Is there a sentence that proves itself is not provable?

[Scott Mayers]

@ logik,

My post response was to the OP. I'm not wasting any time on your insults. My response was to Pete and I'll wait for him to respond, IF he responds, thank you.

Corrective feedback insults you?

OK.... I figured you for somebody who doesn't like ignorance. Guess I was wrong.

All I can suggest is that you try some introspection. Is this insult you are feeling, or is it cognitive dissonance?

Are you Pete?

IF not, then your opinion is irrelevant. I did actually write a response with depth but lost it only to realize that I'm wasting my time attempting to appeal to someone who would only assuredly continue to troll. (By 'troll' I mean, "any one who will not let someone pass regardless of sincerity or appeal to their interests") Prove that you understand ANYTHING I have to say with respect. Considering you think you understand something 'universal' about reasoning, try this one challenge: can you compute an appeal to ME that isn't insulting? If you can't solve this one difficulty you have with me, then you've proven you cannot use your own powers of reasoning to demonstrate all logical problems can be completely solved.

[Logik]

IF not, then your opinion is irrelevant. I did actually write a response with depth but lost it only to realize that I'm wasting my time attempting to appeal to someone who would only assuredly continue to troll. (By 'troll' I mean, "any one who will not let someone pass regardless of sincerity or appeal to their interests").

Ignorance is as sincere as it comes.

Prove that you understand ANYTHING I have to say with respect.

The fact that I am correcting you is proof that I understand. If I didn't understand what you are saying - I wouldn't be able to correct you.

I am observing a false assumption -> I am providing you with corrective feedback.

Your false assumption was that computers are build atop of Boolean algebra. They do not HAVE to be built on boolean algebra.
It is just an arbitrary design decision we made for <reasons>.

Computers compute with or without Boolean logic. See Lambda calculus.

Considering you think you understand something 'universal' about reasoning, try this one challenge: can you compute an appeal to ME that isn't insulting.

Ironic that you should appeal to emotion while talking about reason

If you can't solve this one difficulty you have with me, then you've proven you cannot use your own powers of reasoning to demonstrate all logical problems can be completely solved.

What does navigating around your feelings have to do with logic?

Sure. I can spend an extraordinary amount of time learning what triggers your insecurities and learn how to navigate around them.

Or you can drop your shield and stop being so damn defensive, introspect based on the new information. Acknowledge and correct your errors and move on. Your ego might get bruised, but that's a good sign.

I am only offering free knowledge. If you want kindness and respect - go to a whore house and pay for it.

[Scott Mayers]

IF not, then your opinion is irrelevant. I did actually write a response with depth but lost it only to realize that I'm wasting my time attempting to appeal to someone who would only assuredly continue to troll. (By 'troll' I mean, "any one who will not let someone pass regardless of sincerity or appeal to their interests").

Ignorance is as sincere as it comes.

Prove that you understand ANYTHING I have to say with respect.

The fact that I am correcting you is proof that I understand. If I didn't understand what you are saying - I wouldn't be able to correct you.

I am observing a false assumption -> I am providing you with corrective feedback.

Your false assumption was that computers are build atop of Boolean algebra. They do not HAVE to be built on boolean algebra.
It is just an arbitrary design decision we made for <reasons>.

Computers compute with or without Boolean logic. See Lambda calculus.

Considering you think you understand something 'universal' about reasoning, try this one challenge: can you compute an appeal to ME that isn't insulting.

Ironic that you should appeal to emotion while talking about reason

If you can't solve this one difficulty you have with me, then you've proven you cannot use your own powers of reasoning to demonstrate all logical problems can be completely solved.

What does navigating around your feelings have to do with logic?

Sure. I can spend an extraordinary amount of time learning what triggers your insecurities and learn how to navigate around them.

Or you can drop your shield and stop being so damn defensive, introspect based on the new information. Acknowledge and correct your errors and move on. Your ego might get bruised, but that's a good sign.

I am only offering free knowledge. If you want kindness and respect - go to a whore house and pay for it.

Oh wise one, this still proves that you can't prove you are wiser than your own presumptuous claims. PROVE you are sufficiently wise enough to convince me of your own intelligence as superior to my presumed inferiority. If you can't do that, how can I trust you ARE superior?

[Logik]

Oh wise one, this still proves that you can't prove you are wiser than your own presumptuous claims. PROVE you are sufficiently wise enough to convince me of your own intelligence as superior to my presumed inferiority. If you can't do that, how can I trust you ARE superior?

Observe the language you are using to frame the social dynamic right now. "intelligence", "superior", "inferior".

Looks like you've doubled down on your ego-defence. Such a pity.

I am not "better" or "more intelligent" or "superior" to you. I have more experience. Applied, real-world, large scale, experience at all three of the global technology giants (Google, Facebook, Amazon). What I speak about is based on applied science/systems engineering. Not just reading/running my mouth on a philosophy forum.

In all this time you still insist on PROOF mind you. I must PROVE to you. That's Philosopher ego-defence trick No.2.

For the millionth time. The notion of "proof" applies to deductive/axiomatic systems ONLY. PROOF means "the theorem follows from the axioms".
Nothing more, nothing less. But you can't PROVE any of your axioms - so it's all a castle in the sky.

This place we find ourselves in (our minds, our universe) deduction doesn't work on its own. For the axioms you require in order to DO deduction are first obtained through induction. e.g "ALL swans are white" (because every damn swan we have seen so far has been white).

So the fact that you insist on "proof" in an inductive system is just another error in your reasoning that needs correcting.

I can't give you any "proof", but I can sure provide you with evidence. And best of all - I can provide you with falsifiers.

And if you don't know what to do with falsifiers. Well... maybe you need to start there.

What I do know about "reason" is that it requires induction AND deduction AND abduction AND pattern recognition AND counterfactual reasoning AND...AND....AND

And so your insistence on axioms, beginnings, origins, foundations, Big bangs et all biases all your thinking towards putting deductive reasoning on a pedestal.

Another label for people who rely entirely on foundationalist/deductive reasoning is "dogmatists".

[PeteOlcott]

I reformulated my whole position to make it more clear.

Tarski Undefinability Theorem Reexamined
Tarski proved that the Liar Paradox: G ↔ ~(F ⊢ G) is true in his meta-theory
and not provable in his theory without ever realizing that the only reason it is
not provable in his theory is that it is not true in his theory.
https://www.researchgate.net/publicatio ... Reexamined

The Tarski Undefinability Theorem is an enormously simpler way to examine incompleteness.

I also rewrote portions of this:
Philosophy of Logic – Reexamining the Formalized Notion of Truth
https://philpapers.org/archive/OLCPOL.pdf

[Speakpigeon]

In all this time you still insist on PROOF mind you. I must PROVE to you. That's Philosopher ego-defence trick No.2. For the millionth time. The notion of "proof" applies to deductive/axiomatic systems ONLY. PROOF means "the theorem follows from the axioms".

I'm happy to help here, just to dispel the conceptual fuzziness:

Proof
1. The evidence or argument that compels the mind to accept an assertion as true.

There. Much better.
Everyone sane understands what that means.
You can use it as a test of your sanity of mind.
I recommend it.
EB

[Logik]

Proof
1. The evidence or argument that compels the mind to accept an assertion as true.

There. Much better.
Everyone sane understands what that means.
You can use it as a test of your sanity of mind.
I recommend it.
EB

It compels THE mind? Whose mind, Frenchie? Yours or mine?

We've already determined that evidence does not sway you

[A_Seagull]

In all this time you still insist on PROOF mind you. I must PROVE to you. That's Philosopher ego-defence trick No.2. For the millionth time. The notion of "proof" applies to deductive/axiomatic systems ONLY. PROOF means "the theorem follows from the axioms".

I'm happy to help here, just to dispel the conceptual fuzziness:

Proof
1. The evidence or argument that compels the mind to accept an assertion as true.

There. Much better.
Everyone sane understands what that means.
You can use it as a test of your sanity of mind.
I recommend it.
EB

What you call a 'proof' is what I would call a 'hand-waving argument', ie it has no logical rigour.

[PeteOlcott]

Proof
1. The evidence or argument that compels the mind to accept an assertion as true.

There. Much better.
Everyone sane understands what that means.
You can use it as a test of your sanity of mind.
I recommend it.
EB

It compels THE mind? Whose mind, Frenchie? Yours or mine?

We've already determined that evidence does not sway you

The proofs that I am talking about are mathematical relations between finite strings of characters.

[Logik]

The proofs that I am talking about are mathematical relations between finite strings of characters.

Graph theory contains no "proofs".... only paths.

[Scott Mayers]

I reformulated my whole position to make it more clear.

Tarski Undefinability Theorem Reexamined
Tarski proved that the Liar Paradox: G ↔ ~(F ⊢ G) is true in his meta-theory
and not provable in his theory without ever realizing that the only reason it is
not provable in his theory is that it is not true in his theory.
https://www.researchgate.net/publicatio ... Reexamined

The Tarski Undefinability Theorem is an enormously simpler way to examine incompleteness.

