Tarski anchors his whole proof in the Liar Paradox

[olcott]

*Tarski anchors his whole proof in the Liar Paradox*
https://liarparadox.org/Tarski_247_248.pdf
"x asserts that x is not a true sentence." page 248

https://liarparadox.org/Tarski_275_276.pdf
"x asserts that x is not a true sentence." page 248

is encoded as: x ∉ True if and only if p
"where the symbol 'p' represents the whole sentence x"

before it has been transformed page 275
we replace 'Tr' in this convention by 'Pr'

thus becomes // on page 275
"(1) x ∉ Provable if and only if p"
"where the symbol 'p' represents the whole sentence x"

*Proving that the Tarski Undefinability has an adapted*
*form of the Liar Paradox as the first line of his proof*

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

[immibis]

On 1/24/24 18:46, olcott wrote:
> *Tarski anchors his whole proof in the Liar Paradox*
> https://liarparadox.org/Tarski_247_248.pdf
>   "x asserts that x is not a true sentence." page 248
>
> https://liarparadox.org/Tarski_275_276.pdf
>   "x asserts that x is not a true sentence." page 248
>
> is encoded as: x ∉ True if and only if p
>   "where the symbol 'p' represents the whole sentence x"
>
> before it has been transformed page 275
>   we replace 'Tr' in this convention by 'Pr'
>
> thus becomes // on page 275
>   "(1) x ∉ Provable if and only if p"
>   "where the symbol 'p' represents the whole sentence x"
>
> *Proving that the Tarski Undefinability has an adapted*
> *form of the Liar Paradox as the first line of his proof*
>

How about you stick to the halting problem, which you actually have more
understanding about?

[Ross Finlayson]

You mean Entscheidungs or the branching problem?

Kind of like Chaitin computes the probability that halts,
P(halts), Chaitin's Omega?

Some people have it's about 85%, or, a standard deviation
or two off the mean, others starting at 50%, zero standard deviations.

How about those?

Tarski truth is just a matter of relevance logic really,
it's given the non-contradictory nature of things,
what's unambiguous following derivation,
also the quasi-modal's ex falso is excluded.

I aver that you understand neither Goedel,
nor Tarski, nor Chaitin, nor, Cohen.

Who together help have an overall theory of things.

Aren't all theories in one theory eventually, theory theory, theory?

Comenius language.

[olcott]

Thus Tarski erred in his false assumption that a correct and
consistent truth predicate True(L, x) must be able to correctly
determine the truth value of the non-truth bearer of the Liar Paradox.

[Richard Damon]

On 1/24/24 12:46 PM, olcott wrote:
> *Tarski anchors his whole proof in the Liar Paradox*
> https://liarparadox.org/Tarski_247_248.pdf
>   "x asserts that x is not a true sentence." page 248
>
> https://liarparadox.org/Tarski_275_276.pdf
>   "x asserts that x is not a true sentence." page 248
>
> is encoded as: x ∉ True if and only if p
>   "where the symbol 'p' represents the whole sentence x"
>
> before it has been transformed page 275
>   we replace 'Tr' in this convention by 'Pr'
>
> thus becomes // on page 275
>   "(1) x ∉ Provable if and only if p"
>   "where the symbol 'p' represents the whole sentence x"
>
> *Proving that the Tarski Undefinability has an adapted*
> *form of the Liar Paradox as the first line of his proof*
>

And you clearly don't see that he shows that this is a result of there
being a definition of Truth.

You just don't understand how logic works and are picking pieces out of
context, proving you just don't understand what you are talking about.

[Ross Finlayson]

Don't you mean "non-contradiction in a land of tertium-non-datur,
say what you want otherwise"?


Sounds like you're pretty immune to your own advice.

Yeah, I understand that having one's own criticism turned around really ruffles.

Tasted like chicken.

[olcott]

You may be the only one that can actually understand
what I am saying. You have previously demonstrated
deep knowledge of these kind of things.

[Ross Finlayson]

Doug Lenat's Cyc, well, I would disagree because clearly I am relaying it.

Yet, it does reflect, that restriction of comprehension, is non-logical.

[olcott]

I don't quite follow you on this.
The ZFC restriction on sets in required for set theory
to be coherent.

[Ross Finlayson]

You refer to "inconsistent multiplicities" about "regularity and the rulial".

You really should know class/set distinction, about a theory with one relation,
called elt or element-of, membership, vis-a-vis the class' relation of sethood, or contains,
it's still only one relation, but either way has that there are multiplicities.

So, "singularity theory", is about singularities like "division by zero",
"non-principal roots", singularities are multiplicities, "infinity".

So, regularity, well-foundedness, is a property of some sets, naively.

There are other notions of the regular and rulial, like the well-ordering principle.

The well-foundedness and well-ordering not being exactly the same,
makes for that it's pragmatic for axiomatic set theory and descriptive set theory,
to stipulate via fiat one fact, which is that there's a well-founded inductive set,
Axiom of Infinity, though that free comprehension simply arrives at their
being multiplicities and somehow, "infra-consistent", the objects that exist,
with respect to their singularities and principal branches variously, about
why there are singularities in set theory, in singularity theory, which is multiplicity theory.

And it seemed so nice, ....

[olcott]

BEGIN:(Clocksin & Mellish 2003:254)
Finally, a note about how Prolog matching sometimes differs from the
unification used in Resolution. Most Prolog systems will allow you to
satisfy goals like:

equal(X, X).
?- equal(foo(Y), Y).

that is, they will allow you to match a term against an uninstantiated
subterm of itself. In this example, foo(Y) is matched against Y,
which appears within it. As a result, Y will stand for foo(Y), which is
foo(foo(Y)) (because of what Y stands for), which is foo(foo(foo(Y))),
and so on. So Y ends up standing for some kind of infinite structure.
END:(Clocksin & Mellish 2003:254)

Not really. I actually refer to infinitely recursive structures
that can only be expressed in Prolog and my own Minimal Type Theory.
https://www.researchgate.net/publication/331859461_Minimal_Type_Theory_YACC_BNF

LP := ~True(LP) specifies ~True(~True(~True(~True(...))))

ZFC prevents the same thing with its redefinition of a {set}.
This seems to be a key precedent where undecidability was
eliminated by correcting the incoherent definition of terms.

> You really should know class/set distinction, about a theory with one relation,
> called elt or element-of, membership, vis-a-vis the class' relation of sethood, or contains,
> it's still only one relation, but either way has that there are multiplicities.
>
> So, "singularity theory", is about singularities like "division by zero",
> "non-principal roots", singularities are multiplicities, "infinity".
>
> So, regularity, well-foundedness, is a property of some sets, naively.
>
> There are other notions of the regular and rulial, like the well-ordering principle.
>
> The well-foundedness and well-ordering not being exactly the same,
> makes for that it's pragmatic for axiomatic set theory and descriptive set theory,
> to stipulate via fiat one fact, which is that there's a well-founded inductive set,
> Axiom of Infinity, though that free comprehension simply arrives at their
> being multiplicities and somehow, "infra-consistent", the objects that exist,
> with respect to their singularities and principal branches variously, about
> why there are singularities in set theory, in singularity theory, which is multiplicity theory.
>
> And it seemed so nice, ....
>

[Mild Shock]

I swear I read Rosa Parks!

But it says Ross.a.Finlayson. Whats the a
for? Does its stand for asshole spammer?

Ross Finlayson schrieb:

[Mikko]

On 2024-01-24 17:46:55 +0000, olcott said:

> *Tarski anchors his whole proof in the Liar Paradox*
> https://liarparadox.org/Tarski_247_248.pdf
> "x asserts that x is not a true sentence." page 248
>
> https://liarparadox.org/Tarski_275_276.pdf
> "x asserts that x is not a true sentence." page 248
>
> is encoded as: x ∉ True if and only if p
> "where the symbol 'p' represents the whole sentence x"
>
> before it has been transformed page 275
> we replace 'Tr' in this convention by 'Pr'
>
> thus becomes // on page 275
> "(1) x ∉ Provable if and only if p"
> "where the symbol 'p' represents the whole sentence x"
>
> *Proving that the Tarski Undefinability has an adapted*
> *form of the Liar Paradox as the first line of his proof*

That is not the first line of the proof. A large part of
the proof is proven before that line.

The main parts of the proof are:
(a) if there is a truth formul then a paradox can be proven
(b) a paradox is not true
from (a) and (b) by modus tollens
there is no truth formula

So the provable paradox is at the end of the part a,
not in its beginning.

As you have pointed no error in the proof of (a) we may
assume that you agree with it. You seem to agree with
(b), too. Modus tollens is regarded valid because we
have never observed any situation where some P is true
and some Q is false and P->Q is true.

Mikko