Tag Archives: Learning By Writing

We Are Surfaces

The following passage from Gaston Bachelard’s THE POETICS OF SPACE is extremely suggestive:

The phenomenology of the poetic imagination allows us to explore the being of man considered as the being of a surface, of the surface that separates the region of the same from the region of the other.  It should not be forgotten that in this zone of sensitized surface, before being, one must speak, if not to others, at least to oneself.  And advance always.

Gaston Bachelard, THE POETICS OF SPACE  (Beacon Press, Boston), p. 222

I do not pretend to have a very precise grasp of (certainly not a ‘maximal grip on) what Bachelard meant by the above paragraph, nor of what the best interpretation of that paragraph might be (regardless of what his author’s intention was).  In particular, I do not have much command over his phrase ‘the phenomenology of the poetic imagination’.

I am, however, reasonably confident that I do know what I want to do with many of the same words, namely, these:

Let’s explore the being of man considered as the being of a sensitized surface, of the surface that separates the region of the same from the region of the other.

There is more that I want to draw from Bachelard’s paragraph, but this is what I think (delusionally or not) I currently have the best grasp on.  In the not too distant future — the exigencies of my paid work permitting — I will be articulating what I intend to say with these words (whether or not my intention was also Bachelard’s).

To foreshadow what I want to say:  each one of us is a surface, not an interior space inside a physical cranium or inside the non-physical boundaries of a non-physical mind.  The mind bears a close analogy to the skin.  And once we see this, at least a few philosophical conundrums will come to seem at least a little bit less puzzling.  Maybe.

In articulating this insight (or is it a delusion?), I will be drawing on Berkeley, Leibniz, and Merleau-Ponty.  Will I come up with anything coherent?  We will see!


Today’s homage to Plato’s SYMPOSIUM is Channing Tatum posing as a grease monkey.

Channing Tatum As Grease Monkey

Channing Tatum


Although the denotational power of words certainly fail me, I am able at least to fall back onto the expressive power of a rapturous sigh.












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 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:

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 for Berkeley (I will venture now…though I may end up chipping away at this claim) is always a two-place relation between a Mind that perceives something and the thing that is perceived.  In the case of vision, this relation is for Berkeley a two-place relation between the Mind and an entity 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…object existing in external space (or at least this is what Berkeley cares to state explicitly in black and white in his NEW THEORY OF VISION.)

In the case of vision, I perceive extra-mental object existing in external space only indirectly, or mediately, in a three-place relation between 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 (at least in what he sets down in black and white on the page) 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 how he conceptualizes the (ostensibly just mental) objects of vision.

As I have discussed in a previous post, The Truth Of Bishop Berkeley (Part 0),  Berkeley treats the visible object has properties.  The Visibile Moon, for example, is round, flat, luminous, and of a certain pale cheese-like yellow. If we think of the objects of touch as having analogous properties, those properties would be rough, smooth, hard, soft, and so on.  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 as having properties puts Berkeley straightway on the road to regarding physical objects existing in extra-mental space as the objects of touch.

Touch lends itself to a direct realist interpretation in a way that vision does not.  The seen object at least seems to be at a distance from the sensing surface of the see-er.  How can the visual experience include anything at a distance from this sensing surface?  It would seem prima facie that anything away from that surface would have to be outside the experience. The visual experience would therefore be confronted with the impossible-to-fulfill need to “reach out” to the seen object.  This, at least, is how I try to articulate the intuition that vision poses a problem for a direct realist interpretation of the seen object.

By contrast, 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, engaging my physical hand, has already done the reaching out.  Touch is the direct realist sense par excellence.

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.




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.


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






















The Truth Of Bishop Berkeley (Part 1) — With Green Bungee Cords Again

In a previous post on Bishop Berkeley’s claim that depth cannot be seen, The Truth Of Bishop Berkeley (Part 0), I argued that this claim does follow from Berkeley’s theory of Ideas, at least as I construed that theory in that post.  Here, I want to argue for something like Berkeley’s claim without appealing to any version of his problematic theory of Ideas.  The motivation for doing so is to capture within a Merleau-Pontyian framework what I think is the germ of truth in Berkeley’s claims regarding depth.  This germ is the claim that, at least in the case of the planes seen or imaginatively pictured end-wise to one’s gaze, there is no straightforward (so to speak) visual presentation of depth.

There is, however, a projection of depth that forms the visual field itself.  I will be much occupied with this projection in future posts.

In the process of uncovering the germ of truth in Berkeley’s claims regarding the invisibility of depth, I hope to deal a serious blow to Berkeley’s Theory of Ideas, and advance one step (my first step) in my project, my essay, my attempt to see whether one can transform George Berkeley, bit by bit, into Maurice Merleau-Ponty.

Let me advance the following thought experiment.  The aim of this experiment is to show that as an edge (for the sake of simplicity, let’s say it is the left edge) of an initially wholly-frontal plane moves away from you in depth, you see less and less of any given section of that plane, and, of course, of the plane as a whole.  That is to say, less and less of these get presented visually to you.  Starting from the initial situation in which you see all of the plane and each of its sections, you end up seeing none of these.  At first these get visually presented to you in their entirety; then nothing of them gets presented to you visually.

The Thought Experiment:  Suppose that an extremely, extremely, thin square of gold leaf foil is stretched out in front of you, parallel to your face and to the front of your body.  The thickness of this foil is 0.134 microns, or about 500 gold atoms.  Thinner than the wavelength of light, this is too thin to see.  So were the foil to be turned edge-wise to your eye, it would surely disappear.  Nothing of it would be presented to you visually.

With the mind’s eye, you divide the foil square into four equal sections from the top.  A darker rectangle runs down from, say, in the third section from the right and taking up about a quarter of that section.  (Don’t ask me how this section would be made darker.  This is a thought experiment; you can do what  you like with the gold leaf as long as what you do does not violate physical law too blatantly.  So just do it!  Make the section darker than the rest of the foil square.)

Now suppose that the foil square is steadily turning in such a way that its left edge is moving away from you.  At some point, the darker rectangle will, after first turning into a blur, eventually disappear.  For at some point you are seeing so little of the darker rectangle that your visual system can no longer obtain a clear view of it…and eventually cannot get any view of it at all.

To step out of the thought-experiment for the nonce and into a real experiment, you can try the following.  (Of course, I am sure the claims I made above are not controversial…still…it is always good to cover one’s bases as completely as they can.)  Take a bungee cord, like the polyester-green one shown below.  Taking a gel pen or some other suitable instrument, mark a line segment on it.  At first holding the cord parallel to the front of your body, steadily move the left edge away from you.  You will observe the dark line segment becoming, first, a blur, then disappearing altogether.



Back to the thought experiment.  The fact that you eventually saw so little of the darker section of the foil that it became a blur — and then saw nothing of it — strongly suggests that, as the foil was turning away from you, you were steadily seeing less and less of darker section.

Perceptual Constancy As A Fly In The Ointment (If I May Compare My Claims To Something Creamy and Oily, Such As An Ointment):   However, the phenomenon of perceptual constancy in general, and shape constancy in particular, prevents me from making this claim with absolute confidence.  For if this claim were true, the darker section would be steadily becoming thinner and thinner in the shape it looks to have.  But I have encountered theorists (I am looking at you, professor Suzanne Cunningham) who will deny this because they are prone to making extreme claims about shape constancy.  These theorists will deny that the darker rectangle is looking steadily thinner and thinner, just as they will deny that the two edges of U.S. 285, that absolutely straight road in New Mexico that goes on for mile after mile after mile after mile…these theorists will deny that the two edges of this road look to you to be converging at the horizon even while driving in the scene in New Mexico.  In the photograph, they will say, yes, the two edges converge.  When we project onto a 2-dimensional surface the very 3-dimensional Highway U.S. 285, then we get lines that actually converge.  But in the actual scene itself, one does not see (according to these theorists) lines that converge at the horizon.  Perceptual constancy ensures that we just see two lines in parallel:




So it is claimed.

The point of this rather extreme denialism is to block one argument for the sense datum theory.  (The edges of the physical road do not actually converge; nonetheless, lines are converging; a fortiori there are things that are converging; and these must be something mental, i.e., sense data.)  I do not want to dismiss this hard-line take on shape constancy outright, since I think that, in fact, there is a certain amount of truth to it, and I will be discussing shape constancy in particular and perceptual constancy in general in a later post.

Nonetheless, I will point out now that at some point you no longer see enough of the darker rectangle to see it in a non-blurry fashion, and very soon thereafter, as the foil square turns away from you, you see nothing of the darker rectangle at all.  Were the extreme version of perceptual constancy mentioned above correct, this change from clear and distinct to blurry then invisible would have to be sudden and abrupt, something that strikes me as highly implausible.  Nonetheless, gradual or sudden, the change does occur at some point.

Then, when the foil square is completely edge-wise to your eye, you no longer see it at all.  It has disappeared.  There is no longer a visual presentation to you of the square of extremely, extremely thin gold foil.

As long as the foil was at a sufficient slant to you, there was a visual presentation of it in depth.  There was a visual presentation of depth at a slant.  But when the slant became too extreme, that visual presentation became a mere blur; and when the foil came to be completely edgewise to your eye, that visual presentation to you ceased to exist altogether.

A plane can be seen in depth only when it exists in depth at a slant.  By ‘plane’ I mean a physical surface whose thickness is too small to count and therefore can be abstracted away.  There is no visual presentation of such a plane in depth when that plane is situated completely edgewise to the eye.  If there is a steady diminishment in how much of the plane gets presented to you visually as it turns away from you in depth, as I think there is, then we can say that the more the plane is situated in depth relative to you, the less visible it is.  (Again, fuller argument to come later.)  The more depth, the less visibility (i.e., less gets presented to you visually).  When the plane is completely frontal to you, 100% of it gets presented (subject, of course, to the limitations of your visual system).  When the plane is completely in depth relative to you, 0% of it gets presented to you visually.

When the plane is situated at varying degrees of slant relative to you, then, to corresponding degrees less of the plane gets presented to you visually.  Or so I claim.  We will see whether, in the end, I can get away with this claim.

With these arguments/claims in mind, let’s modify the second paragraph of Berkeley’s A NEW THEORY OF VISION to make him say something like:

II.  It ought to be agreed by all, that Distance [of an object in depth], of it self and immediately, cannot be seen except when this is Distance at a slant.  For Distance being a Plane sufficiently thin as not to have a visible edge, it becomes invisible once it is directed end-wise to the Eye.


I think something like this was the content of the Aha Erlebnis I experienced some decades ago when I encountered Berkeley’s NEW THEORY OF VISION in that cottony-red book in my parents’ library.

So far I have been discussing just visual presentation, which will always include at least an element of receptivity/passivity.  The square of gold foil causally impinges on your physical body, and without this impingement you would not be enjoying/suffering the concrete visual presentation of the foil.  When the foil is situated at a slant to you, you have an experience of depth that includes this passive component.

But the experience of depth also includes an active element, which I would like to briefly discuss now.  This active element is projection.  One can imaginatively project the depth of the plane.  You can, for example, — or at least I can — visually imagine a point that is situated about half-way across the foil that exists edgewise to the eye.  In doing so, you posit, that is to say, place the point at that location.  (Interesting word, that is, ‘place’ — suggestive of a kinaesthetic action.)  The point can be pictured as a spot, say,  with some color (white, black, wine red, sea-glass green, burnt sienna, and so on) with just barely enough size to be visualized.  Or perhaps there need not be any visual image at all.  I might imaginatively feel, probe with the imagination’s finger, so to speak, the distance to what I think is the half-way point of the foil square, with the attendant sense that here is a point that could become large enough to be visualized, a potentially ‘visible’ point.  In other words, there is an easy translation from imagined feeling to imagined seeing.

I will be having much more to say about this imaginative projection in future posts.  In particular, I will be asserting that this imaginative projection is based on a more fundamental motor intentionality ala Merleau-Ponty.

The blur:  I noted above that, in the case of the bungee cord, one will eventually see a blur instead of the mark made by the gel pen, and, in the case of the foil square, a blur instead of the darker rectangular section.  This fact already creates trouble for Berkeley’s concept of a Minimum Visibile, and it becomes completely devastating to that notion when one brings into the picture empirical work attempting to define a threshold at which one becomes aware of a sensation.  And if the concept of a Minimum Visibile goes, then Berkeley’s whole notion of purely mental items called ‘Ideas’ that form the building blocks of our perception goes as well.

If you ever have had the extent of your visual field tested, you will have faced the following conundrum:  you are supposed to say ‘now’ when, keeping your eyes focussed at the center of the tester’s screen, a dot appears at the periphery.  At first, you say ‘now’ when a blur appears in the periphery — it will never be a distinct point with clear boundaries after all.  But did you wait too long?  After all, if you are at all like me, you had the distinct feeling something was there a moment before you said ‘now’.  Doubtlessly if you attended more to what you see (an attention distinguishable of course from the act of focussing your eyes on the point), maybe you would have discerned the point visually rather than merely having the feeling it was there.  You say ‘now’ again.  But did you really see the point at that moment?  Maybe you jumped the gun a bit.  And if you got it right, maybe it was by chance.  So doubtlessly the mapping of points onto the screen that define the limits of your visual field will be a bit irregular.  To get a true picture of the extent of your visual field, perhaps those points need to be averaged out to form a smoother mapping of the boundary.

The psychologists Weintraub and Walker describe this conundrum very well:

When thresholds [such as how close a point has to be to the center of the tester’s screen before it appears to you] are measured, no discrete threshold appears.  There is always a range of stimulus values — from stimuli so weak that detection is no better than chance, through values detected with increasing probability, to values that are always detected.  A ‘threshold’ is an arbitrarily selected value of the stimulus, such as the intensity of stimulation that is detected exactly 50% of the time.  This arbitrary value for the threshold will differ from subject to subject.  It will differ with minor differences in the conditions under which the measurements are taken.  It will differ with even minor differences in the nature of the response that the subject is asked to make, and it will differ widely between two different responses such as ‘accurate verbal report’ and a ‘significant GSR’ [galvanic skin reflex].

Weintraub and Walker, quoted in M.C. Dillon, MERLEAU-PONTY’S ONTOLOGY  (Northwestern University Press, Evanston, IL), pp. 60-61. Dillon takes the quote from Weintraub and Walker, PERCEPTION, (Brooks/Cole Pub. Co., Belmont, CA, 1966), p. 77.


The gel-pen inked line on the bungee cord should never have become blurry in the first place, since as it became “thinner” it should have simply disappeared the moment its size became less than that of a Minimum Visibile.  A Minimum Visibile is a binary affair with sharp boundaries; it is either on or off, distinctly there or not.  For how could it constitute a unit composing perceptual wholes along with other Minimal Visibles?  If their boundaries were fuzzy, would two Minimum Visibiles gradually merge into one another rather than functioning as distinct units?  And even were one to allow the blur, it seems unlikely, based on what Weintraub and Walker describe, that there is a consistent size threshold past which we can no longer say ‘yes, this line is still visible.’

Clearly, then, there are no Berkeleyian (or Humean) Minimum Visibiles that can function as unitary bricks set together to build up the visual field.  How can one build a brick wall when no brick has a fixed, determinate boundary?  (Perhaps we could call these fuzzy-boundaried bricks, subject to mere probabilities, ‘Schrödinger’s bricks’.)  Add to this the fact that anything perceived is always a figure against a background (the background can be in front of and around the figure as well as behind it) and therefore always existing in relation to a context determining what it is, it becomes blindingly obvious that the Theory of Ideas (aka Theory of Sense Data) is dead, dead, dead.1  Certainly any attempt to resurrect that theory without coming to grips with the opening chapter of Merleau-Ponty’s PHENOMENOLOGY OF PERCEPTION is scandalously irresponsible.  (I am looking at you, professor Arnold Vandernat.)

Just as I am quite confident that Bigfoot aka Sasquatch does not exist, I am confident that there are no mental tokens called ‘Ideas’ or ‘Sense Data’.

To sum up:  In this post, I have perhaps succeeded in recapturing the content of the Aha Erlebnis I had when I first encountered Berkeley’s argument that depth is not visible.  In the process, using an experiment with a green bungee cord, I have put ‘paid’ to Berkeley’s notion of a Minimum Visibile in particular and to his Theory of Ideas in general.  (This is perhaps the ten-thousandth time this notion has been conclusively refuted.)

Nonetheless, in future posts I will be indulging a certain affectionate tolerance for this notion when discussing Berkeley’s claims that sight and touch are thoroughly entangled with one another, and that depth is constituted by the tactile/kinaesthetic sense.  For I think Berkeley comes very close to the truth in making these claims.









1 Lawrence Hass is very good at demonstrating this point. See his MERLEAU-PONTY’S PHILOSOPHY (Indiana University Press, Bloomington and Indianapolis, 2008), pp. 28-34.









Given that the today’s post deals so intensively with that Irish Bishop, George Berkeley, it is only fitting that today’s homage to Plato’s SYMPOSIUM should be a red-head.  Plato himself I suspect would have been more acquainted with red-headed Thracians than with red-headed Hibernians.



I am very much into red-heads at the moment.

There is too much beauty walking the earth for anyone to get anything done.



January 16, 2016:  Changed ‘perpendicular to’ to ‘end-wise’ in the first paragraph. Janu

January 17, 2016:  Made some other minor changes in an attempt to hide my scandalous lack of control over the subject matter….er, I mean, in order to streamline the argument a bit.


Lumber Room: Heap Of Scraps Comprising Varying Phenomenological And Philosophical Odds and Ends

In this post I will be collecting thoughts as they occur to me, regardless of whether I am able to fit them into any argument for a larger, more comprehensive and therefore more serious view.  These will be like odds-and-endsy scraps of lumber of varying dimensions that the furniture-maker does not want to throw away now because they think there is always the chance a use for them might be found later.  But for now none fits into any furniture project they have going on now.

Most of these (maybe all of them!) will be drivel, of course, and I will be continually updating this post as it becomes blindingly obvious to me that a given thought is completely unsustainable, at least in its current form.

Lumber Scrap #1:  Maurice Merleau-Ponty and John Searle on pains:

Stephen Priest on Merleau-Ponty:

Although the body-subject is the ‘percevant-percu’ (VI, 202) ‘perceiving-perceived’ (VIT, 248) it is paradigmatically the sensed (‘le senti’ VI, 302) which is the synthesis of the subjective and the material.  We can appreciate this already if we consider that the sensed seems to have both experiential and physical properties.  For example a pain both hurts and is spatially located in a part of the body.  Merleau-Ponty speaks of the sensed as ‘at the same time the culmination of subjectivity and the culmination of materiality.’ (VIT, 248).

Stephen Priest, MERLEAU-PONTY, THE ARGUMENTS OF THE PHILOSOPHERS, Routledge, 1998, p. 74

John Searle on two different senses of the phrase aware of:

I now want to expose the fallacy in the argument [against naive or direct realism].   One could object to various steps, but the crucial step is number three, which says that in both the hallucination and the veridical case we are “aware of” or “conscious of” something.  But this claim is ambiguous because it contains two senses of “aware of,” which I will call respectively the “aware of” of intentionality and the “aware of” of constitution.  You can see the difference if you contrast two  common-sense claims.  First, when I push my hand hard against this table, I am aware of the table.  And second, when I push my hand hard against this table, I am aware of a painful sensation in my hand.

a)  I am aware of the table.

b)  I am aware of a painful sensation in my hand.

Both of these are true and though they look similar, they are radically different.  (a) describes an intentional relation between me and the table.  I had a sensation where the table was its intentional object.  The presence and features of the table are the conditions of satisfaction of the sensation.  In (a) the “aware of” is the “aware of” of intentionality.  But in (b) the only thing I am aware of is the painful sensation itself.  Here the “aware of” is the “aware of” of identity or the constitution of the experience.  The object I am aware of and the sensation are identical.  I had only one sensation:  a painful sensation of the table.  I was aware of (in the sense of identity or constitution) the sensation, but I was also aware of (in the sense of intentionality) the table.

John R. Searle, SEEING THINGS AS THEY ARE:  A THEORY OF PERCEPTION, Oxford University Press, 2015, pp. 14-15

Contra Searle, however, it is clear that when one has a pain in their hand, a certain part of their body gets presented to them under (among other things) the aspect ‘having such and such spatial location and extent.’  One ‘condition of satisfaction’ for this presentation is ‘this part of my body exists at this location’; another is, perhaps, ‘something is wrong with that body part’.  Were one suffering from a phantom limb, the first of these conditions of satisfaction would not be satisfied, but perhaps the second would be (“Hell yes something is wrong with that body part!  It doesn’t exist any more!!!”)  At any rate, having conditions of satisfaction that can be satisfied/fail to be satisfied, one’s sensation of pain is just as intentional as their seeing or feeling the table.

As of this writing, I do not know whether this point poses any threat at all to Searle’s Theory of Perception. Incidentally, I also don’t know what threat, if any, the phantom limb poses to the various Disjunctive Theories of perception Searle expends so much energy sneering


Lumber Scrap #2:  John Searle on the subjective visual field:

This book is about perception….I want to begin by identifying the territory.  Close your eyes and put your hand over your forehead, covering your eyes:  you will stop seeing anything, but your visual consciousness does not stop.  Though you do not see anything, nonetheless you have visual experiences which are something like seeing darkness with yellow patches.  Of course you do not see darkness and yellow patches, because you do not see anything; but you still have visual consciousness.  The area of visual consciousness is quite constrained:  In my case, it extends, roughly speaking, from the top of my forehead down as low as my chin.  I am here speaking about the phenomenology and not about the physiological forehead and chin.  I am talking about how it seems to me consciously.  But the area of my visual consciousness is limited in that, for example, I have no visual consciousness behind my head or under my feet.  But I definitely have visual consciousness in front of my face even with my eyes closed.  That conscious area I just identified I will call the “subjective visual field.”

John R. Searle, SEEING THINGS AS THEY ARE:  A THEORY OF PERCEPTION, Oxford University Press, 2015, pp. 3-4.  I will sometimes reference this work as SEEING THINGS. 

Searle seems to want to identify not one, but two distinct kinds of visual fields:  a subjective visual field and an objective visual field.  And he seems to think we can identify both kinds within our ordinary, waking experience.  Let me start with the subjective visual field.

The subjective visual field is that kind of visual field in which, while one has visual experiences, one does not actually see anything.  The visual experiences have no objects.  Just as one sees nothing when they hallucinate a pink rhinoceros at their side (but they do have a visual consciousness that is like the visual consciousness they would have were they actually to be seeing a pink rhinoceros), one does not see anything in the subjective visual field.

Much of this book is about the relationship between the subjective visual field and the objective visual field.  The most important point I can make right now is:  in the objective visual field everything is seen or can be seen, whereas in the subjective field nothing is seen nor can be seen.

John R. Searle, SEEING THINGS AS THEY ARE:  A THEORY OF PERCEPTION, Oxford University Press, 2015, p. 4

Distinct from the subjective visual field is another kind of visual field, the objective visual field.  Searle defines one’s objective visual field as the set of identifiable-by-a-third-person objects and states of affairs that are visible from their point of view given the current lighting conditions in their environment and given their present physiological and psychological state (SEEING THINGS, p. 106).  Apparently, then, the objective visual field is just that section of space and the objects within it that are visible from one’s point of view (and given….and so on).  These are objects and space existing (normally) outside of one’s cranium.  Needless to say, one can identify the objective visual field in one’s experience because one does have experience of things and space outside of one’s cranium.

By contrast, the subjective visual field exists solely within the confines of one’s cranium:

My subjective visual field, on the other hand … exists entirely in my brain.

John R. Searle, SEEING THINGS AS THEY ARE:  A THEORY OF PERCEPTION, Oxford University Press, 2015, pp. 106-107

The subjective visual field is two-dimensional, but in a sense Searle feels the need to qualify:

Crudely, the subjective visual field is, so to speak, two-dimensional.  … [Of course t]he subjective visual field is not a visible object having two dimensions…. [But] … any impression of depth can be created by two-dimensional surfaces, as is shown by, for example, trompe-l’oeil paintings.

John R. Searle, SEEING THINGS AS THEY ARE:  A THEORY OF PERCEPTION, Oxford University Press, 2015, pp. 138-139

And, as we have seen in the first passage quoted above, Searle feels confident he has identified, and has given instructions for identifying, the subjective visual field by providing an example of one in his experience.  To repeat:

But I definitely have visual consciousness in front of my face even with my eyes closed.  That conscious area I just identified I will call the “subjective visual field.”

John R. Searle, SEEING THINGS AS THEY ARE:  A THEORY OF PERCEPTION, Oxford University Press, 2015, pp. 3-4.  

But, as I am about to show, Searle has identified no such thing.

For contra Searle’s claim that one does not see objects in the subjective visual field, one does in fact see objects when they follow Searle’s instructions to identify a subjective visual field and closes their eyes (the instruction he gives at the end of the first passage quoted above), or closes their eyes and places their hand over their eyes (the instruction he gives towards the beginning of that passage).  One sees objects in a clearly degenerate, drastically attenuated, highly defective way when they follow either one of these instructions, but they do see objects nonetheless.

For at the very least, one is seeing the shadow-side of their eyelids when they follow either of Searle’s instructions.

Let me explain.  And after explaining, let me politely suggest towards the end of this lumber scrap that in fact there are not two kinds of visual field, one objective and the other subjective, but just one single kind of visual field normally comprising both objective and subjective elements.  In certain unusual circumstances, this visual field might conceivably degenerate into one comprising subjective elements only;  nonetheless, there is just one kind of visual field.  In claiming there are two, Searle is seeing double.0

Through A Glass Darkly:  My Explanation:  When I slowly, gradually close my eyes, I visually experience a single horizontal band of somewhat warm darkness moving down at the same rate as my moving my eyelids down.  Along with and “entangled with” (as George Berkeley would say) my visual experience is a tactile experience of this band’s location.  For the band feels like it is on roughly the same vertical plane as my eyelids.  I get additional confirmation of this ‘feeling of location’ when I move my finger down with my eyelids, my finger touching the lids.   The same sense of tactile location and the same method of confirmation give me the sense that the width of the band is the same as (on the left) the outer edge of the eyelid of my left eye and (on the right) the outer edge of the eyelid of my right eye.  But there is no determinate visual terminus defining the band’s left and right sides.  (Promissory note:  this indeterminacy is extremely important, and will need further detailed discussion sometime.)   By contrast, there is a much more determinate, though still rather blurred edge at the bottom of the band.   This bottom edge gets more determinate, a bit less blurred as it moves down, and becomes more like the somewhat rounded edge of a body part such as an eyelid.  In certain lights, I see in a blurred way some striations when the dark band has come close to completing its downward movement.  These striations I confidently identify with my eyelashes.

Clearly the dark band is identical with the shadow-side of my eyelids.  Since this is a single band, not double, two views of my the shadow-side of my eyelids are getting merged into a single visual presentation.1  I am seeing the shadow-side of my eyelids when I see the downward-moving dark band.

That I am in fact seeing a physical object (actually, two physical objects the views of which have been merged into a single view or presentation) is strongly confirmed by the fact that when I move so that I am facing a direct light source, I sense light filtering through and visually experience a lighter, warmer, orangier color.  I am experiencing the visual effect of translucency — of light going through a not-100%-opaque flesh-colored object.  Skin, after all, is just a little bit transparent, as shown by the bluish veins one can see in one’s hand through a thin layer of skin.  Surely the most plausible explanation of this effect is that I am indeed seeing some translucent objects — my eyelids — presented in a single view.

That I am experiencing translucency in this situation is further confirmed  when I move my eyebrows up and down, I experience a darker band at the top of my visual field going up and down, along with (when the movement is down) a darkening, bluing, and cooling of the formerly lighter, warmer, fleshier and orangier color I had been experiencing.  Clearly, my retinas are picking up the shadow cast by my eyebrows where less light strikes them relative to what filters through my eyelids.

Again, when I touch my index finger to my eyelid.  I then see a cooler, darker shadow on my eyelid.  (Naturally, I sense the size of this shadow as equal to the felt size of my fingertip.)  This could not happen if my eyelid were not translucent and therefore visible to me even when it is covering my eyeball.

And again, when, both eyes shut, I partially follow Searle’s instructions above and cover my right eye with my right hand, the color of the dark field on the left remains warm and orangish, but the color on the right side of the field turns cooler and one notch darker.  Clearly my right hand is hindering light from entering through my right eyelid and casting a shadow.

The experience is very similar to pressing the shower curtain as close to my (open) eyes as I can get it.  The individual patterns on the curtain become very, very vague.  I lose most or all sense of the curtain’s texture, so that the curtain becomes (in this particular case) a whitish field of color occupying the entirety of my visual field, with its indeterminate boundary.  Objects beyond the curtain, such as my cat Munti, cast moving shadows across it.

In other words, attenuated as this visual experience is, I am still seeing a (somewhat) translucent objects even when it is extremely close to my eyes. For one, the shower curtain is causing my visual experience of it by transmitting light through it, light that hits my retina.  For another, my experience changes as this causal action changes — my cat moves this way and that, partially blocking this light.  For yet another, I am experiencing (in a defective way) a property of the curtain — its whitish color.  For still yet another, my visual experience occurs in the context of my being situated in a wakeful manner in an actual setting I am in contact with — the bathtub in my bathroom.  It is not like my “hearing” in a dream a lion roaring in a savanna, which sound turns out to be, upon my wakening, the roar of a car engine.  I am seeing a field, a ground, not a figure with demarcated limits on a ground.  But fields aka grounds are also things that I see — for example, the dark green blackboard around and running underneath the chalk figure visible on top of this ground.  Clearly, I am seeing the shower curtain, attenuated and defective as that vision is.

Likewise, I am seeing my eyelids when, in the circumstances described above, I close my eyes.  My eyelids are causing my visual experience by transmitting light through them, light that hits my retina.  My visual experience changes as this causal action changes — my eyebrows moving this way or that, my finger touching an eyelid.  I experience in a defective way the fleshy (though very much darkened and enshadowed) color of my eyelids, a color that, just like my flesh tones as seen normally, varies from orangish to bluish depending upon how the light hits/goes through them.  My visual experience occurs in the context of my continuing to be situated, even with my eyes closed, in the wakeful world of real, solid, tangible objects.  I don’t have any visual sense of the texture of my eyelids, a circumstance that probably lessens the chances that I will recognize that it is, indeed, my eyelids that I am seeing.  Indeed, I have probably spent most of my life not recognizing this.  But this absence of seen texture only means that my visual experience of my eyelids is highly attenuated so that my eyelids, like the shower curtain, get presented as a (single) field or ground, not as objects on a ground.  I am seeing my eyelids just as I would be seeing the shower curtain were snippets of that curtain were to replace the flesh of my eyelids.  (Imagine the transplanted snippets gradually getting more flesh-colored and thicker, so that the experience when I close my eyes becomes identical to that which occurred when my normal eyelids made of flesh were in place.)

Likewise, I am seeing the shadows cast by my eyebrows onto the translucent surface of my eyelids, and the shadow of my fingertip in the situations described above, just as I see the shadow of my cat on the shower curtain.

As Searle’s case clearly demonstrates, one can be seeing one’s eyelids and the shadows cast upon them without seeing that or recognizing that it is one’s eyelids and their shadow-play that they are experiencing.  This fact, though, does not mean that one is not seeing the shadow side of their eyelids when they close their eyes.  For of course one can see x without knowing that it is x.  Seeing is referentially opaque.  When at night, for example, I see a dark shape, just barely distinguishable from the enveloping darkness, I am in fact seeing my friend Chris even though I do not know who or what I am seeing, or even that it is a tangible being and not, for example, a ghost.  And since one’s cognitive concerns in the world almost always go past one’s eyelids and out into the world, it is perhaps not surprising that one’s perception of their eyelids is (perhaps normally and usually) cognitively as well as straight-up visually poor.

My eyelids are translucent.  I am seeing the shadow side of a translucent object, namely, my eyelids, when my eyes are shut and I am facing a direct light.  And even when I am not facing a direct light, it seems to me that I am always seeing the faint shadow, the slightly darker area, at the top of my visual field where my eyebrows — at least at the very upper edge of the eye-socket — are casting a shadow.  I submit, then, that there are no ordinary circumstances in waking experience when one sees nothing when they close their eyes.  I will go out on a limb and assert that, in ordinary circumstances, some light always gets through one’s eyelids.  (This is, of course, an empirically falsifiable statement.)  One can doubtlessly construct a situation in which no light gets through.  But this would be an unusual situation, and therefore useless for an appeal to identify in our ordinary waking experience something that Searle thinks he can identify, name, an object-less visual experience.

One sees the shadow side of their eyelids.  Case closed.  — Almost.

Of course, there is at least one problem here.  Initially, as I have said, the dark band as confirmed by my fingers is about the length from one outer edge of one eye to the outer edge of the other eye.  But when my eyes are completely closed, the length (as determined by my fingers as I press them on one part of the darkness I am presented with and then on another), the darkness I am visually presented with seems more extensive both horizontally and vertically than my eyelids (whose extent I also confirm with my fingers).  How could this be if I am seeing the shadow side of my eyelids?

An autobiographical note is in order here.  Yesterday, on November 26, 2015, I, Clifford Engel Wirt (Sometimes Cliff Engel Wirt, sometimes Clifford Engle Wirt, sometimes Cliff Engle Wirt, much of the time I pronounce the last name as the English ‘Wirt’, but sometimes, when I am tired, I pronounce it as ‘Veert’ … but I digress….) was completely convinced that the extent of this dark area was identical with the extent of what I see of my face when both my eyes are open.  In my case, that is the left edge of my left eye socket and the right edge of my right eye socket,  the lower part of my eyebrows, and part of the area where my cheek bones start jutting out.  (All of these I see in a rather blurry, undefined way, of course.)  This extent was, I assert confidently, was given through a tactile feeling, a feeling that was entangled (Bishop Berkeley again), or, as I prefer, integrated with my visual experience.

But today, on November 27, 2015, I am absolutely convinced that the upper area of the darkness I experience when my eyes are shut is co-extensive with my forehead.  I try to tap the upper part of this dark area, and I end up tapping the middle of my forehead.  Go figure.  I must have been influenced by the description Searle gives in the first passage quoted above.  — Please, Lord, don’t ever cause me to experience this dark area as in front of my face, as Searle would have it, as opposed to the way I currently experience it as coextensive with part of my face! —  Clearly the entanglement in/integration of my visual experience into the tactile sense of the location of the various parts of my face is a highly variable phenomenon, much open to suggestion.

It should not surprise one that this should be so.  For the visual experience I have when I close my eyes is highly degenerate.  It is much like my visual experience of the shower curtain when I press it very, very close to my eyes. I lose all sense of the curtain’s texture and most of its patterning.  It becomes just a white field.  It lacks clear boundaries because those boundaries are the thoroughly indeterminate limits of the visual field.  (See promissory note above.)  The shadows cast through it, say, by someone’s finger pressing against the curtain on the other side, are extremely vague, just as are those I see when I press my finger against my closed eyelid.  My visual experience of the shower curtain is very, very far away from the maximal perceptual grasp so famously discussed by Merleau-Ponty.  As a visual experience it is highly defective.

Even more so, then, will my visual experience of my eyelids be defective.  My eyelids, after all, are even closer to me than the shower curtain pressed to my eyes.  I have even less of a Merleau-Pontyian maximal grasp on this rather amorphous dark field, rather prone to intrusions by afterimages, than I do on the shower curtain.  The light coming in from the outside world and causing me to see my eyelids is, a bit like the light finally reaching that quasi-planet Pluto from the sun, a bit weak.  The visual experience is therefore weak and more vulnerable both to disruption (the intrusive after-images) and to odd influences (passages from Searle’s book, for example).  It should not surprise us, then, that the integration of this visual experience into my sense of bodily location and extent should also be highly variable and unstable.  Degenerate to the utmost degree, we cannot demand of it that it give us an accurate sense of how large the area of darkness is.  This would be contrary to its nature, as if we demanded of a horse that it lie down in a suitably genteel manner on a couch.  I therefore dismiss the notion that one cannot possibly be seeing their eyelids when their eyes are closed because the extent of the dark area visually experienced may not agree with the felt extension of one’s eyelids.

If I see my eyelids when facing a direct light with my eyes shut, I see them even when I am not facing a direct light when my eyes are shut.  The visual experience, after all, is not much different in the two cases.  Would anyone really care to contest this?

I assert, therefore, that I normally see my eyelids when my eyes are shut.

That Searle does not merely suggest, towards the beginning of the first passage quoted above, that one close their eyes, but also has one cover their eyes with their hand, suggests that he may be at least vaguely aware of everything I have said so far.  Searle seems to be aiming at a situation in which no light at all filtrates through the eyelids to strike the retina.  As for myself, I never succeed in getting to this state just by using my hand.  Some light always comes through no matter how hard I try, for example, through the intervals between the fingers which I cannot close completely, or from towards the bottom of the hand, which I cannot get to adhere to my face with suction-cup effectiveness.  So the attempt to follow Searle’s instructions has miserably failed, at least in my particular case, to generate the identification of a purely subjective visual field in which visual experiences have no objects.

Maybe one could take fairly drastic measures to ensure that absolutely no light filters through the eyelids.  I am sure that, with enough dedication and commitment,2 one could achieve this state. Maybe one would then have a purely subjective visual field in which there are visual experiences, but no visual experiences that have objects.  But until I get into this state, and until Searle gets into this state, neither of us has identified a subjective visual field in the course of our experience.  As I said above, Searle has identified no such thing, and he has not given instructions that would enable one to identify such a thing within their experience.

And even if one did have enough dedication and commitment to achieve this singularly unenlightened state, it is not obvious that one has enabled the identification within their experience of a subjective visual field considered as distinct in kind from an objective visual field.  All one has done, I submit, is create an extremely abnormal situation that causes one single visual field to degenerate so much that it no longer contains any objective elements.  All one would have created would be a bunch of flotsam and jetsam left over from the disintegration of a far richer, more integrated (integrating, for example, visual experiences with tactile experiences) visual field.

For it is certainly prima facie the case that in normal situations only a single visual field opens up for one.  This visual field contains both objective elements (the coffee cup when my eyes are open, the shadow side of my eyelids when closed) and subjective elements (the various afterimages I may sense in both the eyes-open and the eyes-closed cases; the “snow” I always “see” that arises from a visual abnormality I suffer from, causing me to wonder sometimes if I am seeing a very light rain outside the office window or if I am just sensing “snow” as usual, showing that the “snow” at least seems to be in the space outside the window; the “fields of force” manifesting themselves in the pulling together of three angles drawn on paper to form a triangle in the illustration from Gestalt Psychology…”fields” that I do not see but which are definitely an element of my visual field…; the silly cat sitting in the bookshelf I am hallucinating with my eyes open (no, not really…what do you take me for?);  the pink rhinoceros standing beside me as I write this (this is my study rhinoceros))….

Searle, then, has certainly not given sufficient warrant for the claim that there are two different kinds of visual fields, one subjective and the other objective.  [Why this matters.  Searle has not identified the territory — we are still lost without a map. ]

Although I am at the moment uncertain how to use the inability to distinguish two kinds of visual fields (one subjective, the other objective) to attack Searle’s theory of perception, the fact that Searle tries to distinguish and identify the two suggests the distinction is critical to his theory and that some sort of attack on these grounds should be possible.

Some strange compulsion forces me to add as a last note that ages ago, in a graduate seminar on St. Thomas of Aquinas, no one seemed to have the slightest idea of what I was talking about when I tried to describe what one sees when they close their eyes.  I think the moral of this is that Thomism will skew one’s perception of absolutely everything.  Or maybe that I am just nuts.  I report; you decide.

Update:  September 16, 2017:  Why should this matter?  It undermines a bit Searle’s attempted distinction between the content (subjective) of an experience and its object (objective).   (The purely subjective visual field versus the purely objective.)  Searle cannot point to an example of this distinction that occurs within normal everyday experience.  He would need to go to extra-ordinary breakdowns of normal experience — total sensory deprivation, for example, or hallucinations.  (The pink rhino grazing peacefully at my feet while I write this.)  Within normal, ordinary visual experience it is not easy to locate something purely subjective that is not a presentation of an object existing in the world.  The tie to the world is not so easily cut.



Lumber Scrap #3:  The coolness of a color and the warmth of a texture. 

My Color Personality is Sea Glass (starting from various shades of Viridian Green and going bluer), says the online quiz sponsored by Better Homes and Gardens on FaceBook.


 While I do have some doubts about the scientific validity of this personality test, I do find the below an interesting example of synaesthesia at work in everyday experience.  The shades of the color sea glass have cool undertones.  Textures such as weathered wood and rattan are warm.  So pair the two!

Give beachy a sophisticated shake with a sea glass palette. These mellow shades of green have cool undertones (meaning they have hints of blue rather than yellow) and pair well with gray blues and light neutrals. Incorporate natural textures such as weathered wood and rattan to add warmth.




That a color can be paired with a texture suggests a commonality.  Here the commonality is something belonging to the domain of tactile feeling:  coolness/warmth.

Color and texture form the most common instances of synaesthesia.  I see the roughness of the bark, the smoothness of polished marble.  Perhaps little tendrils of nerve fibers are sprouting from the visual center of the brain and connecting to whatever tactile center, but however it is done, the tactile is integrated into the visual as a single visual experience of bark or marble.  There are not little unitary bricks of Berkeleyian Minimal Visibiles existing “side by side” as it were with little unitary bricks of Berkeleyian Minimal Tactiles.  There is no ‘and of sensations’ when one sees the bark or marble.  Not matter how hard one tries to introspect (or, for that matter, look at the bark or marble), they will never be able to untangle a purely visual experience of color from the purely tactile experience of texture.

Berkeley actually comes close to this Merleau-Pontyian phenomenon when he tells us that the Visual is so much entangled (his word) with the Tactile in experiences such as seeing rough bark that it is next to impossible to disassociate the two and see them as separate.  But he is incapable of actually arriving at that point.  The two must be separate and distinct, he thinks.  Supposing otherwise would be like accepting A and NOT A as true.  So in his own introspection of his Ideas, he must have told the two (e.g., Visual Idea of a brownish color and Tactile Idea of the Imagination of roughness) apart.  But whatever Berkeley told himself, he surely never did succeed in telling the two apart.


Lumber Scrap #4:  Interesting that Searle’s graphic illustrations in SEEING THINGS AS THEY ARE:  A THEORY OF PERCEPTION always show the relation in breadth, from the view point of a third-person observer.  None is presented in depth, from the view-point of the first-person observer/entangler-entanglee-in-the-world.

Lumber Scrap #5:  A book on n-dimensional geometry I read in High School defined the different spatial dimensions in terms of the ability to move around obstacles.  A point has 0 dimensions.  Considered by itself, it has no freedom of movement at all.  Now place the point inside a line.  Since a line is a one-dimensional object, we have just introduced a higher dimension, going from 0 to 1.  The point now has the freedom to move inside that line.  Now imagine our point as encountering an obstacle in the line — another point — that obstructs its movement.  Our point regains its freedom of movement when we introduce yet another higher dimension — a two-dimensional plane.  The plane gives our point the freedom to move around the obstacle in the line.  Now imagine our point as encountering yet another obstacle — a line in the plane.  Introduce the third dimension.  Voila!  The point has regained its freedom of movement through its ability to bypass the line by moving around it.

Let’s apply this High-School geometry lesson to a phenomenological description of depth.  I am about to argue that this description has to be done, not in terms of a static existing side-by-side of points, but in terms of motion.  Motion of a point?  Motion of my body?

I am sitting inside my car in the parking lot of the HEB on San Felipe and Fountainview in Houston, Texas.  It is dusk.  My head and eyes are positioned in a way such that I see the soft scrim of a tree’s foliage, and, beyond that, the glow (darker red against luminescent yellow) of some gas-station signage spelling out the word ‘SHELL’.  The sign is some distance from me, across San Felipe.  No objects are visible between the foliage and the SHELL signage.

I imagine a glass pane extending across my field of vision on the same plane as the foliage of the tree.  Naturally, I have a (somewhat indeterminate — why this is important and why it makes life somewhat more difficult for me is to be explained later) sense of depth extending beyond this plane and towards the glowing signage.  Taking my cue from my High School geometry — geometry is the science of space, right? — I try to construe the depth I sense as a line segment.  Because I think this will be the purest example of depth, I choose that line segment which is situated in the exact middle of my visual field, extending from the plane in which the haze of foliage is situated, and ending up at the glowing signage across San Felipe Street.  If one extends the line segment in the other direction, it would end up at my eye.  To make things simple, lets pretend that I am looking with only a single eye open.

Of course, this geometrical line segment, lacking thickness, is an abstraction.  It is not something I can sense.  What, then, might my sense of depth consist in?

Well, I can visually imagine line segments of whatever color (wine red, sea-glass green, burnt sienna, white…) to represent the mathematical objects.  Maybe my sense of depth consists in visual imaginings like these!  So let me try to visually imagine a line that I can use to represent the line of depth that exists between my eyes and the gas station signage.

This line has to be imaged as thin as possible in order to make the image as adequate a representation of the geometrical object as possible.  I am imagining a very, very thin line now.  Of course, I can’t use it to represent the line of depth in question because it is, well, a line, extending to my left and to me right…in other words, situated before me.  To make it represent the (geometrical) line of depth in question, I have first to place it in the middle of my visual field, and turn it away from me, a motion much like that articulated here in my thought experiment with the gold foil.  When I have finished turning the line, I end up … with a single point!  (More precisely, with an imagined spot of whatever color and made as tiny as possible to represent a geometrical point.)  Voila!  I have arrived at what I think is the kernel of truth lying in the second paragraph of Berkeley’s A NEW THEORY OF VISION:

II.  It is, I think, agreed by all, that Distance [of an object in depth], of it self and immediately, cannot be seen.  For Distance being a Line directed end-wise to the Eye, it projects only one Point in the Fund of the Eye, which Point remains invariably the same, whether the Distance be longer or shorter.

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

As I’ve said before, I think George Pitcher has pretty thoroughly demolished the actual argument written down in black and white by the actual historical George Berkeley, but I do think that what I have presented above gets at the intuition animating this passage.  And I am reasonably confident (yes, I can be just reasonably confident about this) that it lays out the intuition, the Aha Erlebnis, I experienced when I first encountered this passage some decades ago.

Since I can imagine just a single point (tiny spot image) of the line segment extending from the plane of the foliage to the gas station signage, clearly my sense of that depth cannot consist in the visual imagination of a static array of points, one behind the other.  So I will take a cue from my High School geometry and postulate that what generates the (sensation) of the depth in question is the (imagined) motion of the point from the plane of the foliage towards the gas station signage.

The imagined point is ‘there before me’, in front of my body whose solidness and heaviness occupies a ‘position here’.  The point facing me (in my imagination) is in a position not occupied by my body.

Jumping through a hoop.
More to come in this lumber scrap.

Lumber Scrap #6:  John McDowell makes what many will regard as a striking claim that certain perceptual states are indefeasible.  “But of course perception is always defeasible!” will be the typical response.  “What I am seeing could be an illusion (for example, the weird ‘shape’ of the teapot handle seen through a wine glass), or even a hallucination (for example, the pink rhino I am seeing now grazing contentedly at my feet while I write this)!

Lumber Scrap #7:  My hand is placed on the cool metal bar of the seat in front of me as the Metro train reduces its speed.  As a physical mass with inertia, my my body continues to move forward at the train’s previous, faster speed, causing my hand to press into the metal bar with my body’s weight behind it.  I daresay that I have the kinaesthetic sense of my body moving forward towards the bar; but even more salient than this is the sense of the inertial mass of the bar, in an equal and opposite reaction to my body’s moving forward, pressing into my hand.

When I am intentionally touching something — some smooth silk, for example, or the rough bark of this particular tree — I apply one degree or another, as is appropriate in each case, of pressure to the object or material felt.

In both these cases — the bar impinging upon my hand, my intentionally impinging myself upon the silk or bark — pressure occurs.  The existence of this occurrent pressure highlights one facet of the sense of touch, namely, there is zero distance between the object felt and the sensing surface.

As an aside, I would like to note that in addition to the occurrent tactile pressure noted above, there seems to be also a virtual tactile pressure which, plausibly, constitutes the experience described by some blind people of remote objects.  Through whatever sensory means (echos, differences in air drafts, or whatever else, means not necessarily known to them) these people become aware of an object — a wall, for example — as exerting a kind of virtual pressure on them:

What the blind person experiences in the presence of an object is pressure.  When he stands before a wall he has never touched and does not now touch, he feels a physical presence.  The wall bears down on him. … Perception, then, would mean entering into an equilibrium of pressure….

Jacques Lusseyran, THE BLIND, p. 31, as referenced by Miriam Helen Hill in BOUND TO THE ENVIRONMENT: TOWARDS A PHENOMENOLOGY OF SIGHTLESSNESS, an essay in DWELLING, PLACE AND ENVIRONMENT (ed. David Seamon and Robert Mugerauer, Columbia University Press, 1985)

Pressure is something sensed tactilely.  So the pressure sensed virtually by some blind people of objects at a distance corresponds to the texture objects sensed virtually and at a distance by people gifted with sight when they see the smoothness of marble and silk, or the roughness of bark or of a stucco wall.

This virtual touch will turn out to be highly important.

End of aside.

So far, then, we have a 2-place relation comprising a thing occurrently felt, and a body with a sensory surface at which the thing is felt.  The two terms of the relation are distinct in spite of the fact that zero distance exists between them.

, I feel my hand pressing against the seat.  At the same time, I feel the seat pressing into my hand as it accomplishes its opposite and equal reaction that is to accompany every action on it.

There is just one tactile experience here, one tactile presentation, but encompassing two different things:  the seat in its inertial mass engaging me in my physicality at and through a single “point”, my hand.   The seat, and me, with my hand as a focus.  This tactile presentation, in one stroke, reveals the hardness and mass of the seat and the mass and physicality of my hand.

Pretty much the same dynamic occurs every time I actively feel something with my hand.  As I pass my hand along the small-pebble-ish-rough wall, for example, I unavoidably press my fingers ever so lightly into the wall.  So part of the tactile experience consists in the wall ‘pressing’ into my hand in reaction.  But now, instead of a presentation of a single spot of the seat pressing against a hand occupying throughout this time a single location, my hand covers a spatial range forming a line, or perhaps a linear square, triangle, circle or some irregular zig-zag.  It is as if my felt hand/fingers-felt-press-of-the-wall were the head of a comet leaving a trail behind it to form a line, except that, while comet head and comet tail both exist in the present, the trail left by my fingers has already slipped into the very recent past.  But it does so in such a way that it continues to inform the present, giving the current position of my hand the sense ‘at the head of this advancing line’.

In perhaps much the same way a previously sounded but no-longer occurrent note lingers in the air so as to give the note sounding now a position in a melody.  What gets presented is ‘note sounding now in relation to the notes that have just slipped into the very recent past and sounding therefore in the context of a melody’.  Just so, what gets presented as I move my fingers along the slightly roughish wall (or the coolly smooth marble) is ‘fingers-pressing-upon-getting-pressed-upon-occurrently-in-the-context-of-a-trajectory-formed-by-their-just-past-motion-and their just-past pressing-in-upon-the-wall-and-the-wall’s-just-past-pressing-into-my-fingers’.  This, I assert, is how the presentation of ‘slightly-roughish wall’ (or ‘coolly smooth marble’) is structured.  This is a single presentation encompassing not just finger-spot and hard-surface-spot but also finger/hand trajectory and linear area of hard surface.  Felt fingers/hand felt surface in a single presentation.

So what, exactly, am I arguing against?  I am arguing against the idea that there would be two presentations occurring at the same time.

Lumber Scrap #8:  Cryptic remarks, to be expanded when I am not spending all of my time working.  Empty space plus ‘extending’ (vs. positing) oneself:  one term of the relation drops out. leaving a one-place relation.  A kind of tactile ‘buzz’ outlining a position here at which I am.  When occurrent there is always another object (the ground underneath my feet, the bed underneath my body) distinct from me  but no distance from me (two-place relation).

Spell out what Berkeley does not spell out, and see where we end up.

The emptiness of space makes itself a bit more salient to even my spectatorial awareness when I, for example, imaginatively move my hand underneath my table/desk at work and ‘feel’ its underside.

The “empty”, “massless” space before me (and around me) in which I can freely move is the counterpart of the the weight and mass of my body located at this unique position here, which weight and mass becomes manifest in my constant actual movements (no matter how small) and which ties me down, weighs me down at the aforementioned position here.  The possible versus the actual.  The emptiness of this space arises from its not being actual and present, its being potential and futural.  It is a potential/futural position here and therefore an anti-mass, an anti-weight.

And its indeterminacy makes it a bit problematic to talk about a potential position here — the level of determinacy needed to talk about a position here belongs to the spectatorial imagination.  A possible position here is this possible position here, one determined by the mind’s eye, not totally disassociated from the body’s kinaesthesia.

“A” possible position here automatically brings in the notion of the body’s possible movement.

Lumber Scrap #9:

The sense of ‘going out’ is especially keen — in fact, perhaps gets revealed — when there is a hole in, for example, the scrim formed by a tree or a bush, through which you see an object behind — a building, say, or the Shell Station sign.  (Yes, I need to lead up to this very carefully.)  The line of vision to the sign (to run with that example) is straight-to.  There are no intervening objects in view.  These conditions highlight one important feature of this vector, this ‘going-out’, this ‘ekstasis’ — it is indeterminate.  I become a bit surprised when, after this exercise, I walk past the tree and gain a concrete, determinate sense of the distance from my truck to the sign. Then other tangible objects enter my visual field — for example, the asphalt pavement with the painted traffic lines — , with the result that the distance becomes much more available to an estimation of a determinate length — say, 6 body lengths (36 feet or so).  The line of vision to the sign is no longer straight-on — other tangible objects appear at a slant.  And I become slightly surprised by how much the real distance, the distance in the tangible world, really is. Before, tangible presence had  not shown up in the ‘straight-on’ part of my visual field — there was only a futural possibility — the futural quasi-imaginative (I say quasi because this is not a positing imagination — not the spectatorial imagination) launching of my body through this hoop.

This brings me to Berkeley’s insistence in the NEW THEORY OF VISION that real measure is tangible measure.  You have to slap a physical ruler onto the thing that can have something slapped onto it. Without the tangible measure bringing you into the present, you have only the futural intra-(quasi)-imaginative projection which is surely subjective in some sense, though not in what I take to be Berkeley’s sense in which to be subjective is to be locked up “inside” a mind (considered as a kind of container) in such a way that no part of the object thus locked up is accessible to any other mind.  That there is nothing hidden in Berkeley’s Ideas entails there is nothing accessible in it to anyone else.

Without the intervening tangible things (‘entanglement’ of the tactile into the visual) in the visual field, there is only an in-a-way “subjective” visual field which, (more) divorced from the present and tangible [yes, I know, I need to explain this ‘more or less’ divorced — I do have the sense that the sign I see through the hole in the tree-scrim is further away than than the object I see through the hole in the bush-scrim… but I begin to get a ‘maximal grip’ on the distance only when tangible objects intervene] is indeterminate.  It is therefore indeterminate in the same way that the “longer” line in the Mueller-Lyer illusion is in fact of no determinate, measurable length longer than the “shorter” line.  The two vectors (the Mueller-Lyer illusion and the ‘going out’ in the visual field) are very much alike in this regard.  The ekstasis is a kind of Mueller-Lyer illusion ‘going out’.

The fully-exposed, fully-existing-in-the-present units in a length.  A plenum of brick-units. Depth introduces at the same time futurity, potentiality, and emptiness.   The straight-on line of vision gets stopped by the opaque, tangible object. Futurity is the solvent creating emptiness and distance-away.  [Yes, this is obscure right now, but I am hopefully not delusional in thinking I can unpack it.]

Lumber Scrap #10:

When the polyester-green bungee cord is stretched out lengthwise before me, I enjoy a presentation (much more rarely, should I be hallucinating, a mis-presentation) of (as of) an actual physical object existing in space in the present.  Adopting the spectatorial attitude, I can imaginatively try to resolve this presentation into a series of points, as small as I can imagine them, lying side by side with no space between them.  When the bungee cord is withdrawn, I can still posit these points lying side by side in ’empty’ space in a quasi-presentation.

The temporal dimension of presentation is, naturally enough, the present.  What the presentation is of pertains to the actual, not to the merely potential.  The presentation pertains to the full, to a plenum, not to an emptiness.

But as I think I have shown here, the more the bungee cord (or, to use the example used in the post referred to, the one-atom thick gold tape) is moved away from me, the less there is of a presentation of the cord (or tape).  The more what we are talking about is potentiality, not actuality, the futural, not the present:  the depth into which the gold tape has finally disappeared is something that I can (potentially) move my body (in particular, my arm and hand) through; restricting myself to the spectatorial attitude, and using the amazing powers of the mind’s eye, it is a field through which I can (potentially) move a posited, imagined point through.  The potential is the futural — the future is its temporal dimension.  The futural comprises all of the following:  non-presentation, non-fullness and non-plenum(emptiness), the non-actual (the merely potential).  The space in front of us (presentation mainly though not exclusively through vision) is spatial-temporal, that is to say, spatial-futural.

Lumber Scrap #11:

Space as the ‘through which’, the ‘across which’ — and, introducing a subjectivity of some kind — that which I (sometimes vertiginously) span:

Locality has such a pervasive importance because it is the essence of what space is. By “space” I don’t just mean “outer space,” the realm of astronauts and asteroids, but the space between us and all around us, the space that our bodies and everything else occupy, the space through which we swing a baseball bat or stretch a measuring tape.  Whether you point your telescope at the planets or at the next-door neighbors, you are peering across space.  For me, the beauty of a landscape comes from the giddy sense of spanning space, a sort of horizontal vertigo when you realize the little dots on the other side of a valley really are there and that you could touch them if only your arm were long enough.

George Musser, SPOOKY ACTION AT A DISTANCE, New York, Scientific American/Farrar, Straus and Giroux, 2015, p. 7.  Emphasis mine. 

My project now (my Berkeley and Merleau-Ponty project) is to describe as best and as precisely as I can what this ‘spanning space’ is.

The question of whether space and time are absolute or relative has re-emerged in a new form in modern philosophy and physics as the question of whether space-time is absolute or relative. It remains to be seen whether a holistic unified science which allows the presence of the conscious subject in the universe will ascribe subjective properties to space-time.

