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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory,sci.logic
Subject: Re: True on the basis of meaning --- Tarski
Date: Mon, 13 May 2024 09:34:12 -0500
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On 5/13/2024 3:52 AM, Mikko wrote:
> On 2024-05-12 17:19:48 +0000, olcott said:
> 
>> On 5/12/2024 10:33 AM, Mikko wrote:
>>> On 2024-05-12 14:22:25 +0000, olcott said:
>>>
>>>> On 5/12/2024 2:42 AM, Mikko wrote:
>>>>> On 2024-05-11 04:27:03 +0000, olcott said:
>>>>>
>>>>>> On 5/10/2024 10:49 PM, Richard Damon wrote:
>>>>>>> On 5/10/24 11:35 PM, olcott wrote:
>>>>>>>> On 5/10/2024 10:16 PM, Richard Damon wrote:
>>>>>>>>> On 5/10/24 10:36 PM, olcott wrote:
>>>>>>>>>> The entire body of expressions that are {true on the basis of 
>>>>>>>>>> their
>>>>>>>>>> meaning} involves nothing more or less than stipulated 
>>>>>>>>>> relations between
>>>>>>>>>> finite strings.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> You do know that what you are describing when applied to Formal 
>>>>>>>>> Systems are the axioms of the system and the most primitively 
>>>>>>>>> provable theorems.
>>>>>>>>>
>>>>>>>>
>>>>>>>> YES and there are axioms that comprise the verbal model of the
>>>>>>>> actual world, thus Quine was wrong.
>>>>>>>
>>>>>>> You don't understand what Quite was talking about,
>>>>>>>
>>>>>>
>>>>>> I don't need to know anything about what he was talking about
>>>>>> except that he disagreed with {true on the basis or meaning}.
>>>>>> I don't care or need to know how he got to an incorrect answer.
>>>>>>
>>>>>>>>
>>>>>>>>>
>>>>>>>>> You don't seem to understand what "Formal Logic" actually means.
>>>>>>>>>
>>>>>>>>
>>>>>>>> Ultimately it is anchored in stipulated relations between finite
>>>>>>>> strings (AKA axioms) and expressions derived from applying truth
>>>>>>>> preserving operations to these axioms.
>>>>>>>
>>>>>>> Which you don't seem to understand what that means.
>>>>>>>
>>>>>>
>>>>>> I understand this much more deeply than you do.
>>>>>
>>>>> In and about formal logic there is no valid deep understanding. Only
>>>>> a shallow understanding can be valid.
>>>>>
>>>>
>>>> It turns out that ALL {true on the basis of meaning} that includes
>>>> ALL of logic and math has its entire foundation in relations between
>>>> finite strings. Some are stipulated to be true (axioms) and some
>>>> are derived by applying truth preserving operations to these axioms.
>>>
>>> Usually the word "true" is not used when talking about uninterpreted
>>> formal systems. Axioms and what can be inferred from axioms are called
>>> "theorems". Theorems can be true in some interpretations and false in
>>> another. If the system is incosistent then there is no interpretation
>>> where all axioms are true.
>>>
>>
>> I am not talking about how these things are usually spoken of. I am
>> talking about my unique contribution to the actual philosophical
>> foundation of {true on the basis of meaning}.
> 
> What matters is that you are not talking about those things as they
> are usually spoken of. The consequence is that nobody is going to
> understand you, and the consequence of that probably is that you
> cannot contribute.
> 
>> This is entirely comprised of relations between finite strings:
>> some of which are stipulated to have the semantic value of Boolean
>> true, and others derived from applying truth preserving operations
>> to these finite string.
> 
> Most of that doesn't require any stipulations about semantics but
> can be done with finite strings and their relations. Semantics is
> only needed to choose interesting problems and, if a problem can
> be solved, to interprete the solution.
> 

The only way that a system of formalized natural language can
possibly know that {dogs} <are> {animals} is that it must be told.
See also Davidson's truth conditional semantics.
https://en.wikipedia.org/wiki/Truth-conditional_semantics

The only way that "dogs are animals" acquires semantic
meaning is the stipulated relation: {dogs} <are> {animals}.


>> This is approximately equivalent to proofs from axioms.
> 
> It shouod be exactly equivalent.
> 
>> It is not exactly the same thing because an infinite sequence of
>> inference steps may sometimes be required.
> 
> Infinite sequences create more problem than they solve. For example,
> you can prove that 1 = 2 with the infinite sequence
> 

For real world things that are never required. The various
conjectures seem to require an infinite sequence of inference steps.

>    1, 1, 1, ..., 2, 2, 2
> 
> where every element (except the first one) is equal to preceding element
> so by transitivity every element should be equal to the first one.
> 
>> It is also not exactly the same because some proofs are not restricted
>> to truth preserving operations.
> 
> A sequence of inferences that can derive a false conclusion from true
> premises should not be called a "proof".
> 

When X or ~X can be derived by applying a sequence of truth preserving
operations to a set of expressions that have been stipulated to have the
semantic value of Boolean True then X is True or False. Otherwise X is
not a truth bearer.

This screens out epistemological antinomies from forming the basis
for any derivation of True(L, x). By doing this Tarski Undefinability
is defeated.


-- 
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer