Category Archives: What Follows From What

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.

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My Confidants Will Know What I Am Talking About

In the course of discovering, quite unexpectedly, that I am just one degree of separation away from Barack Obama (this may partially ameriolate my 3-degrees-of-separation connection with Al Capone), I encountered a little fire-fight on the interwebs that I sum up as follows:
 

Person A:  “I was a confidant of Barack Obama when he was an undergraduate.”

Person B:  (Addressing Person A):  “You can’t claim you were a close friend of Barack Obama’s, since you met him only twice.”

Person A:  “I never said I was a close friend of Barack Obama’s; I said I was a confident of his.  The two are not the same.  Someone I meet in an elevator can be my confidant.”

 
Now I have absolutely no intention of going back to the exact wording of the dispute, so please assume, until you have any firm evidence to the contrary,  that any criticism of the arguments of the real people A or B that may seem to be implied here is in fact a straw man.  I am just interested in the narrow question:  Does ‘A was a close friend of Barack Obama’s’ follow from ‘A was a confident of Barack Obama’s’? 
 
I suggest that how much one is a confidant of a person is a measure of how close a friend one is to him.  One might hear, for example:  “I know that you two are close friends, but I don’t know how close, so I am not going to elaborate on this remark I’ve just made because then you might come to know too much.”  One measure of how much one is a confident of a person is how much he is willing to tell you information that he is at pains to withhold from the general public.  Another measure is how long-lasting the relation is and how regularly he confides information to you.  Let’s assume, then, just for the sake of argument, that I am reluctant to divulge to the general public the following items, listed in descending order of the urgency with which i need to keep these things private:
 

1.  My boyfriend is this really cool vampire, but now my love-life has become complicated by this really hot (and I mean really hot) werewolf who has a desperate crush on me … and I am becoming more and more attracted to the werewolf by the minute.

2.  I adore Country Music.

3.  As an undergraduate, I was a fervent adherent to the philosophy of George Berkeley, and I used to argue vehemently, not only that this chair would not exist if no one perceived the chair, but also that sometimes this chair actually does sometimes fall out of existence because, there being no God, God is not around to perceive the chair when no lesser sentient being happens to be around to perceive it.

 
Any one of these three revelations, I believe, would forever dash any presidential aspirations I may have.  Nonetheless, I am much more sanguine about 3) become widely known than I am 2), or, God forbid, 1).  I am not sure how I could live down widespread knowledge of 1). 
 
Now if I meet Philippa Foot once and only once in my lifetime at a philosophy conference, and tell her 3) while we are in the elevator, is Philippa Foot now my confidant?  My own intuition tells ‘well, in a way.  Sort of kind of.’  But I seriously doubt that Philippa Foot’s membership in the set comprising ‘confidants of Cliff Wirt’ is 100%.  Would not the degree of membership be closer to something like 1%?  (Permit me for the moment to use the terminology of fuzzy set theory.)  The urgency with which I want to withhold the information is low.  The relation to my sort-of-kind-of confidant is not a long-lasting one. Nor do I regularly or habitually confide private information to her.
 
Alternatively, should I collar some stranger in the elevator and tell him — outside of any context whatsoever . . . we are not at a conference of Robert Pattinson fans, for example — “My boyfriend is this really cool vampire….”, my intuition is that this is another case in which the membership of this unfortunate person in the set of ‘confidants of Cliff Wirt’ is considerably less than 100%.  The urgency with which I normally withhold this information from the general public is quite high (I don’t know what came over me in the elevator), nonetheless, my sort-of-kind-of confidant is not someone with whom I have a relationship lasting through a significant stretch of time to whom I regularly confide things.
 
But if I confide 1) to someone to whom I regularly confide things and with whom I have associated for a significant amount of time, my intuition is that, yes, this person does have 100% membership in the set comprising ‘confidants of Cliff Wirt.’  But this person also has 100% membership in the set of close friends of Cliff Wirt. 
 
So yes, ‘A was a close friend of Barack Obama’s’ does follow from ‘A was a confident of Barack Obama’s’ when membership in the set of ‘confidants of Barack Obama’ is 100%.  The vagueness of the terms ‘confidant’ and ‘close friend’ might lend support to an evasion of this implication, but at the core (by that I mean ‘at the level of 100% membership in the sets), the implication does hold. 
 
Anyone is welcome to advance differing intuitions here.