Monthly Archives: March 2015

The Red And The Yellow: Pinning Down Some Intuitions

I want to pin down the following intuitions. (Maybe this is a bit like pinning down some bizarre insects in a collection done for a biology class.)  The intuitions have been … provoked, if that is the word…by my reading in Fred Dretske’s classic work Knowledge And The Flow Of Information, and are motivated by some claims I want to make (hopefully in a later post) regarding Relevant Logic (as opposed to Classical Logic).

Suppose that someone has thrown together a pile of apples in an orchard.  (I am picturing my maternal grandfather’s orchard in Iowa, near Council Bluffs.)  The pile comprises some red apples and some yellow apples.  By pure chance, all of the red apples happen to be wormy, while at least some of the yellow apples happen not to be wormy.  I pick up an apple from the pile.  The apple happens to be red.

Now I have the strong intuition that in this situation the following statement is true:

If the apple I have picked up from this pile is red, that apple is wormy.

The statement is true, at least for a particular stretch of time, because any apple I pick up from the pile will be wormy should it happen to be red.  During that stretch of time, the apple from that particular pile will be wormy if it is red. Maybe later someone will throw in a non-wormy red apple, in which case the If-Then statement above will cease to be true.  But for this moment, the statement is true.

Now let’s back up and change the example.  The pile still comprises both red and yellow apples, but now both the yellow apples and the red apples are all wormy.  In this case…well, perhaps saying I have the intuition is too strong…nonetheless, I am strongly tempted to claim that in this other situation the statement under discussion is false:

If the apple I have picked up from this pile is red, that apple is wormy.

Classical Logic thinks the statement is true because both the antecedent and the consequent are (in our thought experiment) true.  Nonetheless, I am at the moment of this writing willing (perhaps foolishly) to stick my head out and say the statement is false because, in this situation, the apple’s being red is no more relevant to its being wormy than any other accidental feature of the apple — say, its still having a leafed twig attached to it.  In this particular situation, neither the apple’s being red nor its still having a twig and leaf attached to it excludes the possibility that it is not wormy.  What does exclude that possibility (for a while, at least) is the apple’s coming from this particular pile.  So the above statement is no more true than this statement (suppose I happen to be driving down Highway 66 at the moment):

If I am driving down Highway 66, then the earth has just one moon.

Classical Logic thinks this statement is true because both the antecedent and the consequent are true; Relevant Logic thinks the statement is false because the fact that I happen to be driving down Highway 66 at the moment is not relevant to the earth’s having just one moon.

I would like to add that the statement remains false even though, 100 percent of the time when I drive down Highway 66, the earth still has just one moon.  (I hope to motivate this claim a bit later.)  In spite of this ‘100 percent of the time’, this reliability, my driving down Highway 66 is not a factor that excludes the possibility that the earth has more than one moon.

Today my homage to Plato’s Symposium will be the singer Von Smith. (According to Plato, one ascends a ladder that starts with the beauty of gorgeous young men, and leads up to the beauty of things like Classical and Relevant Logic.)

Von_Smith

How can anyone get anything done with beauty like this walking the earth?  Especially beauty like this walking the earth and singing.

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