Re: Numbers in the Platonic Realm

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On 30 Nov 2012, at 21:28, meekerdb wrote:```
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```On 11/30/2012 10:02 AM, Roger Clough wrote:
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And a transcendent truth could be arithmetic truth or
the truth of necessary logic.
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True in logic and formal mathematics is just marker "T" that is preserved by the rules of inference.
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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.
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In applications it is interpreted as if it were the correspondence meaning of 'true'.
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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).
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But like all applications of mathematics, it may be only approximate.
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Yes, but for arithmetic it is pretty clear, as we share our intuition on the so-called standard finite numbers.
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Bruno

http://iridia.ulb.ac.be/~marchal/

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