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From: olcott <polcott333@gmail.com>
Newsgroups: sci.logic
Subject: Re: True on the basis of meaning --- Tarski
Date: Sat, 18 May 2024 11:59:24 -0500
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On 5/18/2024 2:46 AM, Mikko wrote:
> On 2024-05-17 17:28:19 +0000, olcott said:
> 
>> 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
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