information that would rule out the the peanut’s being under shell #1 within the currently unknown-to-me part of the actual world. I might, while sleepwalking, for example, have one-twentienth consciously seen Elizarraraz filling shell #1 with cement, rendering the presence of the peanut there physically impossible. (In no possible world nomically accessible from the actual world can a shell filled with cement hide a peanut. I assume.) ]]]]]

[[[[[This visual information might be stored in my brain, ready to pop out at any time, or perhaps accessible only through deep hypnosis, but at any rate information unknowingly possessed by me. In that case, I would possess information that would rule out the situation’s being part of the actual world. This is so even if at the same time I also have the opposite belief. I can be in two cognitive states at the same time whose contents directly contradict one another. This point will become important later when I consider inconsistent situations. ]]]]]]

[[[[[Nonetheless, I rather doubt that anyone would want to gainsay my ‘I know nothing that would ….’ claim should I make it. And certainly there is a fact of the matter regarding whether this claim is true — whether there is nothing in my body of knowledge that would rule out the presence of the peanut under shell #1 in the actual world. ]]]]]]

I[[[The descriptions “the shell is empty” and “the shell hides the peanut” clearly preclude one another; they are metaphysically incompatible. ]]]]] Likewise, I might discover later that what I took to be the hollow of the shell was in fact filled with concrete, rendering its hiding the peanut physically impossible. The descriptions “the shell is filled with concrete” and “the shell hides the peanut” clearly preclude one another; they are physically incompatible.

But until I know things like this, the possible situation in which the peanut lies under shell #1 could be — in some sense of “could be” — a part of the actual world. The ‘could be’ is epistemic, stemming from the epistemic concept of relative ignorance, or lack of knowledge. So far, I do not know anything that would rule out the situation’s being part of the actual world, so this being a part of is still a possibility. Nothing that “automatically precludes from the get-go its being a part of the actual world and therefore something that could eventually be discovered to form part of my comprehensive actual situation.]]]]]

[Logically/metaphysically accessible possible worlds and nomically accessible possible worlds do not need to refer to an agent S. Possible worlds that are epistemically accessible for S do need to refer to an agent S. These are possible worlds that smuggle in the concept of a center. They invite the notion of a situation.]

Two situations are compatible within a possible world at time t if and only if they can (epistemic “can”) hold at the same time within that possible world. Let me produce some examples. [Non-normal situations can be incompatible with themselves. Satisfied descriptions. ]

[[[If my cat Tiger is sitting on a mat (where I have deposited him to keep him off my keyboard) at the same time that the doorbell rings, the situation ‘Tiger is sitting on the mat in my apartment’ is clearly compatible with ‘the doorbell is ringing in my apartment’. That these two situations hold at the same time t in the actual world is proof positive that they are compatible in the actual world at t. Now I know nothing that would rule out the identity with the actual world of the possible world in which this situation in my apartment holds. Which is good, because the actual world is identical with this possible world. The fact that the two situations do hold at the same time in this one possible world, namely, the actual world, shows that they can hold at the same time in this world; and this possibility is (at least) an epistemic possibility. ]]]]

[[[[[[[[[[[[[[[[[[[[[[[[[[Identity a sufficient condition for compatibility for normal situations. Two descriptions — stable. Not flashing this way then the opposite. Not like “This sentence is false”.Bring up the over/under business much much earlier.]]]]]]]]]]]]]]]]]]]]]]]]]]

Now let me circumscribe the rogue peanut world to just one situation s1 within that world, namely, the shell game the Elizarraraz has set up in the Pilsen neighborhood of Chicago, that somber city, within an easy walking distance of Western Avenue.

To rule out is to exclude; to exclude is to render incompatible. submit, then, the following. Our knowledge (at least I hope that is what that is) that rogue peanuts do not exist in the actual world rules out s1‘s being a situation in the actual world. Therefore, s1 excludes my comprehensive actual situation, s0. s1 and s0 are incompatible situations; and s1 is incompatible as well with any situation within s0. To rule out is to exclude; to exclude is to render incompatible. Therefore, no situation drawn from a spawned-from-the-unknown possible world is compatible with my comprehensive actual situation or with any of its sub-situations.

If it were so ruled out. I submit that, conversely, every situation drawn from a possible world that is If it were so ruled out. epistemically accessible for me from my location in the actual world is compatible with my comprehensive actual situation s0 and with every sub-situation of s0. For every such situation is possibly — in the epistemic sense of ‘possible’ noted above (think: ‘the peanut is possibly under shell #1) — a part of the actual world. The description mapping to every such situation fails to get ruled out by my knowledge (if it were so ruled out, it obviously would not be part of a possible world epistemically accessible for me from my location in the actual world). Failing to get ruled out is failing to get excluded is failing to be incompatible. Failing to be incompatible is to be compatible.

[[[[[An example of failing to believe that an item of knowledge is part of my body of knowledge.]]]]]]] Likewise, I may falsely believe that a situation is compatible with my comprehensive actual situation when it fact it is not. Suppose, for example, that I really have taken the eight graduate courses in quantum mechanics (with a grade no lower than a B+ in any of them and I got that B+ in just one of the courses) came in just one course. Suppose, further, that I acquire the knowledge that peanuts cannot, while obeying the laws of nature, behave like electrons in the way described by my undergraduate chemistry TA. But all my friends are still New Age crystal devotees who think that peanuts can behave like electrons and display the same effects as they. In the midst of a party in which I imbibe too much in their company and watch too many You Tube videos with them about quantum physics and stare at too many crystals, the wages of tribal identity set in for a moment and I come to believe during the party that peanuts, which only the moment before had been contently abiding under one of Elizarraraz’ shells, can suddenly find themselves the next moment on the nose of the Mona Lisa. The morning after, I come to my senses, no longer under the intoxicating tribal influence of my peers, and no longer believe this. But during the party I held a belief that conflicted with my knowledge. Beliefs can conflict with other believes and with knowledge.

Even during the party, however, my belief did not determine my comprehensive actual situation. My knowledge, which although not occurrent at the moment, was nonetheless not wiped away by the party, continued to define my comprehensive actual situation. The rogue peanut situation continued to be incompatible with, ruled out by, my comprehensive actual situation.

Satisfaction of a description is important also in analyzing compatibility/incompatibility. The impossible cube is not satisfied by any object in the actual world. Since situations are descriptions (descriptions which are (were/will be) satisfied by the actual world when they are actual situations and not satisfied by the possible world when they are merely possible situations), two situations are compatible | incompatible in a possible world if their defining descriptions can be | cannot be satisfied in that world.

[Why use epistemic could and not, say nomic could? Because we are talking in finite situations. So at least theoretically two situations could be epistemically compatible but nomically incompatible. I submit, however, that we should stick to the epistemic notion of compatibility in analyzing human language and human coping with the world. That my neighbors’ walls could be cornflower blue is quite live and real for me. And, as I will show in a moment, one can use that ‘could’ to provide the truth conditions for “not” in the sentence “The walls of my apartment are not fuchsia” that can be comprehended by a finite human being. The corresponding nomic ‘could’ cannot be used that way. ]

[Finite situations appropriate for human language. This is a concept of compatibility that is in harmony with the notion of situations, which emphasizes their local and fragmentary character. My situation is a bunch of so far as I knows. My situation does not comprise the entire actual world because I am not omniscient. ]

[Henceforth, unless otherwise noted, I will be using “compatible” to mean “epistemically compatible”.]

Cannot be satisfied at the same time. My apartment walls cannot be portobello mushroom and fuchsia at the same time. The two descriptions are not compatible. They cannot be fulfilled by any situation in the actual world at the same time. The portobello mushroom situation and the fuchsia situation cannot obtain in the same possible world.

Identity in satisfied situations and simultaneity, then, are two sufficient conditions for compatibility. But there is a third sufficient condition that I want to consider, namely ignorance, my not knowing everything. Nomic and initial conditions example.

