XPost: sci.logic
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.
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