Re: Analytic Truth-makers

On 7/22/24 8:11 PM, olcott wrote:

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).
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 *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.
 

What makes it different fron Goldbach's conjecture?
You are just caught in your own lies.
YOU ADMITTED that statements, like Goldbach's conjecture, might be true based on being only established by an infinite series of truth preserving operations.
In PA, G (not g, that is the variable) is shown to be TRUE, but only estblished by an infinite series of truth preserving operations, that we can show exist by a proof in MM.
The truth of G transfers, because it uses nothing of MM, the Proof does not, as it depends on factors in MM, so can't be expressed in PA.