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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: comp.theory
Subject: Re: The Foundation of Linguistic truth is stipulated relations between finite strings
Date: Sat, 14 Sep 2024 11:26:16 +0300
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On 2024-09-13 14:38:02 +0000, olcott said:

> 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.

Basically a formal language is just a set of strings, usually defined
so that it is easy to determine about each string whether it belongs
to that subset. Relations of strings to other strings or anything else
are defined when useful for the purpose of the language.

> Thus, given T, an elementary theorem is an elementary
> statement which is true.

That requires more than just a language. Being an elementary theorem means
that a subset of the language is defined as a set of the elementary theorems
or postulates, usually so that it easy to determine whether a string is a
member of that set, often simply as a list of all elementary theorems.

> https://www.liarparadox.org/Haskell_Curry_45.pdf
> 
> Some of these relations between finite strings are
> elementary theorems thus are stipulated to be true.

No, that conficts with the meanings of those words. Certain realtions
between strings are designated as inference rules, usually defined so
that it is easy to determine whether a given string can be inferred
from given (usually one or two) other strings. Elementary theorems
are strings, not relations between strings.

> Thus True(L,x) merely means there is a sequence of truth
> preserving operations from x in L to elementary theorems
> of L.

Usually that prperty of a string is not called True. Instead, a 
non-empty sequence of strings where each member is an elementary 
theorem or can be
inferred from strings nearer the beginning of the sequence by the inference
rules is called a proof. The set of theorems is the set that contains every
string that is he last members of a proof and no other string.

Postulates, theoresm, inference rules and theorems are not parts of a
language but together with language constritue a large system that is
called a theory. In order to discuss meanings and truth a still larger
system is needed where the strings of a theory are related to something
else (for example real world objects or strings of another language).

-- 
Mikko