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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory
Subject: Re: The Foundation of Linguistic truth is stipulated relations
 between finite strings
Date: Fri, 13 Sep 2024 13:06:13 -0400
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On 9/13/24 10:38 AM, olcott wrote:
> On 9/13/2024 6:52 AM, Mikko wrote:
>> On 2024-09-04 03:41:58 +0000, olcott said:
>>
>>> The Foundation of Linguistic truth is stipulated relations
>>> between finite strings.
>>>
>>> The only way that we know that "cats" <are> "animals"
>>> (in English) is the this is stipulated to be true.
>>>
>>> *This is related to*
>>> Truth-conditional semantics is an approach to semantics of
>>> natural language that sees meaning (or at least the meaning
>>> of assertions) as being the same as, or reducible to, their
>>> truth conditions. This approach to semantics is principally
>>> associated with Donald Davidson, and attempts to carry out
>>> for the semantics of natural language what Tarski's semantic
>>> theory of truth achieves for the semantics of logic.
>>> https://en.wikipedia.org/wiki/Truth-conditional_semantics
>>>
>>> *Yet equally applies to formal languages*
>>
>> No, it does not. Formal languages are designed for many different
>> purposes. Whether they have any semantics and the nature of the
>> semantics of those that have is determined by the purpose of the
>> language.
>>
> 
> Formal languages are essentially nothing more than
> relations between finite strings.
> 
> Thus, given T, an elementary theorem is an elementary
> statement which is true.
> https://www.liarparadox.org/Haskell_Curry_45.pdf
> 
> Some of these relations between finite strings are
> elementary theorems thus are stipulated to be true.
> 
> Thus True(L,x) merely means there is a sequence of truth
> preserving operations from x in L to elementary theorems
> of L.
> 

Right, but the claim that such a predicate exist proves that it can't do 
its job correctly, is Tarski showed that, at least for a sufficiently 
powerful system, that we CAN construct in its language, using just the 
axioms of the system, and the assumption that True(L, x) is an existing 
Truth Predicate, the statement: "X (in L) is defined to be ~True(L,x)" 
and then that such an X cause True to be unable to meet its requirements.