Tag Archives: Logic

The Role Of Informational Content In Establishing Relevance In Relevant Logic

“This current version of the notes is not yet complete, but meets I think the
usual high standards for material posted on the internet.”  (Link.  No, I have not read the paper apart from this snippet.)  Please feel free to comment if you have any corrections or objections to the disquisition below, or email me at cliffengelwirt@gmail.com. 

 

Logic first became interesting to me when I entered the DBA field and started reading the works of C.J. Date, Hugh Darwen, and Nikos Lorentzos on the foundations of relational databases.  While reading in logic, I became intensely interested in Edwin D. Mares’ book RELEVANT LOGIC A PHILOSOPHICAL INTERPRETATION, which seemed to tie in — I am apparently not the first to notice this! — in a very natural way with Fred I. Dretske’s classic work, KNOWLEDGE AND THE FLOW OF INFORMATION.  As an exercise in writing to learn Mares’ book I have been for a while entering posts on this blog on the topic of Dretske’s theory of informational content as it relates to Relevant Logic.

Up until now, these posts have been nothing except an effort to decide what my position is on the topic.  They pretend to be nothing more than efforts to get my own thoughts in order.  As a result, I have not been terribly afraid to be (just occasionally, I hope!) simply mistaken and (worse) unclear.

Basically, I was thinking out loud in order to decide what I do think about the topic.  Even though these exercises in thinking out loud were both tentative and preliminary, I have found it to be a useful discipline in performing them in public, where there is always the possibility that someone actually engaging with the posts (in other words, someone who is not merely a troll) may legitimately, pointing to specifics, exclaim ‘THIS IS SIMPLY WRONG!!!!’ or ‘THIS IS CONFUSED!’

Lions And Trolls Oh My! But now that I am suffering under the delusion that I do have my thoughts on the topic in something vaguely resembling order, I am now actively throwing them out to the lions in order to see what survives intelligent, informed criticism. ((I am assuming there are lions out there who are not only hungry, but also intelligent and informed. As regards lions I keep thinking about Ned Rorem’s LIONS (A DREAM) which I once heard on WFMT in Chicago… but I digress.)) Please consider this post and the the posts linked to here as a request for comment.

As each section of this disquisition takes (almost) final shape, the link to it will become active. Each section will be kept as short as possible partly as an troll-control device: the brevity of each piece makes it easier to force the troll to state a specific objection to a specific assertion ((has the troll misstated the assertion (most of the time intentionally but sometimes not)? If so, challenge them to state it in their own words — honestly this time. Once the troll has correctly stated it, do they think the assertion is wrong? If so, why?  Does the troll think the assertion is unclear?)) rather than allowing the troll to rely on abusive innuendo.

The Problem

What Is Relevance Anyhow?

The Relevance-Making Relation Is Not The Causal Relation

The example that at least initially makes treating the relevance-making relation in terms of Dretske’s notion of informational content attractive: Dretske’s Doorbell Example.

This seems to run aground on the tautology IF p THEN p. The revisions needed to accommodate this tautology.

The ‘peanut is under which shell’ example. Will this example end up making Relevant Logic at least as weird and bizarre as Classical Logic by making the truth of implication statements relative to what one knows?

The measles and wormy red apples example.

******

No post of mine can do without an homage to Plato’s SYMPOSIUM. Here the homage will take the form of Channing Tatum.

ChanningTatumTotalBeauty_0

Edit Log: June 04, 2017: Made some minor changes.

June 10, 2017:  Made some minor changes.  Removed a joke I think wasn’t                                                          working.

June 14, 2017:  Added quote at the top.

Advertisements

Doorbells, Rubies, Shell Games, And Implication: An Example That Makes Treating Implication As An Information-That Relation Attractive

The Problem:  What Does Relevance Consist In?  Following Relevant Logic, we can avoid Classical Logic’s paradoxes (or at least weirdnesses) 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.

Two questions immediately becomes pressing:  first:  what does ‘relevance’ mean?  Second, what is it that makes p relevant to q?

First Question:  What Does ‘Relevance’ Mean?  As I intend to use the term, ‘relevance’ in general is a relation/connection that exists between one situation/state of affairs and another and is important to our concerns.  In the case of relevant implication, the aforementioned relation is important to us because it underwrites a guarantee that we can infer q from p. That we can legitimately make inferences is one of our concerns.

Implication is a relation between propositions.  One infers one proposition from another. Following Roderick Chisholm, I will be identifying propositions with states of affairs.  For example, the proposition that this cat, Felix, is sitting on this Persian mat with MAT_ID 1123581321 is identical with the state of affairs consisting in Felix sitting on the Persian mat with MAT_ID 1123581321.  So I will alternate between referring to p and q as propositions and as states of affairs.

By ‘situation’ I mean, roughly, ‘a site comprising one or more connected states of affairs which are available from a possible perspective.  A perspective is always limited and therefore does not have available to it other states of affairs.   The room in which I am typing this constitutes one situation.  In this situation the doorbell’s ringing, when it occurs, is available to me.  The button which, when pushed, causes the doorbell to ring is on the wall outside.  This state of affairs is hidden from me in my current situation.  The immediate vicinity of a person who is about to press the doorbell button outside is another situation.  The states of affairs comprised by the room inside are not available to this person.

Second Question:  What Is It That Makes p Relevant To q?  One at least initially attractive answer to the second question is the following:  p is relevant to q when p is information that q.

Here is one issue that I want to bring out into the open from the very start.  The careful reader will notice, as they go along, that I am vulnerable to the charge of circularity.  I will be analyzing implication in terms of  information and information in terms of situations, which in turn I analyze in terms of perspectives.  But it would seem that perspectives need to be analyzed in terms of information.  You, my gentle reader, my fearsomely implacable  judge, will decide later whether I am successful in defending myself against the circularity charge.