There is nothing so far in what I know that would render the description ruled out by what I know.

Truth:

[[[Situations whose boundaries are determined by the limits of one’s knowledge would divide the actual world into what is exposed to one — the finite situation itself — the dense part of the lump of cheese, the mesa surrounded by the fog — and everything that is hidden from one — the holes in the lump of swiss cheese; the fog surrounding the mesa.]]]

[[[Is the truth of the sentence a matter of change from the perspective of one’s own situation? If yes, then one’s own situation is not making the sentence true. Truth is never a gamble]]]

[[[There is no doubt that there are three shells before my eyes. This is so even if ‘there are three shells before my eyes’ is defeasible. If 1 through 4 have credences of less than 1, every exposed state of affairs within my comprehensive actual situation has a credence of 1. There is no doubt that there are three shells before my eyes. This is so even if defeasible. A credence is a number that is assigned; and I shall assign a credence of 1 to all those states of affairs in my comprehensive actual situation for which any doubt seems merely theoretical, not to be taken seriously in the course of one’s affairs. David Hume, for example would or at least should, assign a credence of 1 to the billiard table and the balls when he gets up from his skeptical studies to play a game of billiards. Certainly he would know nothing that would rule out the identity with the actual world the possible world in which the pool table actually does exist in space/time. But to discuss this further would take me too far afield.]]]

[[[Now if there is anything that could serve as a conduit of information between the hidden situation and my comprehensive actual situation such that states of affairs in the former could become exposed to me in my position in the latter, the probability-as-credence of this state affairs would increase to 1. If my neighbor is completely reliable, for example, the color of his walls would become exposed to me were he to tell me they are wine red. The probability/credence that they are wine red would increase from 1 divided by the number of paint colors to 1. That the walls are this color then becomes part of my comprehensive actual situation.]]]

[[[For a sentence to “reach out” so to speak to a hidden situation and to be ‘made true’ is for the probability/credence to increase to 1 from a lesser number. For a sentence that is about a state of affairs within a finite situation to be made true, it needs to have already been exposed and the garden-variety credence given to it to be 1 already. For a situation to make a sentence true is for the sentence to correspond to an exposed state of affairs.]]]

Within my comprehensive actual situation, the resources are lacking to make 1 through 4 true. As I will show when I get to the truth condition for negation, the resources are also lacking within that situation to make the negations of 1 through 4 true. Let A be any of the sentences 1 through 4. A is not true. If we adhere to a 2-valued logic, this means that A is false within the situation. But, as I will show, the situation also fails to make ~A true. So ~A is also false within the situation. A v ~A would be false because both A and ~A would be false. Bivalence would fail for my comprehensive actual situation.

And once it is turned over, it will be the case, I am rather inclined to think, that nothing in my body of knowledge rules out the identity with the actual world of the possible world in which the peanut always was (from the time Elizarraraz placed it under one of the three shells) present | not present under shell #1 the whole time. But there is something in my body of knowledge that rules out the identity with the actual world of the possible world in which the peanut was present | not present under the shell the entire time — namely, that peanuts do not behave like electrons. Or at least I hope that I know this. I might add parenthetically, by the way, that whether this really is an item in my body of knowledge is independent of whether I believe it to be.

[[[Need to discussion situation types vs. individual situations]]]

So while nothing in my comprehensive actual situation makes it true that either A (“the peanut is under shell #1”) or makes it true that ~A (“it is not the case that the peanut is under shell #1”), one is likely to be proceeding on the strong assumption that this is so. But if we confine ourselves to just the situation, the situation does not have the resources to make either A or ~A true.

[[[Within the worldly situation of such a being, every sentence would either be made true within the situation or fail to be made true. The probability of 1 through 4 each would be 1.]]]

[[[The epistemic version of truth, i.e., the correspondence to something actual, would then be the correspondence to something known to be actual.]]]

[[[So we have local truth on the one hand and global truth on the other. Local truth is not relative truth.]]]

Bivalence

[[Exposure makes the epistemically accessible situation a part of s0. I asserted above that a situation such as the shell #1 situation is epistemically compatible with another situation — say, my comprehensive actual situation — if it is epistemically possible for it and that situation to combine so as to comprise a larger situation. It could be (epistemic could) the case that the peanut is under shell #1, in which case the presence of the peanut there would become, upon exposure (say by turning over the shell or through a sonar device that is designed to detect the presence of peanuts under shells) a part of s0. Or it could be (again, epistemic could) the case that the peanut is not under shell #1, in which base the absence of the peanut there would be what becomes part of my comprehensive actual situation. ]]

[[That the walls of my apartment are portobello mushroom has already gotten exposed in the situation comprising my apartment in particular and in my comprehensive actual situation in general. Even if somehow I haven’t really noticed the color of my apartment walls (say, when I entered the apartment for the very first time), nothing blocks me from focusing my attention on it for a moment and saying “Aha, portobello mushroom”. The color of my apartment walls lies exposed in my situation. ]]

[[[Situations drawn from possible worlds epistemically accessible to S from their position in the actual world are the graveyard for the truth of A v ~A.]]] [[[Important that on my account the compatibility relation could hold between situations in different possible worlds, as long as the situations could be part of the actual world. I don’t know what trouble this will pose for me. Important to discuss the Tiger from a different planet possible world.]]]

[[[But every other sentient being is situated, that is to say, is plunged into a concrete situation that has them as its center and from whom much is hidden, and to whom some is exposed.]]]


Contingent Implication Requires SOME Sort Of Necessity

Some thoughts upon waking up this morning (warning: serious confusions and grossly embarrassing missteps likely to follow): Ed Mares distinguishes between entailment, which is necessary, and implication, which is contingent. Necessity and contingency usually gets analyzed in terms of possible worlds: a proposition is necessarily true if it holds in all possible worlds; it is contingently true if it holds in just some possible worlds.


One problem I am wrestling with, however, is that intuitively, SOMETHING has to be necessary about contingent implication. In contingent implications such as “If the doorbell is ringing, someone (maybe Channing Tatum?) or something (a twig blown by Hurricane Harvey?) is pressing the button outside”, it seems natural to insert a “must” — “If the doorbell is ringing, someone or something must be pressing the button outside”. But if the concept ‘necessary’ applies to contingent implications, the necessity in question would surely have to be weaker than logical/metaphysical necessity. The screed that follows attempts to delineate a weaker concept of necessity that applies to contingent implications.


Let me try to begin sorting this out by discussing two propositions, which I will label A) and B) Suppose that my doorbell apparatus is in perfect working condition (situation s). The proposition A) is as follows:

A) If someone or something is pressing or has depressed (the button could have gotten stuck) the button outside (situation t), then a doorbell sound is occurring inside (situation u).

This contingent implication holds as long as situation s holds (the apparatus is in perfect condition). The implication is contingent, of course, because the doorbell apparatus is not guaranteed to be always in perfect condition. If some wiring comes loose for example (compare with Mares’ flashlight example) so that pressing the button outside does not reliably result in the sound getting generated inside (say, the sound gets generated just 99% of the time), the implication is no longer true. It was true only for a while, while situation s lasted. But during that time, the relation between pressing the button and the generation of the sound was completely reliable because it was nomically necessary — in all possible worlds accessible from the actual world by way of obeying the laws of physics in the actual world, there is no way that the sound can fail to be generated as long as the doorbell apparatus is in perfect condition. — We think (see below).

Now consider a trickier case: B):

B) If the doorbell sound is occurring (situation t), then someone or something is depressing (or has depressed) the button outside (situation u)

Two possible conditions of the doorbell apparatus (situation s) are relevant here.

First possible condition: the doorbell apparatus is in perfect working order. For example, the insulation is not failing in such a way as to allow the sound to be produced without the depression of the button. (Although I am no expert in doorbells, I take it on good authority that a failure in the insulation could do this.)

But now that I mentioned insulation, I want to bring up an important point. Insulation protects the doorbell apparatus from outside physical interference. It prevents (so I imagine — and I hope my imagination is not too far off the mark) whatever electrostatic charges might be forming around the apparatus that from time to time, had the insulation not been there, may send a pulse of charge through the wire that sets off the production of the doorbell sound even without the button outside getting pressed. Or it prevents a current set off by pressing the button from getting diverted from time to time into its surroundings (as conditions vary) and failing to bear fruit in the form of the doorbell sound. The insulation, that is, makes it more likely that the button outside is getting pushed whenever the doorbell sound is produced; and conversely, more likely that the sound is getting produced inside whenever the button outside is getting produced.

Soon, I will be talking, not about physical insulation to protect against outside interference, but about conceptual insulation. So hold this thought for moment.

Second possible condition of the doorbell apparatus: there is a defect in the doorbell apparatus like the one noted above such that the ringing sound gets generated only 99% of the time when the button outside gets pushed or has been pushed. Nonetheless, there is nothing in this defective condition of the apparatus that would account for the generation of the sound getting accomplished independently of the button. Suppose, for example, that anti-static goop is applied to the insulation so as to suppress any electrical energy from coming from the outside. Current inside the wiring, however, is still vulnerable to getting deflected outside. I will assume such a condition of the apparatus is possible, though maybe someone much more knowledgeable about doorbells than I am is about to comment or email me to the effect that this condition is in fact not possible. 

I bring up this second possible condition of the doorbell apparatus in order to account for the fallacious nature of affirming the consequent. That is to say, from the proposition ‘If the doorbell is ringing, someone or something is depressing or has depressed the button outside’, this proposition does not follow: ‘If someone or something is depressing or has depressed the button outside, then the doorbell is ringing inside’. The first proposition can be true in situations in which the second is not.

When either the first or the second condition holds, then 100% of the time, when the doorbell is ringing, the button outside is getting depressed. 100% of the time, that is, SO FAR AS I KNOW. But this ‘so far as I know’ allows for, I claim, at least a weak form of necessity based on the concept of possible “normal” worlds that are epistemically accessible from the actual world for a knower S. Let me explain what a “normal” possible world is first, then turn to epistemically-accessible-to-S possible worlds.

When, given a certain situation, something happens 100% of the time — so far and so far as I know — anything that might cause it not to occur is clearly going to count as a freak — even an unheimlich — occurrence for the people who are accustomed to this regularity. For example, given the perfect condition of the doorbell apparatus in my apartment, 100% of the time when the doorbell rings, someone or something outside is depressing the button outside — so far and so far as I know. Given situation s — the perfect condition of the apparatus — and given the ‘100% of the time so far and so far as we know’ clause, anything — say, a poltergeist — that would cause the ringing sound without the depression of the button would be a freak occurrence relative to s. Any possible world in which nothing freakish like this happens is a normal possible world relative to s.

So far as I know. If some scientist studying doorbells established in a completely adequate way that in fact poltergeists do exist, and do sometimes reside in doorbell apparati; and that even when s holds the doorbell sound gets produced inside by a resident poltergeist one time in a million in the absence of the button outside getting pushed, then for that scientist the doorbell sound’s getting generated in the absence of the button’s getting pushed would no longer be a freak event. Possible worlds in which such events take place would be, for them, normal possible worlds even though, for me and doubtlessly for most people, they would remain non-normal possible worlds until we learned of and accepted the scientist’s work.

A possible world is epistemically accessible from the actual world for a knower S when S knows nothing that would rule out the identity of that world with the actual world in which they exist. For example, not knowing the color of the walls of my neighbor in the apartment adjacent to mine, I know nothing which would rule out the identity with the actual world of the possible world in which that color is Venetian red. That possible world is epistemically accessible for me from the actual world in which I reside.

