Consider Goldbach’s conjecture:
(G) Every even number greater than two can be expressed as the sum of two primes.
No one, mathematician or otherwise, has either confirmed or refuted this conjecture. I suppose this hasn’t happened yet for two related reasons. No human mind has yet been able to cognize a set whose cardinality is ∞, and if they could cognize such a set, the task of confirming the conjecture would be an endless process- there just is no final member of a set with a cardinality of ∞.
But what’s crazy is that Goldbach’s conjecture, regardless of our failure to find it out, is either true of false; which means as of right now the proposition expressed in (G) is either true or false. Okay, so maybe that doesn’t seem crazy yet. But give me a sec.
Consider that propositions are things only minds can be acquainted with. Why so? Because minds are the only things that can think and therefore they are the only things that can be acquainted with propositions. What’s worse is that propositions seem to depend on minds for their existence. Why so? Because propositions are inexorability linked with intentionality; that is, propositions only have meaning in virtue of what they refer to. And minds are the only things that can refer; which is to say, minds are the only things that have intentions. Why so? Because no conglomerate of atoms ever refers to anything, silly. (just for a fun thought experiment think of the merelogical sum of any atoms you prefer (I’m currently thinking of Michelangelo’s David, and, well, my brain), after you have whatever atom conglomerate in your mind, ask yourself what thing those atoms refer to.)
So if propositions depend on minds and any unambiguous proposition whatever has a certain truth value out of de dicto necessity, then it follows there is a mind that is acquainted with the proposition expressed in (G). But if there is a mind that is both acquainted with the proposition expressed in (G) as well as its truth value, this mind must be of an infinite caliber, and this mind is what all men mean by the term ‘God’.
Saturday, August 11, 2007
the argument from propsitions. Redux.
Subscribe to:
Post Comments (Atom)
2 comments:
it seems to me, prima facie, that (G) can be iterated without its veracity verified. thus, Goldbach was able to conceive of its boundaries and what it would be like for G to be true, thus providing you with fuel for blogging. but i guess i don't quite get why talking about the proposition logically entails another proposition:
(H) there is a mind who knows the veracity of G.
also - it doesn't require an infinite amount of time to prove every postulate that involves infinite sets. consider: (A) every even number is divisible by 2. while the set of all even numbers is infinite, a mathematical proof can be composed, which demonstrates the veracity of A. no infinite mind required.
Post a Comment