Re: Analytic Truth-makers

On 7/23/2024 6:30 AM, Richard Damon wrote:

On 7/23/24 12:07 AM, olcott wrote:

On 7/22/2024 9:56 PM, Richard Damon wrote:

On 7/22/24 10:12 PM, olcott wrote:

On 7/22/2024 8:42 PM, Richard Damon wrote:

On 7/22/24 8:44 PM, olcott wrote:

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?
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You are just caught in your own lies.
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YOU ADMITTED that statements, like Goldbach's conjecture, might be
 true based on being only established by an infinite series of
truth preserving operations.
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You seem to be too stupid about this too. You are too stupid to grasp
the idea of true and unknowable.
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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.

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So, is Goldbach'c conjecture possibly true in the formal system of
Mathematics, even if it can't be proven?
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No. If it requires an infinite sequence of truth preserving
operations it is not true in any system requiring a finite
sequence.

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So you LIED when you said Goldbach's conjuecture could bve actually TRUE even if it could only be established to be true by an infinite sequence of truth preserving operations.
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That you stupidly screw up the meaning of what I said in your own head
is your stupidity and not my dishonesty.

 So, what does it mean that it is analytic truth, if not that it is a truth?
 

L is the language of a formal mathematical system.
x is an expression of that language.
When we understand that True(L,x) means that there is a finite
sequence of truth preserving operations in L from the semantic
meaning of x to x in L, then mathematical incompleteness is abolished.
~True(L,x) ∧ ~True(L,~x)
means that x is not a truth-bearer in L.
It does not mean that L is incomplete
--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer