On 4/02/24 01:03, olcott wrote:
> In order to see exactly where arithmetic truth correctly plugs into
> analytic truth we must first understand that this is true:
>
> An analytic expression is: Any expression of language verified as
> completely true entirely on the basis of its relation to other
> expressions of language that derive their meaning from truth
> conditional semantics. (AKA stipulated truth).
>
> *Truth-conditional semantics* is an approach to semantics of natural
> language that sees meaning (or at least the meaning of assertions) as
> being the same as, or reducible to, their truth conditions.
> https://en.wikipedia.org/wiki/Truth-conditional_semantics
>
> *Analytic truth is*
> (a) Expressions stipulated to be true thus giving semantic meaning to
> terms. *similar to axioms*
>
> (b) Expressions derived by applying truth preserving finite string
> transformations to elements of (a) *similar to proofs from axioms*
>
> 'True in Russell's system' means, as was said:
> proved in Russell's system; and
> 'false in Russell's system' means:
> the opposite has been proved in Russell's system
> https://www.liarparadox.org/Wittgenstein.pdf
>
> AKA  True(RS, G) ≡ (RS ⊢ C)
> AKA False(RS, G) ≡ (RS ⊢ ¬G)
>

So you refute that a fact is true in one system by inventing a
completely different system.

You reject truth by contradiction, leading to "constructivist logic"
where the fact that something is proven not to be false does not mean it
is true.

On 2/5/24 9:45 AM, olcott wrote:
> On 2/5/2024 6:33 AM, Richard Damon wrote:
>> On 2/4/24 11:01 PM, olcott wrote:
>>> *You are almost there, and still ahead of both Gödel and Tarski*
>>>
>>> Let's start with the easier one first.
>>>
>>> Do you understand that non-truth bearers are out-of-scope of a truth
>>> predicate?
>>>
>>>
>>
>> Wrong, a Truth Predicate must take every statement that is an element
>> of the System.
>>
>
> You understand that epistemological antinomies are not truth
> bearers. Truth predicates only take truth bearers anything
> else is a type mismatch error.

Nope, predicates take any expression of the language they are in.

>
>> The definition of a Predicate means it can take anything in its domain,
>
> Its domain is expressions of language that are truth bearers.

Nope, statement of the language.

>
> When a halt decider is determining whether or not a TM description
> specifies a halting computation an English poem is invalid input
> only TM descriptions are in its domain.

It depends if that poem looks like the representation of a Halting
Computation or not.

>
>> and the requried domain for Tarski Truth Predicate is any statement in
>> the system L.
>>
>
> Thus an English poem is valid input to a halt decider.
>

Not if the input symbol set allows the poem to be encoded on the tape.

The question is does the input represent a Halting Computation.

>>
>> You keep on making this sort of error, you don't actually know the
>> definitions of terms, so you guess, and are wrong.
>
> Not at all. I was able to understand these definitions at a
> much deeper level by having first-hand understanding instead
> of just memorizing what textbooks say.

So, why do you keep having inputs that are not representaiton of
Computations?

>
> I see ALL of the reasoning behind these definitions thus can
> correctly adapt them to new situations. Others reject these
> new situations because they never read about them in any textbook.

Nope, you MISUNDERSTAND the meanings and perform illlogical operations
on the wrong definition.

>
> Epistemological antinomies are not truth bearers thus cannot
> be included in any formal system. You have a better understanding
> of this that Tarski or Gödel, at least you understand that they
> are not truth bearers. Neither Tarski nor Gödel understood this.
>
>

Yes, a non-contradictory system that support the property of the
excluded middle can not express an Epistemoogical Antinomy in its language.

If adding a "rule" that ends up allowing one to be expressed, then the
system must no longer be a non-contradictory system that supports the
property of the excluded middle.

YOU don't understand what Trski or Godel did in their proof, so you are
not in a position to put them down. You have effectively admitted this
by refusiong to even try to point out the step where they actually USED
an Epistemological Antinomy in a what that assumes it has a truth value.

Thus, you are just admitting to being a pathological liar.