Normal worlds form a subset of possible worlds that are epistemically accessible for me from the actual world. I do not know anything that would absolutely rule out the identity with the actual world of the possible world in which Bigfoot roams the forests of Western Washington State. Nor do I know anything that would rule out the identity with the actual world of the possible world in which Bigfoot does not roam the forests of Western Washington State. [Editor’s note: is the word ‘absolutely’ going to cause problems for you?] Both possible worlds are epistemically accessible for me from the actual world. But given the fact that (so far as I know) no effort to find a Bigfoot roaming the forests of Western Washington State has yet succeeded, the former possible world is a non-normal possible world, and the latter is a normal possible world.

Possible worlds that are both normal relative to me and epistemically accessible for me from the actual world form a subset of possible worlds that are normal relative to me and a subset of possible worlds that are epistemically accessible for me. The world in which s holds but the walls of my apartment are fuchsia instead of their actual portobello mushroom color is a normal possible world relative to my doorbell provided nothing in it is capable of generating a freak event vis a vis my doorbell (for example, there are no poltergeists residing in my doorbell apparatus). But this world is clearly not epistemically accessible for me, since I know something that rules out the identify of this possible world with the actual world: namely, that my walls are portobello mushroom, not fuchsia. And, as we have seen, the possible world in which Bigfoot roams the forests of Western Washington state is epistemically accessible to me, but is not a normal possible world. What I am concerned with here are possible worlds that form the intersection of normal possible worlds and possible worlds epistemically accessible to me.

I know nothing that would rule out the identity with the actual world of the possible world in which poltergeists do not exist that like to cause doorbells to ring even when the button is not getting pushed. The possible world in which such poltergeists don’t exist is epistemically accessible for me from the actual world in which I exist. Likewise, I think it is fairly safe to say that the possible world in which no poltergeists are resident in my doorbell is a normal world. This world is both normal and epistemically accessible for me.

Likewise, I know nothing that would rule out the identity with the actual world of a possible world in which no one has contrived some device using radio waves that somehow activates, without the button ever getting pushed, something in the doorbell apparatus that generates the sound. Currently (but maybe someone is about to email me alerting me to the invention of just such a device as a Junior High Science project) this possible world is also epistemically accessible to me from the actual world in which I exist.

So if I am feeling especially brave — or foolhardy — I might venture the claim that in all normal possible worlds epistemically accessible to me now, the button outside is getting pushed (or has been pushed) when the doorbell is ringing. Given what has become normal for us, any possible world in which freak events relative to the doorbell do not occur would automatically be one that would be both a normal world and epistemically accessible for me from the actual world.

This gives us a form of ‘in all (with restrictions) possible worlds’ type of necessity. This rather weak necessity undergirds the truth of B). The intuition I am starting from, remember, is that even contingent implication requires SOME sort of necessity.

Although A) may at first seem like it is undergirded by a stronger form of necessity — necessity of the ‘in all nomically accessible possible worlds’ persuasion — I think that its necessity must also in the last analysis be analyzed in terms of possible worlds epistemically accessible to a knower S. Consider the following scenario: I press the button outside. Space aliens hovering above my apartment zap my doorbell apparatus, so stopping the normal causal chain. All of this happens in ways completely unknown to us (certainly unknown to me — and I can’t even vouch for the assertion that our current knowledge of the laws of physics would not allow for such a freak occurrence!) but in accordance with the laws of physics of this actual world. The doorbell sound never gets generated. All of this is, of course, extremely implausible. Completely ridiculous. Utterly absurd. Did I mention that this scenario is implausible, ridiculous, and absurd? Yet I also certainly cannot say that it is impossible. At the very least, I should think, it is logically possible.

Nonetheless, for each possible world in which this scenario or anything producing the same result never happens — in short, every normal possible world — it is surely the case that I know nothing that would rule out the hypothesis that that possible world is identical with the actual world. For example, the possible world in which that butterfly fluttering about at GPS location xyz has chartreuse wings but space aliens never visit the earth; the possible world in which that butterfly has violet wings but space aliens never visit the earth; the possible world in which that butterfly has black wings but space aliens never visit the earth…in each case, I know nothing (being ignorant of what is happening at GPS location xyz) that would rule out the hypothesis that that possible world is identical with the actual world. So at least for me, in no normal possible world epistemically accessible for me do space aliens or anything else ever interrupt the causal chain in situation s (the doorbell apparatus is in perfect condition) so as to interrupt the causal flow from pushing the button to the generation of the doorbell sound. I will wager that for no other person living on earth does there exist a normal possible world epistemically accessible for him in which this causal flow can be interrupted in a way similar to the one just described.

So at the very least A) is possesses ‘true in all normal possible worlds epistemically accessible to me from the actual world’ form of necessity. But I do not think that we can know that it possesses nomic necessity, since it is doubtful that we know all physical laws. It might possess nomic necessity — but at present do not know this (and probably never will). But I do think we can safely claim normal epistemic necessity (for S) for A) So the only kind of necessity that we can safely attribute to A) is the necessity that dwells in the intersection of all normal possible worlds and all possible worlds epistemically accessible to me from the actual world.

To sum up: A) and B) are under-girded by perfect reliability — so far as we know and at least by normal epistemic necessity, a weak form of possible-worlds necessity. But both are defeasible. A scientist intensively studying (the very first time anyone has done this, I suspect) both doorbells and poltergeists might publish in NATURE his groundbreaking and impeccable discovery that a poltergeist resides in my doorbell apparatus and that, even though s holds, one time out of a million the doorbell sound gets generated in the absence of the button’s getting pushed through the workings of the poltergeist. B) would be rendered false by this discovery. Likewise, a scientist might always discover that earth does get visited by aliens interested in doorbells who, by way of previously unknown (I assume) physical laws are able to interrupt (even though s holds) the normal causal chain flowing from pushing the button to the generation of the doorbell sound. A) would be rendered false by this discovery.

In contrast to contingent implication, entailment relies on propositions that are true in all possible worlds that are logically/metaphysically accessible from this actual world. These propositions are always true for all time. But the contingent implications A) and B) by contrast, even if they were both nomically necessary, would not true for all time. The wiring in the doorbell apparatus might come loose, rendering A) false. The insulation in the wiring might start breaking up, rendering B) false. Nonetheless, in spite of their being contingent in this way, A) and B) both have a weak sort of necessity. It is just that this necessity is much weaker than logical/metaphysical necessity. Here “contigent” means something like “weakly necessary”.

But in addition to this difference from entailment, A) and B) are both defeasible. Entailment is not defeasible. Mares, however, thinks that contingent implication must be indefeasible; if it is not, it is at best a natural language conditional. Is there any way to make A) and B) indefeasible so that they can count as real, live contingent implicaitons instead of mere natural language conditionals?

We could make A) and B) indefeasible, I think, by a kind of idealization. One can abstract from all these noisome uncertainties regarding poltergeists and space aliens and people who have invented a way to use radio waves to bypass the button and so on. We can simply ignore all freakish and unheimlich possibilities just as the Euclidean geometer, in defining a point as something with no size, ignores away the fact that every real-life point they encounter has size. We ignore away the (surely remote) possibility that poltergeists might exist or that space aliens might be interested in doorbells or the (maybe not as remote) possibility someone might have invented a device to bypass buttons or that anyone might be interested in using such a device on my doorbell. Surely there is not that much risk in this idealization — at least in the case of poltergeists and space aliens. [With this idealization we get perfectly reliable from perfectly reliable so far and so far as we know]

Now s is an informational link between the outside of the apartment and the inside. Let me compare the results obtained so far with what Mares says here:

To be an informational link a relation needs to be perfectly reliable. As Barwise and Seligman argue, causal relations are often not reliable enough to be considered informational links. They use the example of a flashlight with an unreliable connection between the button and the light ((Barwise and Seligman 1997), p. 17). Sometimes pushing the button turns on the light, but sometimes it does not when other factors come into play, such as a wire’s coming loose. The problem is that unreliable connections do not warrant deductive inference. At best, they can be used to justify defeasible inference.

