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Harvey,
To cut a long story short, I both agree and disagree with your position. Math does not really define 'truth' anymore than it defines 'moo' or any other word, so in that sense I agree with you.
When I talk about truth though, I'm talking about a very specific meta-linguistic concept which no word can properly describe. It should be clear to anyone that there are no good words to express meta-linguistic concepts anymore than there are good words to express metaphysical ideas. In order to talk about metaphysics, one must take for granted that the listener will do his or her part trying to figure out the meaning of words which are, essentially, meaningless. It's the same when we talk about language.
With that in mind, I want to show you why the meta-linguistic concept expressed by words such as 'true', 'correct', 'consistent', 'coherent', and so on, is defined not only in mathematics but in any possible means of communication between any two entities (notice I didn't say 'conscious entities', for the concept is just as relevant when it comes to communication between machines)
So here's my one-sentence definition of 'truth':
"Truth is a set of rules which make communication possible"
Notice how the definition makes the concept of truth a complete irrelevance. By the time you understand the set of rules well enough to make sense of the sentence, you must necessarily conclude the sentence adds absolutly nothing to your knowledge. Which is the point I started with: you don't have to know what truth is, but you must necessarily adknowledge that it exists, for the absence of truth is the ultimate paradox: it cannot be true that nothing true can be said. If we put it another way, we could say that the liar paradox is about the fact that nobody can possibly lie all the time. Given any amount of communication, a certain portion of it must necessarily be true.
Back to mathematics, the most striking fact about it is that all mathematically correct ideas can be successfully communicated. If anything, most of mathematics is just a set of statements with which everyone agrees. The search for universal agreement is, in fact, the essence of mathematics. If there is a better word than 'truth' to express that concept, I don't know what it is.
Best regards,
ML |
