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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: sci.logic
Subject: Re: True on the basis of meaning --- Tarski
Date: Sat, 18 May 2024 10:46:45 +0300
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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
> --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*

In my example X is one of those statements that are true according
to what is said above. Y is a syntactically correct formulat but
so compicated that to determine its truth value would require a
considerable effort.

I asked whether one must analyze Y in order to determine whether
X or Y is true. You didn't answer.

-- 
Mikko