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From: Mild Shock <janburse@fastmail.fm>
Newsgroups: comp.theory,sci.logic
Subject: Re: ""self contradictory"" (Was: Analytic Truth-makers)
Date: Tue, 23 Jul 2024 00:49:10 +0200
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I don't have any sentence x, only a propositional
variable. You started with the following definition:

 > I have focused on analytic truth-makers where an
expression of language x is shown to be true in
language L by a sequence of truth preserving operations
from the semantic meaning of x in L to x in L.

BTW: I just notice that it is anyway utter nonsense.
What do you mean semantic meaning of x in L to x in L?

Holy cow, what crap is this? If the two sides x in L left
and x in L right are different things, that can be connected
by a operations, why not use some marker?

Like you go from x^ in L to x in L?

And define x^ the semantic meaning of x^. But what
is x then? What are you doing olli?

olcott schrieb:
> On 7/22/2024 3:46 PM, Mild Shock wrote:
>> And why is there no sequence of
>> logical transformations that leads to:
>>
>> p
>>
>> and no sequence of logical
>> transformations that leads to:
>>
>> ~p
>>
>> Is p self contradictory?
>>
> 
> You have it backwards.
> x ∉ True if and only if p
> where the symbol 'p' represents the whole sentence x
> 
> The above is a very clumsy way of saying
> that x is only true if x is not true.
> 
> We can know this because Tarski said the was using the
> Liar Paradox as his model:
> 
> It would then be possible to reconstruct the antinomy of the
> liar in the metalanguage, by forming in the language itself
> a sentence x such that the sentence of the metalanguage which
> is correlated with x asserts that x is not a true sentence.
> 
>> olcott schrieb:
>>> On 7/22/2024 3:18 PM, Mild Shock wrote:
>>>>
>>>> What do you mean by self contradictory.
>>>> Why is there no sequencce to:
>>>>
>>>> p
>>>>
>>>> or to
>>>>
>>>> ~p
>>>>
>>>> Is p self contradictory?
>>>>
>>>
>>> This sentence is not true is *self* contradictory.
>>> When it is formalized in Tarski formal system it
>>> becomes the basis for his undefinability theorem.
>>>
>>> Tarski's Liar Paradox from page 248
>>>     It would then be possible to reconstruct the antinomy of the liar
>>>     in the metalanguage, by forming in the language itself a sentence
>>>     x such that the sentence of the metalanguage which is correlated
>>>     with x asserts that x is not a true sentence.
>>>     https://liarparadox.org/Tarski_247_248.pdf
>>>
>>> Formalized as:
>>> x ∉ True if and only if p
>>> where the symbol 'p' represents the whole sentence x
>>> https://liarparadox.org/Tarski_275_276.pdf
>>>
>>>
>>>> olcott schrieb:
>>>>> I have focused on analytic truth-makers where an expression of 
>>>>> language x is shown to be true in language L by a sequence of truth 
>>>>> preserving operations from the semantic meaning of x in L to x in L.
>>>>>
>>>>> In rare cases such as the Goldbach conjecture this may require an 
>>>>> infinite sequence of truth preserving operations thus making 
>>>>> analytic knowledge a subset of analytic truth. 
>>>>> https://en.wikipedia.org/wiki/Goldbach%27s_conjecture
>>>>>
>>>>> There are cases where there is no finite or infinite sequence of
>>>>> truth preserving operations to x or ~x in L because x is self-
>>>>> contradictory in L. In this case x is not a truth-bearer in L.
>>>>>
>>>>>
>>>>>
>>>>
>>>
>>
>