In what follows, I will first state what makes treating relevance that way attractive.  After dealing with a counter-example that, at first sight, seems completely devastating, I will argue that the INFORMATION THAT relation remains the basis for understanding relevance as it pertains to implication — at least for the examples that I present or link to in this post.

To state the matter a bit abstractly at first, p is information that q when a channel exists through which information flows from a source site, an at least partially-obscured situation s0 (which includes the state of affairs that q), to a reception site, a situation s2 (which includes the state of affairs that p), making the information that q available in s2. Such a channel exists when some state of affairs that c in a situation s1 renders the conditional probability that q given p 11.

The channel may open up between s0 and s1 because s1 is a physical situation comprising states of affairs whose obtaining during a certain stretch of time makes it impossible without violating physical laws for that p to obtain without that q‘s obtaining.

To bring up an example into which I am about to go into much greater detail shortly, during the time that the wiring to a doorbell is in a certain physical condition, it would be impossible for the doorbell to ring without the button outside getting pushed by someone or something.  Suppose (as is surely the case) that the doorbell could ring without the button’s getting pushed only if a defective physical condition of the wiring, given the physical laws of the universe, could allow for events x, y, or z occurring (for example, an unwanted electrical pulse caused by a short the wiring).  Currently, the wiring is not in this defective condition and will not be so for a stretch of time.  (Nothing, for example, could cause a short, given the physical laws of the universe.)  Given this current condition of the wiring, the doorbell could ring without the button outside getting pushed only were the physical laws of the universe violated.

In the case of the doorbell, the channel is opened up by the physical condition of the wiring, a condition that functions as a constraint disallowing any doorbell ringing occurring without the proper cause — the button’s getting pushed.  This physical constraint underwrites, so to speak, a guarantee that the doorbell will never ring without the button outside getting pushed.

This is a physical, causal constraint.  There may be other constraints as well.  [Including knowledge, perhaps?]

Another factor that will turn out to be pertinent to p’s being information that q is one’s state of knowledge cum ignorance regarding q.  I will be asking later whether this factor poses a problem for regarding p‘s being information that q as the relation that makes p relevant to q by making the truth of an IF THEN statement relative to one’s knowledge.

 

Initially, the following doorbell example, taken from Fred Dretske’s KNOWLEDGE AND THE FLOW OF INFORMATION2 made this account of p‘s relevance to q highly attractive to me.  Warning:  what follows will be a veritable operatic doorbell aria.  Those who are not fans of operatic arias are advised to go elsewhere.

The Doorbell Aria:  You are in a room (s2 ) in which you are able to hear the doorbell.  The wiring of the doorbell comprises situation s1The state of affairs c regarding this wiring is such that in all possible worlds in which the laws of physics of this actual world hold, the doorbell will never ring without someone or something depressing the button outside.  (Situation s0  is the ‘outside’, including the button.)  This never happens, ever, no matter how much time goes by.

The doorbell’s ringing guarantees that someone or something is depressing the button.  There are no poltergeists inside the wiring, no sudden bursts of electrical energy ultimately caused by a butterfly flapping its wings in the Amazon, or anything like that, that will cause the doorbell to ring without the button outside getting depressed.  If one takes each occasion on which the doorbell rings, rolls back the clock, then lets the clock roll forward again, but this time with just one tiny change in the world they find themselves in (say, the butterfly flapping its wings in the Amazon has an orange dot on its wings rather than a maroon dot), and if they repeat this exercise for each possible world whose physics is the same as our actual world, someone or something will be depressing the button outside each time.  Rinse and repeat for each time the doorbell rings.  100% each time.

100% of the time, when the doorbell rings, the button outside is getting depressed by someone or something. Given the doorbell’s ringing, the conditional probability that the button outside is getting depressed is 1.

The wiring is burdened by a defect, however, that results in the doorbell’s occasionally failing to ring even when the button outside is getting depressed.  Let’s say that this failure to ring occurs in 0.001 percent of all the possible worlds in which the laws of physics are identical with those of this actual world.  Suppose that each time the button outside gets depressed the clock gets rolled back, then rolled forward again, but into a another possible world whose physics is the same as our actual world but has just one tiny change (for example, in the color of the spot on the wings of the butterfly in the Amazon).  In 0.001 percent of these possible worlds, the doorbell fails to ring.  Rinse and repeat for each time the button gets pushed.  0.001 percent each time.

0.001% of the time, the doorbell fails to ring when someone or something depresses the button outside.  The conditional probability that the doorbell will fail to ring even when the button outside is getting depressed is 0.001.   The button’s getting depressed does not guarantee that the doorbell will ring.

If we follow Dretske’s definition of informational content, we will see that the doorbell’s ringing is information that the button outside is getting depressed.  We will also see that the button’s getting depressed is not information that the doorbell is ringing inside. This (to anticipate) mirrors the situation in which 3) is true, and 4) is false.

3) IF the doorbell is ringing, THEN someone or something is depressing the button outside.

4) IF someone or something is depressing the button outside, THEN the doorbell is ringing.

Back to Dretske’s definition of informational content:

Informational content:  A signal r carries the information that s is F = The conditional probability of s‘s being F, given r (and k), is 1 (but, given k alone, less than 1)

Fred Dretske, KNOWLEDGE AND THE FLOW OF INFORMATION, Stanford, CSLI Publications, 1999, p. 65

Let me linger a bit on “but given k alone, less than 1”.  k must be your knowledge cum ignorance of the source situation s0 outside.  At the moment, the doorbell is not ringing.  You have zero knowledge of how things stand out there with regard to the doorbell’s getting pushed.  The value of k is therefore zero.  With just this “knowledge” aka ignorance, and in the absence of a signal that the doorbell is getting pushed, the conditional probability that this is happening will be the probability that the doorbell is getting depressed at any given time of the day multiplied by 0.001.  This figure, whatever it is, will be considerably less than 1.

Now the doorbell is ringing.  All of a sudden, the conditional probability that the button outside is getting pushed has leapt to 1.  The doorbell’s ringing is therefore information that the button outside is getting pushed by someone or something.

Correlatively, when I am pushing the button, my knowledge of what is happening inside is zero, provided I am not able to hear the doorbell ringing in any case.  Given this knowledge alone, the probability that the doorbell is ringing is 0.999.  Given my knowledge plus the button’s getting pushed, that knowledge stays 0.999.  Therefore, according to Dretske’s definition of informational content, my pushing the button in this case is not information that the doorbell inside is ringing.

If the INFORMATION THAT relation is what makes for the relevance of p to q in true IF p THEN q statements, then 3) is true because this relation exists between p and q, and 4) is false because this relation does not exist.  Likewise, 1) is false because ‘Cliff lives in Houston’ is not information that the earth has just one moon, and 2) is false because even if Cliff moved to Orange County, California, that item would still not be information that Paris, Texas is the capital of France.  1), 2), and 4) are all false because in each statement the antecedent is not relevant to the consequent.

— “Wait a second!” I hear someone objecting.  “You mean that ‘someone or something is depressing the button outside’ is not relevant to ‘the doorbell is ringing?”  I do think that the notion of degrees of relevance — a relevance spectrum — needs to be introduced here.  The truth of ‘Cliff lives in Houston, Texas’ presumably adds exactly 0 to the probability that the earth has a single moon.  The truth of ‘I am pushing the button outside’ adds 0.999 to the probability that the doorbell is ringing inside.  The truth of the former statement lacks any relevance at all to its consequent.  The truth of the latter statement … well, it is not exactly completely irrelevant to its consequent.  But I do think this is a matter of ‘close, but no cigar’.  The truth of ‘I am pushing this button outside’ is not relevant enough to ‘the doorbell is ringing inside’ to make 4) a true statement.

Assume that an INFORMATION THAT relation exists between p and q in the following truth table except, of course, when the truth value of q makes it impossible for such a relation to exist.  (When this happens, of course, the IF THEN statement is also false.)  In that case, we would get a truth table for implication that is exactly like the one set forth by proponents of Classical Logic.  Except now the truth table makes intuitive sense — even the last row.  This is the row in Classical Logic’s truth table for implication that seems absolutely counter-intuitive to anyone sane.

Truth Table For Implication
p q IF p THEN q
T T T
T F F
F T T
F F T

 

Let’s consider the rows one by one:

  1.  ‘Doorbell is ringing’ is true, as is ‘the button outside is getting pushed’  IF p THEN q is obviously true in this case provided that p really is information that q.
  2. ‘Doorbell is ringing’ is true, while ‘the button outside is getting pushed’ is false. That q is false while p true guarantees that p is in fact not information that q, so IF p THEN q is guaranteed to be false.
  3. The doorbell is not ringing even though the button outside is getting pushed.  p remains information that q when that p is the case, so IF p THEN q is true.
  4. The doorbell is not ringing, and the button outside is not  being pushed.  Nonetheless, p would be information that q should that p obtain.  So IF p THEN q is true because the INFORMATION THAT relation still exists between p and q.

In short, provided this treatment of relevance is correct (which it is not quite — but I will get to that later), IF p THEN q is true if and only if p is information that q.  When (on this treatment of relevance) p is not information that q, then IF p THEN q is false no matter what the truth values of p and q are. This means of course that IF p THEN q cannot be treated in relevant logic as equivalent to NOT p OR q, as it is in Classical Logic.

This, then, is what makes treating relevance as consisting in INFORMATION THAT initially so attractive. First, the INFORMATION THAT relation at work in the doorbell example mirrors in a satisfyingly intuitive way the truth of 3) and the falsity of 4). Second, this treatment provides an intuitive explanation for the fourth row of the truth table for implication given above.  Proponents of Classical Logic are notorious for coming up with nothing more satisfying in this regard than ‘If you believe a false statement, you will believe anything’.

As side note, I would like to add that what I discussed in this post is the INFORMATION THAT relation as stemming from physical laws.  Here (but this needs to be re-worked) I discuss the INFORMATION THAT relation as stemming from what at first looks like logical principles but which, I think, may be more aptly described as the laws of probability.  I do want, after all, to base logic ultimately on something similar to INFORMATION THAT in a non-circular way.

[To sum up:  the relevance of p to q is a relation — a connection — between the state of affairs p and the state of affairs q which is important to us because it underwrites inference by guaranteeing q given p.]

Incidentally, the shell-game example discussed in the post just linked to clearly shows that the relevance-making relation cannot be the causal relation, at least not in all cases.  Turning over shell #3 to reveal a peanut is a signal carrying information that the peanut is under shell #4, but this action does not cause the peanut to be under shell #4.

However, there is a fly in the intuitive ointment. How is one to deal with statements like the following:

5) IF there is a ruby exactly 2 kilometers underneath my feet, THEN there is a ruby exactly 2 kilometers underneath my feet

or, more generally, with:

6) IF p THEN p

?

It would be a bit strange to suggest that a channel exists between the situation s0 (the way things stand exactly two kilometers underneath my feet) and the exact same situation s0.  It would seem, then, the relevant-making relation cannot be identical with the INFORMATION THAT relation after all.3  Although an identity relation clearly exists “between” s0 and s0, it would seem there is never an INFORMATION THAT relation between “them”.

However, while there are clearly cases in which no INFORMATION THAT relation exists between s0 and s0, adopting Roderick Chisholm’s notions of direct evidence and self-presenting states of affairs suggests that, in some other cases, we can treat that p as information that p.  I won’t be implying that Chisholm is correct in thinking that there is such things as direct evidence and self-presenting states of affairs.  If there is such a thing, however, it would suggest that sometimes INFORMATION THAT is not always a three-place relation(source, channel, receiver), but sometimes a one-place relation.

Let’s look at Chisholm’s (simpler) statement of what direct evidence consists in:

What justifies me in thinking I know that a is F is simply the fact that a is F. 

Roderick Chisholm, THEORY OF KNOWLEDGE, SECOND EDITION, Englewood Cliffs, New Jersey, Prentice-Hall, Inc., p. 21.  Henceforth TOK. 

For example, when I suffer a sharp pain in my shoulder to which I point and say ‘here’, what justifies me in thinking I know I am suffering a sharp pain here is simply the fact that I am suffering a sharp pain here.

Likewise, if someone asked me the (somewhat strange) question ‘how can you tell there you are suffering a sharp pain there?” I could only answer:

7)  I can tell I am suffering a sharp pain here because I am suffering a sharp pain here.

But information consists in what one can tell.  It follows, then, that:

8)  My suffering a sharp pain here is by itself information that I am suffering a sharp pain here.

A knock at the door (to use something other than the doorbell example for once) announces that someone or something outside is impacting the door.  Something not identical with this person or thing does the announcing.  The pain, by contrast, is self-announcing.  The information in this case doesn’t travel or flow from a source site to a reception site because the source and reception sites are identical.

If one insists that information has to travel from a source site to a reception site, so that self-announcing information cannot really be information, we still have something that is very much like information.  For to have information, or at least something that is like information, it suffices that one be able to tell something (that someone or something is depressing the button outside, that the peanut is under shell #4, that I feel pain here). One is able to tell something in all these cases, including the self-announcing case.

This gives another twist to:

9)  IF I suffer a sharp pain here, THEN I suffer a sharp pain here.

Here p is relevant to q because q (alternatively p) is a self-announcing state of affairs that is either a case of INFORMATION THAT, or is something very much like INFORMATION THAT.

….

Let me turn now back those cases in which s0 clearly is not information that s0. ….

I argue, however, that 5) (and, to generalize, 6) are true because, were a ruby to exist exactly two kilometers underneath my feet, the conditional probability that there is a ruby exactly two kilometers underneath my feet would be 1.

Compare with:  were the doorbell to ring (given c described above), the conditional probability that the button outside is getting pushed is 1.  The doorbell example describes a case of a signal carrying information that because two distinct situations are in play, a source situation that is at least partially concealed from those inhabiting a reception situation.  The (at least partial) concealment of a source situation from the perspective of a reception situation concomitant with the (at least partial) ignorance that is inherent in k is required for an INFORMATION THAT relation to exist.  Without this, any signal arising from s would be “old information”, that is to say, not information at all.

So I would like to revise Dretske’s definition of informational content to the following:

Informational content:  A signal r in reception situation s2 carries the information that t in source situation s0 is F = Because c is G in situation s1, the conditional probability of t‘s being F, given r (and k in s2), is 1 (but, given k alone, less than 1)

This guarantees the truth of IF p THEN q when p is information that q. When there is only a single situation, s0, knowledge (ignorance) k drops out of the picture because there is no longer any situation s2 from whose perspective one has (at least partial) ignorance of what is happening in s0. The signal r also drops out of the picture because we are no longer talking about INFORMATION THAT. What remains, however, is:

The conditional probability of t‘s being F in situation s0 is, given t‘s being F in situation s0, 1.

I think it requires only a moderately keen grasp of the obvious to grasp this point.

So what is common to both the doorbell and the ruby examples is a conditional probability of 1.  You get the ‘conditional probability is 1’ feature of the ruby IF p THEN p example by removing features from the INFORMATION THAT relation existing in the doorbell IF p THEN q (where p and q are about states of affairs in distinct situations).

I submit, then, that the two-place relation4 that makes p relevant to p in the statement IF p THEN p is a derivativedegenerate case of the INFORMATION THAT relation.  It is what you get by removing features from the IF THEN relation in order to accommodate the drastic simplification of a richer, complex situation s comprising s0, s1, s2 (and k in s2 ) into a more impoverished, simple situation s comprising just s0. This relation is degenerate enough to no longer count as INFORMATION THAT; all that remains of the INFORMATION THAT relation is the ‘conditional probability is 1’ feature;  nonetheless, INFORMATION THAT remains the touchstone for understanding all the cases of implication presented or linked to so far — the doorbell case, the shell-game case, and the ruby case.

Or so I am thinking at this moment.  We will see if this conclusion will survive consideration of further examples of implication.

 

 

 

 

1 I think this is identical with the theory of relevance developed by Jon Barwise and later by Greg Restall, as presented in Edwin D. Mares, RELEVANT LOGIC A Philosophical Interpretation, Cambridge and New York, Cambridge University Press 2004, pp. 54-55. Henceforth RELEVANT LOGIC.  

I mention situations because I have in mind the Routley-Meyer truth condition for implication, to wit:

AB‘ is true at a situation s if and only if for all situations x and y if Rsxy and ‘A‘ is true at x, then ‘B‘ is true at y. (RELEVANT LOGIC, p. 28.)

What I, at least, am calling a situation is what comprises one or more states of affairs available to one (or more, if the situation is shared) sentient creatures whose limitations prevent them from having direct access (in the absence of a signal) to other states of affairs.  The room inside which a person is able to hear the doorbell ringing is situation s2 — the reception situation.  The area immediately outside, where another person may be pressing the doorbell, is situation S0. — the source situation.   The wiring to the doorbell, which perhaps a gremlin or poltergeist is inhabiting, is situation s1 — the channel situation.

Of course, the fact I am bringing both situations and possible worlds into the discussion is probably a signal, that is to say, a dead-giveaway that I do not yet sufficiently understand the distinction between situations and possible worlds. Keep in mind that this post is an exercise in writing to learn.  So I want to issue a warning to non-experts in the field:  I probably know less about this stuff than may at first seem to be the case.  Needless to say, the actual experts, won’t be fooled.

2 Fred Dretske, KNOWLEDGE AND THE FLOW OF INFORMATION, Stanford, CSLI Publications, 1999, pp. 54-55.

3 cf RELEVANT LOGIC, p. 55.

4 — “Wait”, you say. “This is a two-place relation? Isn’t p identical with p?  So why isn’t this a one-place relation?” Yes, p is identical with p.  But the relation in question is a two-place relation because p is getting stated twice.

****************************

Today’s homage to Plato’s SYMPOSIUM is Channing Tatum, who is welcome to fix my pickup truck anytime. (In fact, I think I will buy a pickup truck just so that I can invite him to fix it.)

To distort Plato’s SYMPOSIUM just a little bit, pining after Channing Tatum is the first step on the ladder of Beauty that leads shortly thereafter to appreciation of the beauty of Classical Logic and Relevant Logic, and then, finally, to the form of Beauty — Beauty itself. Of course, my enemies say that I should avoid logic altogether and stick to pining after Channing Tatum.


Re-Igniting An Old Flame

A few weeks ago my interest in the French Philosopher Maurice Merleau-Ponty (1908-1961) suddenly got re-ignited upon finding out that a paper I published in a previous life (THE CONCEPT OF THE ECSTASIS, Journal Of The British Society For Phenomenology, 14(1):  79-90, 1983) actually got listed in the bibliography of Stephen Priest’s MERLEAU-PONTY:  THE ARGUMENTS OF THE PHILOSOPHERS.

The sudden explosion of this renewed interest is a bit like the result of throwing a lighted match on a bunch of rags soaked in gasoline.  In its heat, I’ve decided to start a new category of blog posts comprising an attempt to gain a deeper, fuller understanding of the topic of that paper.  What positions stated in the paper do I still hold?  What positions must I mark to market?  (<yes I am being ironic>Doubtlessly none — surely my paper is sacred text.</yes I am being ironic>) What can be stated more clearly, argued for more carefully?  Doing this kind of thing is what blogs are ideal for:

…you can work around the edges of an idea over days and weeks and months [and years] and really   come to understand it. It’s this process that blogging does better than pretty much any other medium.

Anil Dash On Blogging

 

The topic of my paper is, essentially:

The question concerning corporeity connects also with Merleau-Ponty’s reflections on space (l’espace) and the primacy of the dimension of depth (la profondeur) as implied in the notion of being in the world (être au monde; to echo Heidegger’s In-der-Welt-sein) and of one’s own body (le corps propre).

Wikipedia Article On Maurice Merleau-Ponty

 

So in the months and years to come I will be re-reading, working through, and blogging on Merleau-Ponty (THE PHENOMENOLOGY OF PERCEPTION, THE VISIBLE AND INVISIBLE, and other works) in order to really come to understand, truly get my head around, get a maximal grasp of this notion of ‘the primacy of the dimension of depth as implied in the notion of being in the world and of one’s own body.’  As part of this effort, I will be re-reading and blogging on George Berkeley’s works as well, which, partly as foil, partly in a kind of concurrence, shed light in an interesting way on Merleau-Ponty.

These efforts will fall under the category ‘Primacy Of The Dimension Of Depth.’

Of course, I am far from having finished the other two main categories I have been working on in this blog, to wit: ‘The Argument That Tagalog Lacks A Subject’ (a thread inspired largely by Paz Buenaventura Naylor’s article), and ‘Material Implication And Information Theory’ (inspired largely by Fred Dretske’s KNOWLEDGE AND THE FLOW OF INFORMATION and by Edwin D. Mares’ RELEVANT LOGIC).  I intend to continue working on these threads at the same time that I am re-igniting an old flame, my crush on Merleau-Ponty.

 

MerleauPontyArgumentsOfPhilosophers

 

If I bore anyone, tough.  You don’t have to read these incoherent/semi-incoherent ramblings.  I am writing largely in order to learn, to get as much clarity as I can in my own head regarding these topics.

Of course, it would be nice if someone else were interested in them, and, even better yet, had something useful and interesting to say about them, whether in disagreement or agreement with me.

It would also be nice if Ashton Kutcher gave me a call.

 

ashton_kutcher-4036

 

(No post even touching on philosophy would be completed without an homage to Plato’s SYMPOSIUM.)  I wonder if Alkibiades was as gorgeous.

 


Some Boring MetaBlogging

Number 14 of this pretty much describes what I am trying to do here.  In particular:

…you can work around the edges of an idea over days and weeks and months [and years] and really come to understand it. It’s this process that blogging does better than pretty much any other medium.

This is what I am trying to do with the Relevant Logic/Material Implication/Information Theory viewed through the eyes of Fred Dretske stuff (repeated endlessly).  Who knows, I might even do some endless blogging someday to gain a ‘maximal grasp’ (Merleau-Ponty) on the Roderick Chisholm stuff.


Measles, Wormy Red Apples, And God (And Peanuts)

In his Knowledge and the Flow of Information, Dretske argues that what information a signal carries is relative to what the receiver already knows about the possibilities at the source:

To illustrate, suppose that there are four shells and a peanut is located under one of them.  In attempting to find under which shell the peanut is located, I turn over shells 1 and 2 and discover them to be empty.  At this point, you arrive on the scene and join the investigation.  You are not told about my previous discoveries.  We turn over shell 3 and find it empty.  How much information do you receive from this observation?  How much do I receive?  Do I receive information that you do not receive?  … [Dretske goes on to argue that the answer is ‘yes’ because the amount of information and what information is received depends upon the reduction in possibilities achieved in each case.  Information is all about reduction in possibilities.] … This constitutes a relativization of the information contained in a signal because how much information a signal contains, and hence what information it carries, depends on what the potential receiver already knows about the various possibilities that exist at the source.

Fred Dretske, KNOWLEDGE AND THE FLOW OF INFORMATION, Stanford, CSLI Publications, 1999, pp. 78-79

The third shell’s proving to be empty when it is turned over is, for me, information that the peanut is hidden under shell 4.  But for you, it is not information that the peanut is hidden under shell 4.  What information a signal carries (here the signal is the third shell’s proving to be empty when turned over) is relative to what one already knows.

Let’s apply this conclusion to the measles and wormy read apple examples.

Suppose that one has received information that all of Herman’s children have the measles.  Should one then discover (say, a friend tells them this) that this layabout in front of one’s shop is a child of Herman’s, that this person is a child of Herman’s is now, all of a sudden, information that this person has the measles.  Before one knew that all of Herman’s children have the measles, that this person is a child of Herman’s was not information that the person has the measles.

The same reasoning applies mutatis mutandis to the wormy red apple example.  If one has information (say, received from a person who has previously examined all of the apples in the pile)  that all of the red apples in the pile are wormy, then that the apple in one’s hand drawn from this pile is red is information that the apple is wormy.  Before one has received the information that all of the red apples in the pile are wormy, a signal that the apple in one’s hand is red is not information that it is wormy.  In both the measles and the wormy red apples examples, what information a signal carries depends upon, is relative to, what one already knows.

So if one claims that If p Then q is true only when the occurrence of p is information that q, then the truth of these sentences (henceforth the ‘measles’ and  ‘wormy red apple’ statements)…

If this layabout loitering about on the front of my shop is a child of Herman’s, then this person has the measles.

and

If this apple (drawn from this particular pile) in my hand is red, then it is wormy

…is relative to what one already knows.  They will be true relative to the person who already knows that all of Herman’s children have the measles (without necessarily knowing that this particular person in front of their shop is a child of Herman’s) and that all of the red apples in this pile happen to be wormy.  They will be false relative to the person who does not already know these things.

In previous posts, I noted as an autobiographical fact that I had the strong intuition that both statements above are true, regardless of what one already knows.  But perhaps this intuition, in spite of its being my intuition, should not be regarded as totally sacrosanct.  For I will venture that most people would not be bothered by the relativity of this statement (henceforth the ‘third shell proves empty’ statement):

If the third shell proves to be empty, then the peanut is located under the fourth shell

Clearly (although I say ‘clearly’ with some trepidation, in the spirit of ‘let me throw this piece of spaghetti onto the wall, and see if it sticks,’ or, alternatively, ‘let me see if I can get away with this statement without too many screams of protest’), this statement would be true in the situation occupied by the person who already knows that the first and second shells are empty, and false in the situation occupied by the person who does not already know these things.

What can be learned from, inferred from, concluded from the third shell’s being empty, the apple’s being red, the layabout’s being a child of Herman’s, depends upon the situation one is in that is defined by what one already knows.  There isn’t, I think, anything controversial or counter-intuitive about this.  IF-THEN statements have everything to do with what can be learned from, inferred from, concluded from a given situation.  So the truth/falsity of the corresponding If p Then q statements is also relative to the situation one is in as defined by what one already knows.

And if one is still bothered by this, would one rather return to the paradoxes of Material Implication?

(Begin aside:  Remember that what is motivating this entire attempt to argue that If p Then q is true only when p is information that q is to escape from the paradoxes of Material Implication, which would count both of the following statements as true:

If Calypso music originated in Wisconsin, then the earth has two moons

and

If Paris is the capital of France, then the earth has one moon

To escape these paradoxes, we need to find a way to make p relevant to q in some way.  And the most plausible way to do this, I assert, is to insist that p be information that q.  End Of Aside.)

To undermine my initial intuition further, suppose that one has obtained information that all of the apples in the pile — both yellow and red — are wormy.  In that case, should one (blindfolded) handle each apple in turn and say ‘If this apple is red then it is wormy’, his statement would be (I venture) false.  For the redness of the apple is, in this situation, no longer what excludes the possibility that it is not wormy, or, put another way, is no longer the factor that renders as 1 the probability that the apple is wormy.  That factor is now the fact that the apple is from this pile, not that it is red.  Since the apple’s being red is no longer relevant to its being wormy (is no longer what makes the probability the apple is wormy 1), one cannot learn from, conclude from, infer from its being red that it is wormy. The apple’s being wormy no longer hinges on its being red. The statement is now false for exactly the same reason that ‘If Paris is the capital of France then the earth has one moon’ is false.

One might try to preserve a version of the intuition that the measles and wormy red apple statements are true regardless of anyone’s knowledge by proposing that these are true independently of what any finite intelligence knows or doesn’t know.  What if there were an infinite intelligence — a God who knows everything in general, and the measles status of Herman’s children, the worminess status of the red apples in the pile, and the location of the peanut under the fourth shell in particular.  One could then accurately say the ‘measles’, ‘wormy red apples’, and ‘the third shell proves empty’ statements are true objectively, that is to say, sub specie aeternitatis, even if they are true or false as the case may be, from the subjective standpoints of this or that finite intelligence.

The analogy would be with Galilean motion studied in High School physics.  An object may be moving at 10 miles per hour given one reference frame and 60 miles an hour given another reference frame; nonetheless, there was to be some absolute reference frame embracing all of them which would let one give an absolute, non-relative value to the object’s speed.

But the intuition cannot be rescued this way.  For clearly, nothing could ever be a signal, could be information-that, for an infinite intelligence that knew everything.  Such an intelligence with its penetrating x-ray vision would already know, for example, that the peanut was located under the fourth shell.  Given this knowledge, the third shell’s proving empty would not reduce to 1 for this intelligence the number of possibilities regarding the location of the shell.  For the number of such possibilities was already 1 for this intelligence.  Likewise, for this all-knowing intelligence, that this particular layabout is a child of Herman’s would do nothing to reduce to 1 the probability that this person has the measles.  Nor would the fact that this particular apple is red reduce for this intelligence the number of possibilities regarding the worminess status of the apple from 2 (the apple is wormy or non-wormy) to 1 (the apple is wormy).  With no reduction of possibilities, there is no signal carrying information-that in any of these cases.

God’s knowledge cannot serve as the equivalent in logic of the Galilean absolute reference frame.

Not only is information-that relative to what one already knows, it also requires finitude.  No limitation on one’s knowledge — no hiddenness — no information-that.  And if the truth of If p Then q statements requires that the occurrence of p be information that q, the truth of these statements also require finitude.

One final note:  how can one account for the illusion (if it is that) that both the measles and the wormy red apply statements are true regardless of what one already knows?  I think the answer lies in the fact that, after completely talking through one’s hat at time 1 with the statement “If this apple is red, then it is wormy,” one were later at time 2 to examine all of the red apples and discovered they were all wormy (and that just some of the yellow apples were), it would seem that, since the statement is true at time 2, it would have to have been true at time 1.  The truth value of a statement like this can’t change, can it?  Maybe we would prefer to accept the paradoxes of Material Implication after all.  But it seems to me that one should accept that, at least in the case of the ‘third shell proves empty’ statement, the truth value of that statement can change with time as one obtains more knowledge (you later get information that the first and second shells also proved to be empty).  So the truth value of the measles and wormy red apples statements changing over time should not prove to be an absolute obstacle.

     *****

The entire point of this exercise is not just to make grandiose metaphysically-existentialist-sounding statements such as ‘logical implication requires finitude’ (although I must admit this is one of my aims), but also to escape from Classical Logic’s paradoxes of Material Implication by insisting that there must be some relation between p and q that makes p relevant to q, and that this relation consists in p‘s being information that q.

In the previous post, I noted two apparent counterexamples (the measles and wormy red apple statements) that would seem to preclude identifying this hoped-for relevance-making relation with information-that.  These statements seem to be true even though in these cases p is not information that q.  Also, identifying this relation with information-that would make the truth of IF-THEN statements relative to what one already knows, an implication that may make one prefer the paradoxes of Classical Logic’s Material Implication.

In this post, I employ the ‘third shell proves empty’ statement, as well as the close connection (I claim) that IF-THEN statements have with what one can learn from, infer from, or conclude from a situation to remove whatever counter-intuitiveness might adhere to the notion that the truth of IF-THEN statements is relative to what one knows.  (Of course what one can learn, infer from, conclude from a situation depends upon what one already knows.  Of course the truth/falsity of ‘the third shell proves empty’ statement depends as well upon what one already knows.)  If one can accept the relativity of IF-THEN statements, they will be in a better position to accept the idea that those cases in which p is not information that q (the redness of the apple sometimes fails to be information that the apple is wormy; that this person is a child of Herman’s sometimes fails to be information that this person has the measles)  are also cases in which If p Then q is false.

This leaves the third difficulty mentioned in the previous post:  what to do about the statement If p Then p?  Is a channel of information supposed to exist between p and the self-same p?

Do I have a song and dance that will eliminate this difficulty?

*****

Today’s homage to Plato’s SYMPOSIUM is the soccer player James Rodriguez.

James_Rodriguez

From math teachers to soccer players…How can anyone get anything at all done with beauty like this walking the earth?


Measles And Wormy Red Apples: IF-THEN Statements And INFORMATION THAT (An Apparent Counter-Example)

It would seem that there are some clear counterexamples to the idea that If p Then q is true when p is information that q.

Consider the following (somewhat gruesome, in the light of the irresponsibility of our contemporary anti-vaxxers) measles example from Fred Dretske.  Dretske, by the way, does not discuss this example in the light of IF-THEN statements.

…an exceptionless uniformity … is not sufficient for the purposes of transmitting information.  Correlations, even pervasive correlations, are not to be confused with informational relations.  Even if the properties F and G are perfectly correlated (whatever is F is G and vice versa), this does not mean that there is information in s’s being F about s‘s being G (or vice versa).  It does not mean that a signal carrying the information that s is F also carries the information that s is G.  For the correlation between F and G may be the sheerest coincidence, a correlation whose persistence is not assured by any law of nature or principle of logic.  All Fs can be G without the probability of s‘s being G, given that it is F, being 1.

To illustrate this point, suppose that all Herman’s children have the measles.  Despite the “correlation,” a signal might well carry the information that Alice is one of Herman’s children without carrying the information that Alice has the measles.  Presumably the fact that all Herman’s children (living in different parts of the country) happened to contract the measles at the same time does not make the probability of their having the measles, given their common parentage, 1.  Since this is so, a signal can carry the information that Alice is one of Herman’s children without carrying the information that she has the measles despite the fact that all Herman’s children have the measles.  It is this fact about information that helps to explain (as we will see in Part II) why we are sometimes in a position to see that (hence, know that) s is F without being able to tell whether s is G despite the fact that every F is G.  Recognizing Alice as one of Herman’s children is not good enough for a medical diagnosis no matter what happens to be true of Herman’s children.  It is diagnostically significant only if the correlation is a manifestation of a nomic (e.g., genetic) regularity between being one of Herman’s children and having the measles.

