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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.logic,comp.theory
Subject: Re: True on the basis of meaning --- Tarski
Date: Fri, 17 May 2024 21:07:53 -0400
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On 5/17/24 1:28 PM, olcott wrote:
> On 5/17/2024 10:56 AM, Mikko wrote:
>> On 2024-05-16 16:00:59 +0000, olcott said:
>>
>>> On 5/15/2024 3:43 AM, Mikko wrote:
>>>> On 2024-05-14 15:18:22 +0000, olcott said:
>>>>
>>>>> On 5/14/2024 4:16 AM, Mikko wrote:
>>>>>> On 2024-05-13 14:34:12 +0000, olcott said:
>>>>>>
>>>>>>> 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.
>>>>>>
>>>>>> That is not known. There are real world problems that are not yet
>>>>>> solved without an infinite seqeunce of inference steps and there
>>>>>> remains the possibility that some of them, or one that is not yet
>>>>>> thought to be a problem but will be, that cannot be solved without
>>>>>> an infinite sequence of inference steps.
>>>>>>
>>>>>> Anyway, whether real world problems are solvable without an infinite
>>>>>> sequence of inference steps is irrelevanto to the topic "True on the
>>>>>> basis of meaning".
>>>>>>
>>>>>
>>>>> My whole purpose with this whole thread is to show exactly how
>>>>> epistemological antinomies can be recognized and rejected thus
>>>>> not form the basis for any undecidability proofs or Tarski's
>>>>> undefinability theorem.
>>>>
>>>> There are provable sentences of the form A -> B where A is some
>>>> hypthesis and B is an epistemological antimńomy. How are these
>>>> true statments handled when B is rejected?
>>>
>>> Epistemological antinomies have no truth value and implication
>>> requires a pair of truth bearers that have a Boolean value thus
>>> your expression is rejected as a type mismatch error.
>>
>> So if X is true and Y something complicated we cannot trust that
>> X or Y is true without analyzing that Y?
>>
> 
> The lack of any sequence of truth preserving operations from
> expressions of language that have been stipulated to be true
> --set of finite string semantic meanings that form an accurate
> --model of the general knowledge of the actual world.
> to x or ~x indicates that x is not a truth bearer and must
> be rejected as a type mismatch error in any formal system of
> bivalent logic.
> 
> *This seems to screen out any any all undecidable inputs*
> 
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