A defeasible inference is one that may not hold if extra information comes to light. Implication, in the sense that we mean it here, is a non-defeasible relation between propositions.

It may be, however, that many of our inferences about other situations are in fact defeasible. In this case, we may take implication to be an idealization. As we shall see in chapter 7 below, we present a view of natural language conditionals in which conditionals are interpreted to license defeasible inferences about situations and the connections between them.

Mares, pp. 44-45

Since extra information can always come to light, no matter how implausible this “can” may be (certainly in the case of poltergeists and space aliens), it seems to me that the only contingent implications (which must be indefeasible) can be true only as idealizations. As indefeasible idealizations, A) and B) can warrant deductive inferences. My next task will be to see why it is important for relevance that they do so. Why contigent implication needs to mirror deductive inference.

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Reworking this.

The best way to show that something is (nomically) possible is to show that it is actual. I know that any given mass is also a wave. The identity of any given mass with a wave is something actual. It is a feature of the actual world. Therefore, this identity is possible.

Any given possible world in which any given mass is not identical with a wave is therefore not nomically accessible from the actual world, since the natural laws that hold in the actual world do not hold in this possible world. Also, any such world would fail to be epistemically accessible for me (and for anyone who knows that masses are also waves) from my location in the actual world, since there is an item in my body of knowledge that rules out the identity with the actual world of this possible world. This item is, of course, my knowledge that in the actual world any given mass is also a wave.

So every possible world that is epistemically accessible for me from my location in the actual world is a world in which every mass is also a wave. It is therefore epistemically necessary for me that a mass be identical with a wave. It is epistemically impossible for me for a mass not to be identical with a wave.

Now let me turn to Dretske’s boiler example. Suppose that the monitoring apparatus is in perfect physical condition at the moment. Suppose also that, as long as it is in perfect condition, and as long as there are no interfering factors which would make the pressure a mere contributing factor [Galileo dropping a feather and a cannonball from the Leaning Tower of Pisa; air friction is a contribuint factor in the former case], it could only fail to generate the correct reading if some physical law of the actual world were violated — say, some particular mass in the apparatus suddenly ceased to be a wave. Only if some physical law were violated or something interfered — say space aliens hovering nearby and zapping the apparatus from their space ship — could the dial point to 7 and the pressure in the boiler not be 7 whatever units, and vice versa. It is therefore nomically necessary that — as long as the monitoring apparatus is in perfect condition — the pressure be 7 units when the dial points to 7, and that the dial point to 7 when the pressure is 7 units. All other nomic possibilities are ruled out. That is so say, given the the physical condition of the monitoring apparatus is perfect, no nomically accessible possible worlds in which the pressure can be other than 7 units and the dial point to a number other than 7, or vice versa.

I know something that rules out the identity with the actual world of any possible world in which a mass is not also a wave. Namely, I know that a mass is also a wave. So in one fell swoop, I can refer to all such possible worlds. It is epistemically impossible for it to be nomically possible for a mass not to be a wave. Likewise, it is epistemically impossible for it to be nomically possible for the dial to point at 7 and the pressure in the boiler not to be 7 whatever units, given that the physical condition of the monitoring apparatus is perfect and that there is no outside interference (no alien spaceship hovering nearby sending down a beam to disrupt the normal causal flow from water pressure to position of the dial). I know that no possible world in which, given these conditions, one 7 happens but the other does not can be identical with the actual world. There is the causal flow just as water flows downhill. In all epistemically accessible possible worlds, worlds that could be identical with the actual world (I know nothing that would rule out the identity), the one 7 does not happen without the other given the aforementioned conditions. It is epistemically necessary this (the one 7 with the other 7) be nomically necessary. A law-governed causal link such that the one 7 cannot fail to happen (given the aforementioned conditions) provided the other 7 happens. All other possible worlds are ruled out. That is to say, all other possibilities are ruled out. This is the “surely there must be some kind of necessity” I was looking for.

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