Monday, January 10, 2011

A Cuppa Java

I don’t believe in the existence of infinitely many primes because of some philosophical reason;  I believe it because Euclid proved it.  And I don’t believe in the existence of this coffee-cup for metaphysical reasons;  I believe it on the practical and by no means logically conclusive grounds, that it has so far done a good job of holding my coffee. Should it turn out I’m only a brain in a vat, worse luck:  no coffee-cup after all.  But the number of primes will still be infinite.

Thus far the thoughts of a simple man, after a tasty cup of coffee.  Then come the objections:  And why do you trust your sense-perceptions of that cup?  Simple answer: Because that’s what creatures do; I’m like the bunny, trusting the carrot.  Surrejoinder: a years-long onslaught of the findings of philosophy and physics.  Somewhat chastened, I revise the periphery of my ontology in complicated ways, demoting a number of  entities to various levels of Meinongian subsistence.  But the coffee-cup stays just as it was.  There is still a frenziedly skeptical attack on that (the brain-in-a-vat bit), which I cannot logically refute; but I meet it with faith, which in this case requires no great leap.

As for the integers…Well I know of no attack that even needs meeting.  There are attacks on various characterizations of what numbers “are” (rather than, so to speak, what they “do” – divide evenly into twelve, and so forth);  these are harmless, perhaps even true.  They do not strike at the heart of numbers, any more than a bad statue or overidealized painting  strike at the reality of Napoleon.

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