Stephen Priest, THE EMPIRICISTS, Second Edition, New York, Routledge, 2007, p. 138.

Want to pin down, when I have time, a pertinent passage from Renaud Barbaras’ THE BEING OF THE PHENOMENON.

Lumber Scrap #12:

There is zero distance between me (my body) and the wooden board (say, the smooth, unobtrusively varnished, beautiful board of my ‘computer station’ desk) that I am pressing into/is pressing against me.  Nonetheless, the board remains obdurantly outside me.  It has not come so close to me that it now occupies the space that I occupy. Describing just what is tactically presented, there are two sides:  the side of the board outside me — the ‘other side’ — and ‘this side’:  my side.  The ‘this side’, with all its weight and heft, is what is in my case the position here.  It is that position (to bring sight into the picture now) from which I engage with, view, and sometimes confront visible things/objects.


Lumber Scrap #13: Outline:  

The red and yellow apples example interpreted in the light of elementary probability theory.  Intuitions.  Then apply to the perhaps more solid examples of irrelevance.

Knowledge bzw ignorance needed for any probability less than one.


Lumber Scrap #14:  Bishop Berkeley’s Visibile Ideas in the NTV:  

In his NEW THEORY OF VISION, Berkeley starts off by presenting Visibile Ideas as rather robust creatures — the Visibile Moon, for example.  But as he proceeds, Visibile ideas become more and more paltry, especially as they get stripped of their “entanglement” with Ideas of Touch.  We end up not even being entitled to say of them that they have planar shapes!  In their poverty, it seems to me, they match the visual presentation of darkness one experiences when they close their eyes, a presentation that can have an off-and-on relationship with potential tactile experiences that affect the perceived size of the dark area (identical, I argue above, with the shadow-side of one’s eyelids).


Today, for my Homage To Plato’s SYMPOSIUM3 I offer an image of someone who clearly participates in Plato’s Form Of Ginger Gorgeousness:


Clearly the Form Of Ginger itself participates in the Form of Absolute Beauty.  How can anyone get anything done with Beauty like this walking the earth?

0 Hahahahaha. Seeing double. Get it? Get it? … Okay, okay, I’ll shut up….

1 This merging of two views is not a totally unheard-of phenomenon, given the stereoptical nature of normal vision

2 The phrase ‘dedication and commitment’ is, of course, a reference to a famous snippet of conversation overheard by a certain undergraduate at U.C. Berkeley. A certain phenomenologist told Searle: “Derrida is not a total fraud. He is good on Husserl.” Searle’s reply was: “No, Derrida is not a total fraud. It takes dedication and commitment to be a total fraud.”

3 Though perhaps professor Searle, who, unfortunately, at times performed homophobic speech acts in some of his classes in the late 1970s, would not approve.

November 26, 2015 and November 27, 2015:  Drastically rewrote lumber scrap #2.  It would be safest to assume the worst:   namely, that I did so in a probably failed attempt to hide my lack of control over the subject matter and the confused nature of my thinking.

The Truth Of Bishop Berkeley (Part 0)

Essay:  Noun:`
  1. a short literary composition on a particular theme or subject, usually in prose and generally analytic, speculative, or interpretative.
  2. an effort to perform or accomplish something; attempt.
  3. a tentative effort; trial; assay.
Essay:  Verb (used with object)

  1. to try; attempt.
  2. to put to the test; make trial of.


This Essay:  Transforming George Berkeley Into Maurice Merleau-Ponty

There is a not-completely inchoate notion lingering in my head that if we tweak this or that position held by that Irish Anglican Bishop George Berkeley ( 1685 – 1753 — about the same time Johann Sebastian Bach lived) — especially his positions regarding visual depth and the relation between vision, touch, and the motions of the body — we will end up with something like Merleau-Ponty ( (1908 – 1961).  The effect may be a bit like those step-by-step transformations of a picture of one celebrity into a picture of another celebrity.

I propose then a series of posts, starting with this one, which will be an essay — a trial, an attempt — to try to do just this.  (Change George Berkeley’s nose just a little bit, then lengthen the chin a notch, then….)  I will be putting my currently somewhat inchoate notion to the test, making a trial of it, to see if I can come up with genuine insight into Merleau-Ponty, or better, into the phenomena he was concerned with.

Clearly, Merleau-Ponty advances positions that directly contradict Berkeley’s.  But along with this opposition that makes Berkeley an excellent foil to Merleau-Ponty, there is, I think, a surprising degree to which Berkeley is on the same wavelength as Merleau-Ponty, with the consequence that Berkeley can illuminate Merleau-Ponty in a way other than just being a foil to him.1 Just as Merleau-Ponty recognizes a ‘truth of solipsism’, I think a Merleau-Pontyian might recognize a ‘truth of Berkeley’ — or at least a truth regarding Berkeley’s claims regarding depth which will illuminate our perceptual opening onto a world that is at once our “flesh” and not us.  In this opening, I claim, the perceived object is both immanent and transcendent . . . and this is my essay towards making sense of this.  Will I succeed?

Apart from illuminating some of the phenomena described and explicated by Merleau-Ponty, one of my sub-aims is to work through (in subsequent posts — not this one) the arguments of an article I published in a previous life (Cliff Engle Wirt, THE CONCEPT OF THE ECSTASIS,2 Journal of the British Society for Phenomenology, 14, 79–90, January 1983) in such a way as to make those more arguments more intuitive, or at least less absolutely repellent, to a certain person of my acquaintance . . . a person who is, I think, a bit too uncritically enamoured of a certain British Empiricist.  (No, not George Berkeley, but John Locke.  But never mind.)  This person would sometimes say things to the effect of “If what you were saying applied only to what’s inside the mind, I would consider it.”  So I want to see how far I can go in sticking to the framework of ‘just what is immanent to the mind.’  Then later, I will see what, if anything, I can make ‘transcendent’ of the mind — or, more precisely, of the body in its subjectivity.

The essay comprising all these posts may not be exactly short, but perhaps we can re-interpret ‘a short literary composition’ in the definition of ‘essay’ shown above to mean something like ‘less lengthy than Tolstoy’s WAR AND PEACE’.  In what follows, I will retain Berkeley’s not-quite-modern capitalization and spelling practices in my own text when the concept is Berkeley’s, or at least taken by me to be Berkeleyian.  (I won’t be attempting, however, to be absolutely precise or consistent in this endeavor.)


George Berkeley On The Visibility (Invisibility) Of Depth

Let me make a start in this (possibly dubious) endeavor by jumping into Berkeley’s assertions regarding the visibility (invisibility) of depth in his AN ESSAY TOWARDS A NEW THEORY OF VISION.  Berkeley’s claims regarding depth nicely motivate my claims about the ekstasis and the claims I make about the ekstasis would be less likely to freak out a dualist when made inside a Berkeleyian context.   Berkeley’s claims about the invisibility of depth are true in the real, non-Berkeleyian world only in special cases; nonetheless, this will still be enough to motivate my claims about the ekstasis.

Berkeley plunges into an argument that depth is invisible in the second paragraph of his AN ESSAY TOWARDS A NEW THEORY OF VISION. 

II.  It is, I think, agreed by all, that Distance [of an object in depth], of it self and immediately, cannot be seen.  For Distance being a Line directed end-wise to the Eye, it projects only one Point in the Fund of the Eye, which Point remains invariably the same, whether the Distance be longer or shorter.

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


This passage produced in me a sudden Aha Erlebnis ages ago, when I first encountered it in a little cottony-red cloth-bound book my parents had bought in their college days in the 1940s.  I experienced a flash of intuition to the effect that no, depth cannot be seen.  The passage still produces this Aha Erlebnis in me even now, even though that Erlebnis very much resists getting cashed out analytically.  Something seems right about it.

Naturally, the passage is ambiguous and what, exactly, the argument is, is not completely clear.  Is Berkeley talking about Lines and Points in Euclidean geometry?  Is he talking (as he probably is) about Lines as rays of light bouncing off an Object and striking a spot or Point on the retina?  Is he talking about Visible Lines that can be Blue, Red, Green, Orange, Purple, Violet, or Burnt Sienna?  I will be going into a little bit more detail below about these three different interpretations of what ‘Line’ means in Berkeley’s paragraph II.

But for now I will just note that I follow George Pitcher, who surmises in his BERKELEY:  THE ARGUMENTS OF THE PHILOSOPHERS that Berkeley is talking about rays of light and the retina.  If so, Berkeley’s argument fails for essentially the reasons that Pitcher points out in Chapter II of his book (though naturally I don’t agree with everything Pitcher says).  Nor does any one of the other explicitly-stated arguments made by Berkeley that I have encountered so far work.

Nonetheless, I think it is possible to argue for Berkeley’s assertion that depth cannot be seen by relying on the Berkeleyian concept of a ‘Minimum Visibile’ and some other notions Berkeley holds about Ideas of Vision.  If these concepts are valid, Berkeley’s claim about depth does hold, regardless of the validity of his argument quoted above.  In future posts I will then use the Berkeleyian-world arguments and the real-world arguments to motivate the claims I make about the ekstasis.

As it happens, I don’t think Berkeley’s concepts are valid.  (Please — I am not completely nuts.)  Nonetheless, I will ignore this disagreement long enough to accomplish the task noted above, namely, making certain arguments that may seem to the dualist utterly wild outside the realm of Berkeleyian Minds filled with their Ideas.


Berkeley’s Visual Ideas:  A Minimalist Presentation

The subheading of course is a pun:  I am launching into a minimal presentation of Berkeley’s theory of Visual Ideas, and the basic unit of Berkeley’s Visual Ideas is itself a minimal presentation.

Infinitely Thin Slices Of Yellow Cheese:  Berkeley’s Visual Ideas are what we see.  They are the objects of sight.  For example, I see the moon.  The moon is the object of my vision. It is a Visual Idea.  Let’s call it the Visible Moon.

Visual Ideas have properties. For example, the visible Moon is “…a small, round, luminous Flat…” (Paragraph XLIV).  I do not doubt in the slightest that Berkeley would add ‘of a whitish or a beautiful pale yellow color not totally unlike certain cheeses” to the list of properties possessed by the visible Moon.

Although I may find myself contradicted as I read further in A NEW THEORY OF VISION and other works by Berkeley, I will go out on a limb and assert that for Berkeley, a Visibile Idea (or an Idea of any kind) can have only those properties that appear to one (get presented to one) in their Mind.  If an Idea has a property, that property gets presented to the Mind. In other words, I am wagering that for Berkeley there is nothing hidden in an Idea.  For how can something be before the Mind at the same time it is hidden from the Mind?  We are talking about Ideas, after all, which should be purely Intelligible.  There should be nothing hidden or obscure about them.

As a corollary to this, I will also wager that for Berkeley, if the Mind cannot tell two Ideas apart based on their properties, the Mind in fact has one, not two Ideas before it.  Nothing being hidden from the Mind in an Idea, the (putatively) distinct Ideas cannot differ by virtue of some property hidden from the Mind (such as the location of one Idea “behind” the other.  See below) .

The Ideas of Sight are individuated by their properties since the Mind tells them apart by their properties.  So what I call the ‘visible Moon’ is, actually, a set of different Visible Ideas going under the same verbal heading, ‘visible Moon’.  For were I to get right up close to the moon, what I see would be different, since it has different properties.  It would be, for example, much larger, taking up most or all of my visual field.  Doubtlessly its color would be different.  So what I see would be different.  It would be a different Object of Vision, a different Idea of Sight.  For if two things have different properties, they cannot be the identical Object, right?

The visible Moon (I mean the one I see now, as I am standing on the earth) does not exist outside my Mind.  It is immanent in my Mind.  For the visible Moon has a color, and colors exist only in the mind.  We cannot separate out even in thought Extension (for example, the width and height of the visible Moon) and Color:

Is not the Extension we see coloured, and is it possible for us, so much as in Thought, to separate and abstract Colour from Extension?



So if the visible Moon’s pale yellowish color is in my Mind, so are its width and height.  The visible Moon therefore exists only inside my mind, and not outside of it.  (Don’t worry, I am not hogging the sole visible Moon to myself.  You have another visible Moon in your mind.  This is just another case of a set of different Objects going under the same verbal heading, ‘visible Moon’.)

The ’round, luminous Plain’ that is the visible Moon, Berkeley says, is “of about thirty visible Points in Diameter” (A NEW THEORY OF VISION, paragraph XLIV).  A visible Point is the Minimum Visibile, i.e., that Object of Sight that is of a size just large enough to be seen.  Berkeley takes it to be self-evident that the Minimum Visibile cannot have parts:

…the Minimum Visibile having . . . been shewn not to have any Existence without the Mind of him who sees it, it follows there cannot be any Part of it that is not actually perceived, and therefore visible.  Now for any Object to contain several distinct visible Parts, and at the same time to be a Minimum Visibile, is a a manifest Contradiction.



Being simple, without parts, the Minimum Visibile cannot have structure.  It is merely a (barely) visible Point, with a kind of size (but with this notion of size some issues start to intrude which I will simply ignore for the moment — for at least as long as I am not absolutely forced to consider them), to be sure, but very little of that.


Arguments Using Berkeleyian Concepts

Enough of Berkeley’s Ideas of Vision for the moment, except for two last notes.  First note: above, I have been using ‘visual Idea, Visible Idea, Idea of Sight, Object of Vision, and Object of Sight interchangeably.  I will be continuing to do so.

Second note:  although Berkeley thinks of Ideas of Sight as themselves having colors, I myself share Daniel C. Dennett’s opinion that “…there are no sense-qualia, that is, no ‘inner figment[s] that could be colored in some special, subjective … sense.'”  (Dennett as quoted in Lawrence Hass, MERLEAU-PONTY’S PHILOSOPHY, Indiana University Press, 2008.)  And one wonderful milepost in my philosophical journey was James W. Cornman’s MATERIALISM AND SENSATIONS (Yale University Press, 1971), in which he uses the adverbial theory of perception to get rid of, for example, the blue of a blue afterimage, this blue standing in the way of his desire to identify the afterimage with a brain event.  But for now, I will be pretending that there are such critters as Berkeley’s Ideas of Sight that themselves have colors and (two-dimensional) shapes.

[Also discuss the fact that the notion of ‘size’ is a bit problematic if we don’t have a unit of measure for it — centimeters, inches, whatever.]

Depth Considered As A Line Ala Berkeley:  My arguments using Berkeleyian notions will start with how Berkeley explicitly conceives of depth in paragraph II of his A New THEORY OF VISION, i.e., as Distance considered as a Line extending from the Object seen to the retina one one’s eye.  (Until further notice, I will consider just one eye, as if we were Cyclopean creatures.)  Then I will turn to a conception of depth as a kind of funnel extending from the eye to the Object.

As I suggested above, there are several possible candidates — four, in fact, that I have uncovered so far — for what Line might be regarded as identical with depth considered as Distance.  It is not totally impossible, I suspect, that Berkeley is mushing all four candidates together.

Let me note at the start that the idea that a Line becomes invisible when it is completely end-wise to the eye suggests that it is visible when it is not completely end-wise to the eye — for example, when it extends horizontally in front of you.  Otherwise, what would be the point of showing that one special type of Line — the type comprising those Lines directed end-wise to the Fund of the Eye (i.e., the retina) — is invisible?  Why single out depth as if it were a special case?  Why not launch into a discussion of the claim that both breadth and depth are invisible?

First, the line could be a line in Euclidean geometry.  But these lines are invisible because they have no width or thickness, and Berkeley seems to be implicitly contrasting lines extended in breadth, which can be seen, and the non-visible line that is identical with breadth.  Breadth, i.e., a line in breadth, can be seen, he seems to imply, but depth, i.e., a line in depth, cannot.  If all Lines were invisible, there would seem to be little point in claiming that a Line visible to me because it lies horizontally before me would become invisible to you because it is directed end-wise to your eye.

Second, the line could be a light ray.  This is the interpretation that George Pitcher favors in his BERKELEY:  THE ARGUMENTS OF THE PHILOSOPHERS.  Berkeley’s topic is optics, after all, and apart from that, a light ray is what one would normally think of when talking about lines extending from the object and projecting a point onto the retina.  But I do have to wonder a bit if this is 100% of Berkeley’s meaning — for are not individual light rays traveling horizontally in front of you also invisible?  And isn’t Berkeley implying that lines in breadth are visible?  At any rate, Pitcher shows rather definitively that Berkeley’s argument will not work if the Line is considered to be a light ray.

Third, the line could be a Visible Line (and the Point he mentions in the passage above a Visible Point), such as the Blue Line and a Red Line that Berkeley says he can conceive as having been added together to form a larger line (A NEW THEORY OF VISION, paragraph CXXXI).  In addition to Berkeley’s Blue and Red Lines, I am about to introduce into the picture a Green Line.  But Line considered as a Visible Line does not fit with perfect cleanness into Berkeley’s passage above either, since it is hard to give a sense to the notion that such a Line could project a Point onto the retina, that is, extend from the Object into the eye and onto the Fund of the Eye.  Would not such a Line become invisible at some point beyond the cornea?

No, I do not intend to conduct a Buñuelesque experiment with a thin visible plus tangible wire — certainly not on my eye! — to determine at exactly which point the wire ceases to be visible and remains merely tangible as it penetrates the eye.  But bringing the wire into the picture introduces yet another candidate for Berkeley’s Line — this is the fourth possibility — i.e., a Tangible, as opposed to Visible Line.  The person already acquainted with Berkeley (perhaps more than I am at the time of this writing) will note that Berkeley makes a sharp distinction between the two — a Visible Line may be closely associated with, but is never identical with, a Tangible Line.  Visible Lines and Tangible Lines are always two different critters.  But this Tangible Line would always be invisible, even in breadth, so running afoul of what I take to be Berkeley’s implicit contrast between Lines in depth which are invisible vs Lines in breadth which are visible.

In Berkeley’s terms at least part of the Visible Line would suffer from a ‘failure to exist’ at some point past the cornea.  Yet Berkeley seems to imply that there is such a Line projecting a Point from the Object to the Fund of the Eye.  Therefore this Line cannot be a Visible Line.  So a Visible Line cannot be a candidate for what ‘Line’ means in Berkeley’s Paragraph II.

This of course already establishes part of Berkeley’s argument that depth considered as a Line is invisible, since the Visible Line cannot even be a candidate for the Line projecting a Point onto the retina that Berkeley says is depth.  But since it is still possible that such a Visible Line would be visible at, e.g. some point in front of the retina, it would not suffice to establish all that I suspect Berkeley thinks he has established regarding the invisibility of depth, that is, that depth is invisible tout court.  I will try to establish below some further considerations that, I claim, do establish this, given certain Berkeleyian notions.

To sum up:  while Line as light ray is doubtlessly the interpretation that fits Berkeley’s passage the best, the fact that not one of the four interpretations fits that passage with total cleanness heightens my aforementioned suspicion that all four may be at play — doubtlessly unconsciously — in Berkeley’s mind as he writes the passage.3  At any rate, I assert that an argument for Berkeley’s claim that depth is invisible can  be constructed based on Visible Lines, Minimum Visibles, and at least one conception of Berkeleyian Ideas (the one offered above).  This argument, I assert, does work — provided one grants Berkeleyian Minimal Visibles and the other items in the apparatus of (what I take to be) his Theory of Ideas.

Let me proceed then by introducing into the picture a Green Line  — in fact, not just a Green Line, but a bright chemical polyester Green Line.

Suppose I see a length of bright chemical polyester green bungee cord that my friend is now holding in front of me. In Berkeleyian terms, to see a length of the bungee cord is to see a succession of visible Points, an array of bright green Minimum Visibiles, one next to the other.  Nothing problematic about that.  (But notice that I suddenly shifted from ‘bright chemical polyester green’ to just ‘bright green’!  I hope to argue in a later post that ‘bright chemical polyester green’ as opposed to just ‘bright green’ requires a structure that the Minimum Visibile does not have.)  The Visual Idea of Length would then be a composite Idea comprising an array of Minimum Visibles.  This composite Visual Idea would have the property Length, and this property would appear to one, be visually presented to one, in their Mind.

By analogy, then, to see depth — to have an Idea of Sight of the Line extending endwise to the Eye, would be to see an array of Minimum Visibiles one behind the other.  This would have to be a composite Visual Idea which has the property depth, which property appears to one, gets presented to one in their Mind.  But of course the Minimum Visibles comprised by this Idea cannot have the property bright green!  Nor can these Minimum Visibiles have any other color … or at least any opaque color.   To see why, consider (per impossible) any given such Minimum Visibile.  That Minimum Visibile would be hiding the Minimum Visibile behind it.

Well, let’s consider a Minimum Visibile that is not opaque, but translucent or even transparent.  Consider the transparent Minimum Visibile first.  It cannot be completely transparent, for then it would be an invisible Object of Sight, a seen Object that is not seen.  This would obviously be a contradiction.  The Minimum Visibile would than have to have some property that would let us say that we see enough of it for it to indicate a plane in space — the plane ‘directly’ (more on this shortly) in front of the Minimum Visibile behind it.  Say, there is some sort of highlight of the sort that one might see on a (mainly) transparent sheet of cellophane or acrylic that indicates there is something occupying a particular spatial plane.  For the Visibile Minimum to have anything like this, it would have to have parts — a structure.  One part would have to be the highlight, and another part could have to be translucent somehow….not invisible.  (I will get to this translucency business in a moment.)  But we have seen that Berkeley’s Minimum Visibile cannot have parts.

Well then, let’s consider, not an (impossible) Minimum Visibile with a cellophane-like highlight, but a simply translucent one with no variation in color or light.  Let’s say it is a nice translucent light blue.  Behind it (per impossible I am sure) there is a minimal Visible of a darker blue luminously showing forth through the first Minimum Visibile.  But how would the color of the first, foremost light blue Minimum Visibile show itself to the Mind?  It must, given my postulation above that every property of a Berkeleyian Idea must present itself to the Mind, that in a Berkeleyian Idea nothing is hidden.  But as a Minimum Visibile, our light-blue Idea has no parts, such that one part could show the darker blue of the Object behind it, while another part would show its own light-blue color.  What gets presented is just the dark-blue color.  Because an Idea must present a property to the Mind if it is to have that property, the light blue idea I have postulated cannot exist.

Okay then, lets postulate a translucent “first and foremost” Idea that is the same hue of dark blue as the Idea it covers.  But since there is just one color-and-light property of luminous blue at this minimally visible point, the ‘first and foremost’ Idea cannot be distinguished by the Mind from the Idea behind it.  Moreover, the two Ideas have the same size (both being minimally visible) and the same shape (presumably round, since they are Points.)  This, I do believe, pretty much exhausts the arsenal of properties of Berkeleyian Visual Ideas that would serve to distinguish one from the other in the Mind.  The (putatively) two ideas differ in their locations, of course, but there does not seem to be any purely visual property that would enable the Mind to distinguish the two locations (one Idea with this color, luminosity, and shape on this plane; the other Idea with this other color, luminosity, or shape on the plane behind it) and get a handle on the different positions of the Ideas.  If the Berkeleyian Mind cannot distinguish (putatively) two different Ideas, those (putatively) distinct ideas are in fact one.  So in this case there is just one Idea of blue getting presented to my Mind.

So because there would have to be two Ideas were one Idea to show through behind another Idea, one Idea cannot show through another.  All Berkeleyian Ideas are opaque.  Any impression to the contrary, any apparent translucency, would have to be explained by something other than an Idea of Sight entering the picture (so to speak).  (Any takers for Ideas of Feeling and Kinaesthesia?)

Therefore, if one allows Berkeley’s notion of the Minimum Visibile, depth considered as a Line extending endwise to the Eye cannot be seen.  There is no such Object of Sight, no such visible Idea.  There cannot be a succession of Minimum Visibiles, one arrayed behind the other.  There can be only a single Point presented to one in their Mind.

This aligns nicely with the passage quoted above from A NEW THEORY OF VISION, in which Berkeley says:  “For Distance being a Line directed end-wise to the Eye, it projects only one Point in the Fund of the Eye, which Point remains invariably the same, whether the Distance be longer or shorter.”  Take the bright polyester chemical green bungee cord so that it extends end-wise towards the eye, mentally reduce that end to a single Minimum Visibile, and — voila!  One sees just that one Point, which will remain the same (abstracting away all perturbations of that Point) regardless of whether the Line behind it becomes shorter or longer accordingly as the bungee cord is stretched or allowed to relax.




Depth Considered As A Funnel:  Can we rescue the notion that there exist visual Ideas of depth if we no longer insist that depth be conceived of as a Line?  What if we thought of depth as a kind of funnel extending from the eye to the Object?  Any given Visual Idea that is in front of another one could then have the structure necessary for it to appear in front of the Visual Idea behind it, since, no longer being a Minimum Visibile, it can now have parts.  (Perhaps the behind-most Visible Idea could be a Minimum Visibile without parts.)

But this attempt to prevent the notion of a Visual Idea of depth from biting the dust fails once one asks themselves whether Visible Ideas can have a Minimum Thickness as well as a Minimum Diameter.  Since such a thickness could never appear (can one turn a Visible Idea around so as to see its side?), and since an Idea cannot have (I am assuming so far) any property that does not appear to one in their Mind, it would seem that the Minimum Visibile could not have a thickness.  (The Visible Moon in that regard would be like an infinitely thin slice of yellow cheese.)   In that case, it would, like a plane in geometry, have only two dimensions — height and width.  In spite of Berkeley’s hesitation (at least I am getting hints at such a hesitation as I go through A NEW THEORY OF VISION) to treat Ideas as objects in a Euclidean Geometry, I think he would be forced to do so at least in regard to the distance between a Visual Idea and any Visual Idea behind it.  Between any two such Visual Ideas there would have to be an infinite number of planes, since between any two points on a Euclidean line there are an infinite number of other points.  There would, then, have to be an infinity of Minimum Visibiles (differentiated somehow, say, by color?) stretching from the Object (say, the bright polyester chemical green bungee cord your friend is holding) you see to your Eye.  This would be so no matter how shallow the depth is.

But such a Line would be a Visible Line, i.e, a sensible Extension by hypothesis.  And Berkeley is sure that sensible Extension is not infinitely divisible:

For, whatever may be said of Extension in Abstract, it is certain sensible Extension is not infinitely Divisible.  There is a Minimum Tangibile, and a Minimum Visibile, beyond which Sense cannot perceive.  This every ones Experience will inform him.



Therefore, it would seem, Berkeley would have to reject that notion that there can be a succession or array of (non-minimal, i.e., composite) Visible Ideas lying one behind the other in a kind of funnel.

But maybe it could be objected that Berkeley’s argument that a sensible Extension cannot be infinitely divisible because it is a composition of Minimal Visibiles applies only to visible Lines in breadth, and only to finite minds.  The fact that (in Berkeley’s world) a Minimal Visibile would disappear should its breadth decrease prevents a sensible Line in breadth from becoming divided infinitely.  But no such consideration would hinder an infinite number of composite Ideas lying one behind the other for any intelligence that could perceive an infinite number of Ideas at the same time.   (For now I will leave the ‘at the same time’ part as an exercise for my ((probably)) non-existent reader; I really should get back to this at some point, though.)

It would seem that by the time he writes A TREATISE CONCERNING THE PRINCIPLES OF HUMAN KNOWLEDGE, he flat-out rejects that idea: “There is no such thing as an infinite number of parts contained in a finite quantity.” At the time of this writing (November 08, 2015), I do not know if Berkeley’s argument for this claim would fail to hold in the case of composite Visibile Ideas lying one behind the other.  So for now I will leave open the possibility that perhaps an infinite intelligence, i.e., God, could perceive depth visually.  But how odd that would be, since depth is always perceived from a particular finite perspective!  (More on this later, I promise.)

Anyhow, since us mere mortals, I assume, cannot perceive an infinite number of Ideas — certainly not at the same time! –, I think Berkeley has to reject the idea that depth could be visible to merely finite intelligences such as human beings as a kind of funnel composed of composite Ideas of Vision.


No Visible Idea Of Depth Considered Either As A Line Or As A Funnel:  To sum up, then:   there is no Visible Idea of depth considered as a Line because the Minimum Visibiles composing this line cannot have structure because they cannot have parts.  And there is no Visible Idea of depth considered as a funnel because a sensible Line cannot contain an infinite number of parts.

A Berkeleyian Idea can never have anything behind it.  Possessing no element of hiddenness, it is all frontal.  “[V]isual appearances are altogether flat”, as George Pitcher puts it.

That there is no Visible Idea of depth means that we cannot see an Object at a distance — at least not strictly speaking, or, as Berkeley would put it, ‘immediately and of itself’.  For on Berkeleyian terms seeing an Object at a distance would surely have to be a combination of the visible Idea that is identical with that Object (say, the visible Moon) plus the visible Idea of depth.  But there is no visible Idea of depth available to combine with the visible Moon.

Speaking for myself, at least, I never currently experience, and do not remember ever experiencing visually, objects that are not at least some quasi-distance from me considered as the critter seeing.  Who knows how I experienced things before I was three, the age at which memories start to become permanent.  But now, at at least, the closest I can come to a visual experience of objects not at a distance (from…?)  occurs when I shut my eyes, and experience after-images floating against a dark ground which I take to be the shadow-side of my eye-lids.  (I take it that I am seeing my eyelids when I visually experience this background because, after all, I do get experience an ocher-ish translucency when light from the sun hits my closed eyelids directly.)  There is no definite distance of the afterimages from the ground behind them.  Nonetheless, behind is a distance concept — it is just that here we are talking about a degenerate case of distance, an infinitely poor cousin of the phenomenon in its full-blown reality.  Likewise, the afterimages are there before me without being any definite distance from … I want to say (fully realizing that I risk sounding like a complete weirdo without the slightest trace of academic respectability) ‘that ground of invisibility that I am qua see-er and that is directly in front of the after-images’.  Pretend for the moment that this ‘ground of invisibility that I am qua see-er’ stuff makes any sense at all or represents anything that can be communicated to a rational person.4  This would make me qua see-er a field, a background to what I experience visually, would make me, myself, a background for my after-images (what a thought!), an instance of what Lawrence Hass is alluding to when he says:

Indeed, the conditioning “background” for a perceptual figure isn’t necessarily behind it, but is often before and around it.

Lawrence Hass, MERLEAU-PONTY’S PHILOSOPHY, Indiana University Press, p. 30


But there before and directly in front of are of course distance concepts, even though these concepts as applied here are degenerate, poor-cousin instances of the real thing.5

So I am myself unable to imagine seeing an object that is not at some sort of at least quasi-distance (from me as field of invisibility in front of the after-images?).  Nonetheless, I have encountered someplace without currently being able to dig it up again, an account of a young (Asian) Indian person who regained sight after having  been blind from birth.  This person described, if I remember correctly, their vision as being like touch (a sense they would be more familiar with obviously than sight) in that (to paraphrase from memory) ‘there is no distance between me and what I see’.  Clearly, the fact that I cannot imagine this does not preclude this from being a fully accurate description of what this person experiences.  Quite possibly, then, there may be unusual, degenerate cases of visual experience that match what Berkeley takes to be proper to vision taken by itself:  i.e., visual experience of flat after-image-like patches with no depth at all (and no sense of solidity or resistance at all, if I may throw this in here now…see Berkeley’s paragraphs L and LI below) and at no sensed distance at all — not even a quasi-distance — from the experiencer.

In the normal, usual, non-degenerate case, of course, we normally do have quite a strong, powerful sensation of depth when we open our eyes.  And Berkeley would even say that there is a (weak) sense in which we do see depth then.  For in normal vision the visible Ideas suggest and are associated with Tangible Ideas, including Ideas of the body’s possible motion.  These, Berkeley argues, are so entwined with and entangled with Ideas of Sight that it is difficult to distinguish the two.  But distinguish them one can, Berkeley think, provided one gives the endeavor sufficient effort, attention, and “narrowness”.  One will then see, Berkeley is persuaded, that “. . .neither Distance, nor things placed at a Distance are themselves, or their Ideas, truly perceived by Sight” (A NEW THEORY OF VISION, paragraph XLV).  If one can be said to see Distance, or Objects placed at a Distance, it is only in the sense that through the Idea of Sight we can get to the Tangible Idea of depth.  One “mediately” sees depth in this sense — and we still call it ‘seeing’ depth because the effort to separate out the visual Idea from the Tangible Idea is so great that out of laziness and lack of ambition we label the Visual/Tactile combination with the name ‘Idea of Sight.’  Immediately, truly, and of itself, however, we do not see depth.

But as they say so often on the InterWebs, read the whole thing yourself:

L.  In order therefore to treat accurately and unconfusedly of Vision, we must bear in mind, that there are two Sorts of Objects apprehended by the Eye, the one primarily and immediately, the other secondarily and by Intervention of the former [mediately].  Those of the first sort neither are, nor appear to be without the Mind, or at any Distance off:  they may indeed grow greater, or smaller, more confused, or more clear, or more faint, but they do not, cannot approach or recede from us.  Whenever we say an Object is at a Distance, whenever we say it draws near, or goes farther off, we must always mean it of the latter sort, which properly belong to Touch, and are not so truly perceived, as suggested by the Eye in like manner as Thoughts by the Ear.

LI.  No sooner do we hear the Words of a familiar Language pronounced in our Ears, but the Ideas corresponding thereto present themselves to our Minds:  in the very same Instant the Sound and the Meaning enter the Understanding.  So closely are they united, that it is not in our Power to keep out the one, except we exclude the other also.  We even act in all respects so if we heard the very Thoughts themselves.  So likewise the secondary Objects, or those which are only suggested by Sight, do often more strongly affect us, and are more regarded than the proper Objects of that Sense; along with which they enter into the Mind, and with which they have a far more strict Connexion, than Ideas have with Words.  Hence it is, we find it so difficult to discriminate between the immediate and mediate Objects of Sight, and are so prone to attribute to the former, what belongs only to the latter.  They are, as it were, most closely twisted, blended, and incorporated together.  And the Prejudice is confirmed and riveted in our Thoughts by a long Tract of Time, by the use of Language, and want of Reflection.  However, I believe any one that shall attentively consider what we have already said, and shall say upon this Subject before we have done, (especially if he pursue it in his own Thoughts) may be able to deliver himself from that Prejudice.  Sure I am it is worth some Attention, to whoever would understand the true Nature of Vision.

A NEW THEORY OF VISION, paragraphs (of course) L and LI.  Emphasis mine.


As I continue in this project, I will have a great deal to say in a Merleau-Pontyian framework about the “Ideas” of Sight and Touch getting closely twisted, blended, and incorporated together in such a way as to generate, not just our perception of depth, but our opening out onto the brave new extra-mental world outside our skulls . . . this world so full of extraordinary things such as bark whose roughness and hardness we can see, silk whose smoothness we can see, glass whose brittleness we can see, the doorknob whose hard metallic coolness we can see, the Maple syrup whose viscosity we can see, the linen whose dryness we can see from a certain fold in it, the little mound of yellow ocher oil paint whose essential gookiness we can see, and the carpet with that peculiar woolly red.  Not to mention the bungee cord regaling our senses with that bright chemical polyester green.



Today’s homage to Plato’s SYMPOSIUM is Taylor Lautner.


Now if only a werewolf that hot were longing for me in feverish desperation, I wouldn’t mind that much the problems this would cause.  (For example, what would I do with my James Dean-like vampire boyfriend Edward?)










Let me define ‘foil’ here as ‘a person or thing that contrasts with and so emphasizes and enhances the understandability of another’.


Henceforth, following Stephen Priest, I will refer to the phenomenon discussed in the paper as the ‘ekstasis‘.


3 If I may be permitted a certain amount of snark, I will entertain the possibility that these four different possible meanings of the word ‘Line’ followed one another in a kind of tag game in Berkeley’s mind so quickly that he failed to distinguish between them.


4 Fine, I’ve laid out what I actually think. So sue me. I fully expect to forever lose any chance at all of gaining any academic respectability — even more so than if I were an artist. (I am 9/10 joking, of course, as may be evident.)


5 Interesting that visual ground/background concepts should be so closely tied to distance/depth concepts.










From 09/19/2015 to 10/25/2015:  Made numerous changes.

11/01/2015:  Added paragraphs attempting to articulate the possibility that there are unusual cases of visual experience, among some formerly blind people who have regained sight, which may involve no sensation of distance at all — not even of degenerate, poor-cousin sensations of distance.

11/07/2015:  Added a discussion of the various possible meanings of the word ‘Line’ in Berkeley’s Paragraph II.

11/08/2015:  Revised the discussion of the notion that a sensible Extension cannot be infinitely Divisible.

Shells And Peanuts Again (And Again…And Again…In A Never-Ending GROUNDHOG DAY)


So one more time — but this time with feeling:  following Relevant Logic, we can avoid Classical Logic’s paradoxes of Material Implication, according to which the following statements are true…

1) If Cliff lives in Houston, Texas, then the earth has just one moon

2) If Cliff lives in Orange County, California, then Paris, Texas is the capital of France

…by insisting that the antecedent p be relevant to the consequent q.  The question of course now is:  what is the relation that makes p relevant to q?  In my previous post, one can, if they are sufficiently drunk, just barely make out the answer:  ‘whatever condition c along with (in the case of subjective probability) knowledge k makes the conditional probability of q equal to 1 given p is what makes p relevant to q.   Sometimes this ‘whatever’ is identical with an INFORMATION THAT relation (p is information that q); sometimes it is not.

( When the relation is identical with the INFORMATION THAT relation, c is the channel of information that allows p to be information that q. When the relation is not identical with the INFORMATION THAT relation, c consists in background conditions, especially causal laws, which, just as in the channel-of-information case, make the conditional probability of q given p 1. My current claim is that even when the relation is not identical with an INFORMATION THAT relation, it has a structure in common with the INFORMATION THAT relation.)

What I propose to do now in the next several posts is go through the> various examples I’ve mentioned previously (shell games, children with measles, wormy red apples, the ringing of defective doorbells, and so on) and a) work out when, in the example, the IF-THEN relation is identical with an INFORMATION-THAT relation and when it is not, and b) see what strange conclusions arise from this account of the relevance-making relation.  Maybe some of these will be so awful that one would prefer Classical Logic’s paradoxes of Material Implication.

In this post I propose to work through Dretske’s famous shell game example.  In that example, one will remember, a peanut is hidden under one of four shells.  I know from whatever reliable means that there is a peanut under 1 of the shells.  This knowledge reduces the probability that (a | the ) peanut is under shell #4 from 1 in whatever billions to just 1 in 4. Maybe my waffling here between ‘a’ and ‘the’ opens up a can of worms; I am unsure. I turn over shell #1.  There is no peanut under that shell.  The conditional probability that the peanut is under any given one of the remaining shells is now 1 in 3.  I turn over shell #2.  Empty.  The conditional probability that the peanut is under any given one of the remaining shells is now 1 in 2.  I say:

If shell #3 is empty, Then the peanut is located under shell #4

And what I say is surely true!  True, true, twue!!!!!  For if shell #3 turns out to be empty, then the conditional probability that the peanut is under shell #4 is 1.  The condition c that makes this conditional probability 1 given p is the characteristic that objects have — at least those objects large enough to be immune to whatever quantum weirdness — of persisting in one place unless molested.  The electron (at least according my remembered ((and almost certainly garbled in my memory)) pronouncement of a chemistry TA I had as an undergraduate) one finds orbiting this or that particular atom could have been on the nose of the Mona Lisa before getting observed, and might be there again a moment later.  But the peanut is not going to jump around like that, leaping to shell #1 one moment while unobserved, and onto the nose of the Mona Lisa the next moment.  It is going to stay placidly and inertially where it is — under shell #4 — while one turns over shell #3 and observes it to be empty.  Given this background fact about objects the size of peanuts, shell #3’s proving to be empty rules out the possibility that the peanut is not under shell #4.

Here the relevance-making factor — what makes the IF-THEN statement I uttered true — is also that factor that would make shell #3’s turning out to be empty INFORMATION THAT the peanut is located under shell #4.

But let’s turn back the clock.  I am now back at the point at which I am turning over shell #1.  Empty.  If I now jumped the gun and said (as if this were the movie GROUNDHOG DAY ((which I have not seen, by the way)), in which one atrocious day gets repeated again and again so that…”The phrase “Groundhog Day” has entered common use as a reference to an unpleasant situation that continually repeats, or seems to.”):

If shell #3 is empty, Then the peanut is located under shell #4

what I say would surely be false. Or at least it must be false if what I said in my first paragraph is true.  For were I to turn over shell #3 and discover it to be empty, the conditional probability that the peanut is located under shell #4 would not be 1, but 1/2.  So the same IF-THEN statement would be true at one time, and false at another.  And it would be true relative to my knowledge k at one time (I know that shells #1 and #2 are empty), and false relative to my lack of that same knowledge at a different time.

Not coincidentally, the (possible) emptiness of shell #3 being information that the peanut is located under shell #4 is something that is true at some times and false at other times, and is relative to one’s knowledge (or lack thereof) in exactly the same way.  In this particular case, what makes the If p Then q statement true is identical with what makes p information that q.

Now turn back the clock yet one more time (I warned you that this is another iteration of GROUNDHOG DAY).  This time I already know from a reliable source of information, even before I have turned over any shells, that the peanut is located under shell #4.  I turn over shell’s #1 and #2 as before.  Both are empty, as before.

But now, shell #3’s proving to be empty upon turning it over would no longer be INFORMATION THAT the peanut is located under shell #4.  This is so for at least two reasons.  First, according to Information Theory, “old information” is an oxymoron.  It is not information at all.  Shell #3’s turning out to be empty is not going to tell me, inform me, show me, that the peanut is under shell #4 because I already have this information.

Second, to generate information is to effect a reduction in possibilities.  In Dretske’s example of an employee selected by a succession of coin flippings to perform an unpleasant task, the eventual selection of Herman out of 8 possible choices reduced the number of possibilities from 8 to 1.  The selection of Herman generates INFORMATION THAT Herman was selected because of this reduction in possibilities.  But in my situation, already knowing that the peanut is located under shell #4, the number of possibilities regarding where the peanut is located is already just 1.  Turning over shell #3 to prove that it is empty does not reduce the number of possibilities from 2 to 1 — that number was 1 in the first place.  So in my situation shell #3’s proving to be empty does not generate, is not information that, the peanut is located under shell #4.

That the number of possibilities is in my situation just 1, not 2 means of course that the conditional probability that the peanut is located under shell #4 is not 1/2, but 1.  This means that shell #3’s proving to be empty does not make the conditional probability that the peanut is located under shell #4 equal to 1.  For that conditional probability was already equal to 1.  We are supposing that I already know that the peanut is located under shell #4, but I would not know this if the conditional probability were not already 1.  The very strange conditions that would have to obtain to make the conditional probability say, 1 in 2 would rule out this knowledge.  The peanut would have to exist under both shell #3 and shell #4 at the same time while unobserved, then “collapse” to a single location under one of the shells upon turning over the other shell and observing its empty condition.  So to say that I already know the location of the shell is to say that the conditional probability the peanut is at that location equals 1.

Now in the first paragraph of this screed I said (maybe ‘pontificated’ is the better word):

…whatever condition c along with (in the case of subjective probability) knowledge k makes the conditional probability of q equal to 1 given p is what makes p relevant to q.

Here my knowledge k (the peanut is located under shell #4) presupposes certain conditions c (the peanut does not exist in a kind of locational smear when unobserved, only to collapse to a single location when an observation is made).  Here p (shell #3 proves to be empty) along with k and the presupposed c definitely does not make the conditional probability of q equal to 1.  This conditional probability was, given k and its presupposed c, already 1.  So in my situation, p is not relevant to q.

So were I, in my situation of already knowing that the peanut is located under shell #4, to  utter GROUNDHOG-DAY-wise:

If shell #3 is empty, Then the peanut is located under shell #4

My statement would be false for exactly the same reason that the following is false:

If Cliff lives in Houston, Texas, then the earth has just one moon

In both cases, the antecedent is irrelevant to the consequent by failing to make the conditional probability of the consequent 1, rendering the corresponding IF-THEN statement false.  The antecedent “If shell #3 is empty” is in my situation irrelevant to the consequent “the peanut is located under shell #4” in exactly the same way that “Cliff lives in Houston” is irrelevant to “the earth has just one moon.” (In exactly the same way?  Yes, at least according to the perhaps narrow definition of relevance I postulated above.  But does this narrowness weaken my claim?  Might the emptiness of shell #3 be relevant to the peanut’s being located under shell #4 in some ((perhaps)) vague way even given my knowledge k?)

To re-iterate (this is a GROUNDHOG DAY post after all), the shell statement is false in my situation for exactly the same reason that “shell #3 is empty” fails to be information that “the peanut is located under shell #4.”  In this particular case, the relevance-making condition which is lacking is identical with an INFORMATION THAT relation.

If so, however, one is faced with a consequence that may strike some as at least equally unappealing as the paradoxes of Material Implication.  (Warning:  I am about to wallow in more GROUNDHOG DAY iterations.)  For when I utter:

If shell #3 is empty, Then the peanut is located under shell #4

the statement I utter is false, but when you hear:

If shell #3 is empty, Then the peanut is located under shell #4

and your situation is such that you have seen both shells #1 and #2 are empty and you do not know that the peanut is located under shell #4, the statement you hear is true!  The same statement is both true and false at the same time, given different situations.  Put another way, what is true or false (at least for a certain class of IF-THEN statements) is not the statement, but the statement as it shows up in a particular situation.

At least in the case of subjective probability, then, truth is relative in much the same way that Galilean motion is relative.

On a purely autobiographical note, I am not sure this relativity bothers me any more than Galilean relativity (there is the possibility of an ultimate reference frame) or for that matter Einsteinian relativity (there is no ultimate reference frame which would assign a single value to the speed of a moving object) does.  The idea that a person walking inside a flying jet is moving at a speed of 1 mile per hour relative to the reference frame of the jet but at a speed of 501 miles per hour relative to the reference frame of the earth (suppose the jet’s speed is 500 miles per hour) is perfectly intuitive even though it means a contradiction is true (the person is both moving at a speed of 1 mile per hour and is not moving at a speed of 1 mile per hour).

Likewise, the contradiction of claiming that (GROUNDHOG DAY alert):

If shell #3 is empty, Then the peanut is located under shell #4

Is both true and false at the same time seems to me to be intuitive if one casts it as a matter in which a conclusion’s following (not following) from its premise hinges upon what other knowledge or evidence one has (does not have).  But I do suspect that some would prefer to this relativity of truth and the attendant tolerance of contradiction the weirdness of Classical Logic’s Material Implication which arises from treating Implication as purely truth functional.


This statement (GROUNDHOG DAY alert):

If shell #3 is empty, Then the peanut is located under shell #4

is variously true or false — even at the same time — depending upon the already-existing knowledge (or lack of it) of the person uttering or hearing the statement.  By contrast, the following statement is true regardless of what anyone knows, and true in any situation:

If the peanut is located under shell #4, Then the peanut is located under shell #4

In other words:

If p Then p

That the peanut is located under shell #4 clearly suffices to make the conditional probability that the peanut is located under shell #4 1.  So according to my account of what makes p relevant to q, p is relevant to p. p is relevant to itself.  p is in a relation to itself.  I am of course beginning to sound very weird (or maybe weirder) and very Hegelian…and I am beginning to wonder if I can get out of this weirdness by talking about 1-place relations, which are perfectly respectable mathematically.  (Not just 1-place relations!  0-place relations are also quite respectable mathematically!  What is more, Chris Date’s Relational Algebra recognizes two 0-place relations, TABLE DEE which is identical with the that weird proposition in logic TRUE, and TABLE DUM, which is identical with the equally weird proposition in logic FALSE!!!!!!!)

In this section of my post, I will decide that I am Relational-Algebra-weird by treating “If p Then p” as a 1-place INFORMATION THAT relation.  This in turn is part of my larger project to go through each example of IF-THEN statements I’ve adduced in previous posts and decide whether the relevance-making RELATION is in that particular case an INFORMATION-THAT relation or not.

Remember that to generate information is to reduce the number of possibilities to one.  When Herman is selected through 3 successive coin flips out of 8 candidates to perform the unpleasant task, the number of possibilities is reduced from 8 to 1.  The probability of Herman’s getting selected was initially 1 in 8, then became 1.  Whenever any event occurs, some states of affairs comes to obtain, some thing acquiring some property, the probability of that occurrence goes from 1 in (some usually gargantuan number) to just 1.  So any occurrence of p (Herman’s getting selected, shell #3 proving to be empty, a ruby having formed through whatever geological processes exactly one mile underneath where I happen to be sitting now typing this disreputable screed into a WordPress blog, the doorbell’s ringing) generates information.  Sometimes the occurrence of p generates information that q (that the peanut is under shell #4…that someone or something is depressing the button outside….).  But whatever else the occurrence of p generates information about, it generates at the very least the information that p.  Herman’s selection generated the information that Herman was selected, whether or not this information gets transmitted from the source situation in which the selection occurred (the room where the employees performed 3 coin flips) to the situation which is waiting for the information (the room where the boss is sitting).  When the information does get transmitted from source to receiver, the INFORMATION THAT relation is a 2-place relation comprising two situations, source and receiver.  When the information does not get transmitted, but stays where it is in the source, the INFORMATION THAT relation is a 1-place relation, comprising simply the source situation.

When the relevance-making relation that makes If p Then q true is an INFORMATION THAT relation, the occurrence (obtaining, existence) of p generates the information that q.  We have just seen that the occurrence (obtaining, existence) of p generates the information that p. So we get:

If p Then p

as a 1-place INFORMATION THAT relation.  Rather than saying, rather weirdly and rather Hegelianishly, that p is related to itself by virtue of being relevant to itself, we simply say that there exists a 1-place relation comprising the source at which the information that p was generated, and only that source.  This remains an INFORMATION THAT relation even though nothing ever tells me, informs me, shows me that, for example, a ruby exists exactly 1 mile beneath where I am now sitting, typing this disreputable screed into WordPress, or that the peanut is in fact underneath shell #4.  It is just a 1-place, not a 2-place relation, and an INFORMATION THAT relation to boot.

So in all of the following,

If a ruby exists exactly 1 mile underneath where I am now sitting, Then a ruby exists exactly 1 mile underneath where I am now sitting

If the peanut is located underneath shell #4, Then the peanut is located underneath shell #4

If Herman was selected to perform the unpleasant task, Then Herman was selected to perform the unpleasant task

the general relevance-making relation, i.e., the occurrence (obtaining, existence) of p making the conditional probability that p equal to 1, is identical with an INFORMATION THAT relation.  (My ((probably non-existent)) reader will remember that the relevance-making relation is not always an INFORMATION THAT relation.)

And this (after having brought in a ruby example and a Herman’s getting selected example) concludes my working through of most of the peanut-under-a-shell examples.  I still have one more peanut and shell example to work through, namely,

If I turn over shell #4, I will see the peanut

which I will work through in a future post.


Today’s homage to Plato’s SYMPOSIUM is Channing Tatum, who has recently appeared in MAGIC MIKE II.


Channing Tatum is the very walking, talking, breathing, living definition of the words ‘age 35 and beautiful and sexy.’  One of these days I will get around to contemplating Plato’s Form of Beauty itself.  For now, though, I will rest content just contemplating the form of Channing Tatum.


July 18, 2015:  extensive revisions made in probably futile attempt to hide the vastness of the extent of my confusion.

July 21, 2015:  made one more revision in order to try to hide the lack of control I have over the subject matter.

August 02, 2015:  made yet another revision for the same dubious reasons as listed above.

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Shells, Peanuts, And Doorbells: Subjective Probability And The Relevance-Making Relation

So far then, we have the following:  following Relevant Logic, we can avoid Classical Logic’s paradoxes of Material Implication, according to which the following statements are true…

1) If Cliff lives in Houston, Texas, then the earth has just one moon.

2) If Cliff lives in Orange County, California, then Paris, Texas is the capital of France.

…by insisting that the antecedent p be relevant to the consequent q.  The question now is:  what is the relation that makes p relevant to q?  I propose that this relation (henceforth the ‘CONDITIONAL PROBABILITY IS 1 relation) can be stated as follows:  given p, the conditional probability of q, (under conditions c, and possibly given knowledge k) would be, or would become 1.

We will see that this relation involves a dependency on p of the value of the conditional probability of q; this dependency though is different from the dependencies I’ve discussed in the previous posts. This dependency is the relevance-making relation we are looking for in our quest to escape from the evil clutches of the Classical Logician.


There are two items in the way I have just stated the CONDITIONAL PROBABILITY IS 1 relation that cry out for discussion.  The first item is the distinction between subjective and objective probability.  (I am a bit surprised that I have not yet seen so far a discussion of this distinction by Dretske, though perhaps I have run across such a discussion but forgotten about it.) The second item is the phrase ‘given that.’

OBJECTIVE VS. SUBJECTIVE PROBABILITY:  In the doorbell examples given in the post below, the CONDITIONAL PROBABILITY IS 1 relation is in both cases objective. In the non-poltergeist example, were the doorbell ringing, the conditional probability would be 1 that someone or something is depressing the button outside. This probability would be 1 regardless of what anyone thinks, knows, or feels. The probability is objective. Likewise, in the poltergeist example, the conditional probability that the doorbell is ringing inside were I to press the button outside would be 1, regardless of what anyone thinks, knows, or feels. In both the poltergeist and the non-poltergeist examples, the CONDITIONAL PROBABILITY IS 1 relation is objective.

By contrast, when I first come across the four shells (in a situation in which I already know that there is a peanut located underneath one of the shells), the conditional probability that the peanut is underneath shell #4 would become 1 in three were shell #1 to prove to be empty; would then become 1 in 2 were shell #2 prove also to be empty, and finally would become 1 were shell #3 to turn out to be empty.  In each case, starting from the very beginning, the conditional probability hinges upon what I already know about the situation and changes with the alterations in my knowledge.  The CONDITIONAL PROBABILITY IS 1 relation in this case is subjective.

Henceforth I will use the phrase ‘would be’ to suggest that the CONDITIONAL PROBABILITY IS 1 relation is objective, and ‘would become’ to suggest that the relation is subjective.  ‘Would be’ suggests that the conditional probability is set from the very beginning and does not change with changes in a person’s knowledge of the situation; ‘would become’ suggests that the conditional probability is not fixed from the very beginning, and does change with increases (or decreases) in a person’s knowledge.

If we allow both objective and subjective probability and identify the relevance of p to q with the CONDITIONAL PROBABILITY IS 1 relation, we then get the result that IF-THEN statements are relative when the relevance relation is based on subjective probability.  In your situation, when you have first come upon the 4 shells (and you may not even know that there is a peanut is located underneath one of the shells!), the statement:

1)  If shell #3 turns out to be empty, Then a (the) peanut is located under shell #4

is false, because in your situation the Conditional Probability that a peanut is located under shell #4 would clearly not become 1 were shell #3 to turn out to be empty.  But in my situation, given what I know, that statement is true.  The Conditional Probability would definitely, in my situation, become 1 were shell #3 to prove to be empty.  So at least those IF-THEN statements belonging to a certain class — i.e., those whose relevance relation is based on subjective probability — display a relativity similar to the Galilean relativity of motion.

If one wants to avoid this (possibly, for some — at least for me –) counter-intuitive, paradoxical-seeming result, they may want to rule out subjective probability and base IF-THEN statements only on objective probability.  But what would ‘objective probability’ be in the case of the shell game?  I think it makes intuitive sense to claim something like:  ‘given that the peanut was located under shell #4 from the very beginning, chances were always 100% (the conditional probability was always 1) from the very beginning that the peanut was under shell #4.  (In other words, given p, the conditional probability of p is 1.  OMG — If p Then p!)   But let’s take a closer look at the phrase ‘given that’.

GIVEN THAT:  ‘Given that p, the conditional probability of q is 1′ means, I take it, that what the conditional probability of q is hinges upon, depends upon, p.  In the non-poltergeist doorbell example, that conditional probability of the button outside being pushed is 1 hinges upon the doorbell’s ringing.  If there is no ringing, the conditional probability of the button’s being depressed is not 1, but 1/100, or 1/100,000, or whatever.  (Remember that the conditions c of the doorbell’s defective wiring are such that 1% of the time the doorbell does not ring when the button outside is getting pushed.)  No ringing, no conditional probability equaling 1.   In the poltergeist doorbell example, that the conditional probability of the doorbell’s ringing inside is 1 and not 1/2, or 1/10,000, or whatever, hinges upon my pressing the button outside.  (Remember that in this example the conditions c of the doorbell’s defective wiring are such that 1% of the time the doorbell rings even when no one or nothing is depressing the button, creating the impression that a poltergeist must be dwelling inside the doorbell apparatus.)  No pressing of the button, no conditional probability equaling 1.

Note that this is a case of the value of the conditional probability of q hinging upon p.  This is to be distinguished from, for example, the ringing’s causally depending upon the button’s getting depressed, or the fact that I am about to see the peanut causally depends upon my lifting shell #4 (plus other factors).

Now if we do not allow subjective probability, the only GIVEN THAT relation that holds in the case of the shell game example is ‘given that the peanut is under shell #4, the conditional probability of the peanut’s being under shell #4 is 1’.  This is the only case that does not depend upon what a person already knows.  So statements 1 through 3 below would all be false for exactly the reason that 4) is false:  there is no longer any relation that would make p relevant to q by p‘s giving the conditional probability of q the value of 1:

1)  If shell #3 turns out to be empty, Then a (the) peanut is located under shell #4

2) If shell #1 turns out to be empty, Then a (the) peanut is located under shell #4

3) If shell #2 turns out to be empty, Then a (the) peanut is located under shell #4

4)  If Cliff lives in Houston, then a (the) peanut is located under shell #4

But there are situations in which statements 1 through 3 are true — situations in which my knowledge and yours vary.  I submit then that the price of jettisoning subjective probability is one that is too high to pay.  We need to keep subjective probability, and along with it the Galilean-like relativity of those IF-THEN statements whose relevance-making CONDITIONAL PROBABILITY is 1 relation is an instance of subjective probability.

Let me see what I will make of all of this in the morning, when I am sober.

Today’s homage to Plato’s SYMPOSIUM comprises Sal Mineo and the guy he crushed on, James Dean.


Beauty so wonderful, so fleeting.