Fred Dretske, KNOWLEDGE AND THE FLOW OF INFORMATION, Stanford, CSLI Publications, 1999, pp. 73-74

Myself, I would rather choose a less gruesome (given the sometimes horrific consequences of measles), even if still somewhat gross, example.  Suppose that there is a pile comprising red and yellow apples in my grandfather’s orchard.  By pure chance, some of the yellow apples happen to be wormy, while all of the red apples are so.  Given his measles example, Dretske would surely claim that just the fact that a given apple from the pile is red would not constitute information that the apple is wormy.  But suppose that, blindfolded, I handle each apple in the pile one by one, saying each time:

If this apple is red, Then it is wormy.

In my mind’s inner ear, my intuition is shouting to me:  “This is TRUE TRUE TRUE TRUE TRUE!!!!!!”

Likewise, surely the following statement is also true:

If this person loitering here in front of my shop among all these other disreputable-looking lay-abouts is a child of Herman’s, Then she has measles.

This statement would be true, it (strongly) seems to me, even if the person uttering it is talking completely through their hat, even randomly, and has absolutely no evidence that ‘this person’ has the measles, or that she is a child of Herman’s, or that there is any connection at all, even an accidental one, between Herman’s children and the measles.

Therefore, there would seem to be clear cases in which an If p Then q statement is true even when the occurrence of p is not information that q.

Nonetheless, I (at least as of this writing) think I can show in a later post that Dretske’s discussion of the relativity of information drastically undercuts what he thinks his measles example shows.  (I am also thoroughly confident, by the way, that if my doubts are valid, they have already been discussed a thousand times already by everyone and their uncle.)  So the idea that what makes p relevant to q in any true If p Then q statement is an informational relation . . . this idea might find a rescuer after all.

 *****

I hope that today’s homage to Plato’s SYMPOSIUM has never suffered from the measles.  This gorgeous hunk is a math teacher in Great Britain (perhaps hailing ultimately from Italy) who moonlights as a model.

pietronew

I am confident that this math teach will inspire many of his students, both male and female, to start the ascending the platonic ladder whose lowest rung consists in the contemplation of the Beauty of Gorgeous Guys, whose next rungs consist in the contemplation of the Beauty of Math and Logic, and which finally leads to the contemplation of the Form of Beauty Itself.

For now, however, I will linger a bit at the lowest rung, the Contemplation of the Beauty of Gorgeous Guys.  I will get to the Form of Beauty Itself sometime.


IF-THEN Treated As INFORMATION THAT

Relevant Logic tries to resolve the following paradoxes of Classical Logic’s Material Implication by insisting that for any If p Then q statement, p must be relevant to q:

If Cliff Wirt resides in Houston, Texas, Then the earth has just one moon.

If Calypso music originated in Wisconsin, Then the earth has two moons.

According to Classical Logic, both of the above statements are true because they fulfil the truth-functional requirements of true IF-THEN statements.  (T T and F F.  According to Classical Logic, F T also yields a true IF-THEN statement; the only truth-table combination that yields a false IF-THEN statement is T F.)  Nonetheless, one may be excused if they think that regarding the two statements as true is a bit paradoxical, to put it mildly.  One cannot conclude, infer, or learn from Cliff Wirt’s residing in Houston that the earth has just one moon.  Even less can one conclude, infer, or learn from the “false fact” that Calypso music originated in Wisconsin the equally “false fact” that the earth has two moons.  One would think that both IF-THEN statements are false because in both, the antecedent, p, is irrelevant to the consequent, q.

So the truth-functional account of the IF-THEN statement has to go, I am thoroughly persuaded, because it can take into account only the truth or falsity of the antecedent and consequent, leaving completely out of view the relevance of the antecedent to the consequent.

What, then, would make the antecedent relevant to the consequent?  What is the relation between p and q when we say If p Then q?  I am partial to the hypothesis that the relation is informational.  If p Then q is true when the occurrence of p is information that q.  If the doorbell is ringing, then someone or something outside has depressed the button; that the doorbell is ringing would be information that someone or something outside has depressed the button.  The first is information that the second because there is a channel of information extending from the button to the ringing sound, such that, when that channel is in good working order, the probability that the button is being depressed is 100% when the ringing sound occurs.

Because this informational relation exists between the ringing sound and the button’s being depressed, one can conclude from, infer from learn from the doorbell’s ringing that someone or something is depressing the button outside.  So — oh my god! — there is a close affinity between If p Then q and p’s being information that q.

There are, however, several obstacles in the way of treating the IF-THEN statement as an informational relation.

First, how would one deal with If p then p?  Is there somehow supposed to be a channel of information between p and itself?

Second, there are (seemingly) clear cases in which If p Then q is true when p is most definitely not information that q.

Third, the informational relation is both intentional and relative, as described by Fred Dretske in his KNOWLEDGE AND THE FLOW OF INFORMATION.  Treating If p Then q as an information relation would make implication both intentional and relative.  The very same If p Then q statement would be true inside some frameworks and false inside others.  Rather than accept this, some would perhaps rather accept Classical Logic’s paradoxes of Material Implication.

*****

Today’s homage to Plato’s SYMPOSIUM takes the form of a very kalos Bruno Mars.  According to Plato, one ascends a ladder whose first rung consists in the beauty of gorgeous young men, whose middle rungs consist in the beauty of things like Classical and Relevant logic, and whose final rung consists in the Form of Beauty Itself.

bruno-mars-promo

I will get to adoring the Form of Beauty Itself eventually.  For now, I will content myself with adoring the Form of Bruno Mars.