Re: Analytic Truth-makers

On 7/22/2024 7:17 PM, Richard Damon wrote:

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.
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 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.
 

You seem to be too stupid about this too.
You are too stupid to grasp the idea of true and unknowable.
In any case you are not too stupid to know that every
expression that requires an infinite sequence of truth
preserving operations would not be true in any formal system.

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.
 

No stupid that is not it.
A finite sequence of truth preserving operations in MM
proves that G is true in MM. Some people use lower case g.
Here is the convoluted mess that Gödel uses
https://www.liarparadox.org/G%C3%B6del_Sentence(1931).pdf

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.

No stupid that is not how it actually works. Haskell
Curry is the only one that I know that is not too
stupid to understand this.
https://www.liarparadox.org/Haskell_Curry_45.pdf
--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer