XPost: comp.theory, sci.logic, sci.math
From: acm@muc.de
[ Followup-To: set ]
In comp.theory olcott wrote:
> On 11/28/2025 3:08 PM, Alan Mackenzie wrote:
>> dart200 wrote:
>>> On 11/28/25 9:36 AM, Alan Mackenzie wrote:
>>>> dart200 wrote:
>>>>> does the logical construction:
>>>>> "this sentence is false"
>>>>> place a hard limit on our ability to understand truth:
>>>>> yes/no???
>>>> No, not at all. Anybody beyond early childhood will recognise it as a
>>>> mere frivolous distraction from any seeking after the truth.
>>> so why does anyone think such a construct places a meaningful limit in a
>>> formal system then?
>> People, in general, don't, apart from one or two exceptions.
>>> "this sentence has no proof"
>> That is a world apart from "This sentence is false.". It's the kernel
>> of Gödel's proof (as you know, of course). "This sentence has no proof"
>> turns out to be true and unprovable (for a precisely defined meaning of
>> "unprovable").
> *Within A new foundation for correct reasoning*
> (a) Every element of the body of knowledge that can
> be expressed in language is entirely composed of
> (1) A finite set of atomic facts
> (2) Every expression of language that is semantically
> entailed by (1)
> (b) a formal language based on Rudolf Carnap Meaning
> Postulates combined with The Kurt Gödel definition
> of the "theory of simple types"
> https://en.wikipedia.org/wiki/History_of_type_theory#G%C3%B6del_1944
> Where every semantic meaning is fully encoded syntactically
> as one fully integrated whole not needing model theory
> We have now totally overcome Gödel Incompleteness
> and Tarski Undefinability for the entire body if
> knowledge that can be expressed in language. It
> is now a giant semantic tautology.
You can't "overcome" these theorems, since they're not obstacles.
They're fundamental truths.
>>> "this program loops forever iff it's decided that it halts"
>> As you also know, this is the contradiction reached in one of the proofs
>> of the Halting Theorem. This is also not the same as "This sentence is
>> false.", though it is inspired by that nonsense.
> It is isomorphic.
Stop using mathematical terms you don't understand. There is no
isomorphism here. Your assertion is a category error.
>> None of these sentences/nonsenses limit our ability to understand truth.
>> They are part of the truth that we understand. They delineate
>> fundamental boundaries of what can be known and proven, in particular
>> that truth is more subtle than provability.
> That is bullshit as I have just proven.
Every time you use the word "proven" you appear to be lying. I can't
recall any occurrence where you were telling the truth.
> Within the giant semantic tautology of knowledge that
> can be expressed in language everything is proven or
> not an element of this body.
Your scheme is limited indeed, in that it is not powerful enough to
represent unprovable propositions. I (along with the vast majority of
mathematicians, scientists, philosophers, ....) do not accept such
limitations. These limitations involve not being able to do arithmetic
at all.
>> This opens the possibility that some mathematical conjectures may be
>> true but unprovable. That's just part of existence.
>>> --
>>> a burnt out swe investigating into why our tooling doesn't involve
>>> basic semantic proofs like halting analysis
>>> please excuse my pseudo-pyscript,
>>> ~ nick
> --
> Copyright 2025 Olcott
> My 28 year goal has been to make
> "true on the basis of meaning" computable.
> This required establishing a new foundation
> for correct reasoning.
--
Alan Mackenzie (Nuremberg, Germany).
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