On 6/15/2015 8:15 AM, Brian Tenneson wrote:
Therefore, perhaps proof of truth is an unattainable goal in math. Perhaps proof of truth is an unattainable goal anywhere.
Math isn't concerned with true, it's only concerned with what theorems follow from given axioms. Traditionally the axioms are assumed to be true, but this concept of true is no more than a marker like #t which marks a property preserved under logical inference rules. The other kind of true, as when we say "It's true that the Earth is round." is a rough or approximate relation between a statement, "The Earth is round." and some facts in the world which can in principle be tested empirically. It's like truth in jury trials, we may believe it beyond reasonable doubt, but we're never sure.
So when you say truth is unattainable you need to distinguish the different uses of the concept. I think it is possible to determine that some things are true beyond a reasonable doubt.
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