Re: Analytic Truth-makers

On 7/22/2024 7:01 PM, Richard Damon wrote:

On 7/22/24 12:42 PM, olcott wrote:

I have focused on analytic truth-makers where an expression of language x is shown to be true in language L by a sequence of truth preserving operations from the semantic meaning of x in L to x in L.
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In rare cases such as the Goldbach conjecture this may require an infinite sequence of truth preserving operations thus making analytic knowledge a subset of analytic truth. https://en.wikipedia.org/wiki/Goldbach%27s_conjecture
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There are cases where there is no finite or infinite sequence of
truth preserving operations to x or ~x in L because x is self-
contradictory in L. In this case x is not a truth-bearer in L.
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 So, now you ADMIT that Formal Logical systems can be "incomplete" because there exist analytic truths in them that can not be proven with an actual formal proof (which, by definition, must be finite).
 

*No stupid I have never been saying anything like that*
If g and ~g is not provable in PA then g is not a truth-bearer in PA.
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Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer