Re: Analytic Truth-makers

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.
 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
 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.
  

 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.
 

 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.

So, is Goldbach'c conjecture possibly true in the formal system of
Mathematics, even if it can't be proven?
If so, why can't Godel's G be?

 

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.

But the rules of construction of MM prove that statements matching
certain conditions that are proven in MM are also true in PA.
And G meets that requirements. (note g is the number, not the statement)
We can show in MM, that no natural number g CAN satisfy that
relationship, because we know of some additional properties of that
relationship from our knowledge in MM that still apply in PA.
Thus, Godel PROVED that G is true in PA as well as in MM.
He also PROVED that there can't be a proof in PA for it.

 Here is the convoluted mess that Gödel uses https://www.liarparadox.org/G%C3%B6del_Sentence(1931).pdf

And your inability to understand it doesn't make it wrong.
It makes YOU wrong.

 

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
 

Really, then show what number g could possibly sattisfy the relationship.
I don't think you even undertstand what Curry is talking about, in fact, from some of your past comments, I am sure of that. (Note, not all "true" statements in L are "elementary statements" for the theory L as I believe you have stated in the past.