On 12/2/2012 1:07 AM, Bruno Marchal wrote:


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).

On the contrary, I'm pointing out that they are NOT the same thing.

Brent

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/ <http://iridia.ulb.ac.be/%7Emarchal/>



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