On 30 Nov 2012, at 21:28, meekerdb wrote:
On 11/30/2012 10:02 AM, Roger Clough wrote:
And a transcendent truth could be arithmetic truth or
the truth of necessary logic.
True in logic and formal mathematics is just marker "T" that is
preserved by the rules of inference.
This makes no sense. You confuse the propositional constant T, with
the semantical notion of truth. The first is expressible/definable
formally (indeed by T, or by "0 = 0" in arithmetic), the second is not
(Tarski theorem). When we say that truth is preserved by the rules of
inference, we are concerned with the second notion.
In applications it is interpreted as if it were the correspondence
meaning of 'true'.
Like in arithmetic. Truth of "ExP(x)" means that it exists a n such
that P(n), at the "metalevel", which is the bare level in logic (that
explains many confusion).
But like all applications of mathematics, it may be only
approximate.
Yes, but for arithmetic it is pretty clear, as we share our intuition
on the so-called standard finite numbers.
Bruno
http://iridia.ulb.ac.be/~marchal/
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