I also rewrote portions of this:
Philosophy of Logic – Reexamining the Formalized Notion of Truth
https://philpapers.org/archive/OLCPOL.pdf

Yes, thank you. I recognized this and why I presented my argument. I prefer Turing because I like a mix of both the symbolic reasoning alone with the analogue of a computing device. The concept is the same but more intuitively grasped for my own personal taste. [I am troubled with using foreign symbols that you can't easily find on a regular keyboard with ease. Pictures, though symbols also, enable you to map them to reality making, what to my opinion about logic and reality, in sync with each other. j

You need a trusted initial complete and consistent logic to act as the mechanism of reasoning you use to judge about other systems. But because you can't use ALL domains as input to a given system, such as not being able to input your own system AS input to your own system to reason with, you can't solve all possible problems with one logic unless you expand the meaning of 'logic' to include inconsistency and incompleteness itself.

[This doesn't mean I understand your position though. I'd have to examine your updated rewrite to determine this.]

[Logik]

I am troubled with using foreign symbols that you can't easily find on a regular keyboard with ease. Pictures, though symbols also, enable you to map them to reality making, what to my opinion about logic and reality, in sync with each other.

If Mathematicians had their way for every meaning there would be one symbol. 1:1 mapping.

It would also be the death of language because it would become incredibly difficult to communicate anything until you learn the entire Alphabet which is "consistently adopted by everyone".

Alphabets are the problem AND the solution. You have 26 letters in English with which to construct ALL meaning.

You could have 100000 letters or 2.

The choice is arbitrary. Less letters - means more verbose expression. More letters means more succinct expression.

Still. English is the most efficient language when measuring the information transfer per letter.
https://www.realclearscience.com/blog/2 ... guage.html
https://www.irif.fr/~dxiao/docs/entropy.pdf

[PeteOlcott]

Yes, thank you. I recognized this and why I presented my argument. I prefer Turing because I like a mix of both the symbolic reasoning alone with the analogue of a computing device. The concept is the same but more intuitively grasped for my own personal taste. [I am troubled with using foreign symbols that you can't easily find on a regular keyboard with ease. Pictures, though symbols also, enable you to map them to reality making, what to my opinion about logic and reality, in sync with each other. j

You need a trusted initial complete and consistent logic to act as the mechanism of reasoning you use to judge about other systems. But because you can't use ALL domains as input to a given system, such as not being able to input your own system AS input to your own system to reason with, you can't solve all possible problems with one logic unless you expand the meaning of 'logic' to include inconsistency and incompleteness itself.

[This doesn't mean I understand your position though. I'd have to examine your updated rewrite to determine this.]

Of course it makes no sense to ask if a box of rabbits is greater than the integer three.
That is why all of the formal sentences that I specify can have type qualifiers.

Three universal Truth predicate axioms:
(1) ∀F∈ Formal_Systems ∀x ∈ WFF(F) (True(F, x) ↔ (F ⊢ x))
(2) ∀F∈ Formal_Systems ∀x ∈ WFF(F) (False(F, x) ↔ (F ⊢ ~x))
(3) ∀F∈ Formal_Systems ∀x ∈ WFF(F) (~True(F, x) ↔ ~(F ⊢ x))

The whole language for doing this is specified here:
https://www.researchgate.net/publicatio ... y_YACC_BNF

[Scott Mayers]

@PeteOlcott

I'm trying to interpret:

Because formal systems of symbolic logic inherently express and represent the deductive inference
model formal proofs to theorem consequences can be understood to represent sound deductive
inference to true conclusions without any need for other representations such as model theory.

From this, I am reading you making a claim of 'possibility' since the main verb is, "can be understood", and with a limiting possible conditional, "without any need for other representations", with an instance example of other representations, "...such as model theory".

By "model theory", as an instance of what you mean, I interpret this to be about asking what is or is not 'possible'. Given you are asserting a thesis about what is possible, then you appear to be just saying there is no need for some judgement about the truth-value of its inputs other than (that) one or the other is the set of what is 'possible' (verus what is 'not possible).

Are you suggesting that 'truth' about something is itself sufficiently defined through formal (deductive) systems without concern to the initial inputs being used? That is, I am asking if you mean that the concept of 'truth' with respect to reality (ie soundness) is sufficiently found in a theorem as represented by some formal system's axioms without a need for 'sound' inputs?

If so, I can accept this position. But I'm not sure if the way you present this sentence on your opening to your paper is clear enough....at least for the 'layperson' you may be targeting as an audience. Let me know if we understand each other before I may suggest any other way of expressing this in some other way.

[PeteOlcott]

@PeteOlcott

I'm trying to interpret:

Because formal systems of symbolic logic inherently express and represent the deductive inference
model formal proofs to theorem consequences can be understood to represent sound deductive
inference to true conclusions without any need for other representations such as model theory.

Are you suggesting that 'truth' about something is itself sufficiently defined through formal (deductive) systems without concern to the initial inputs being used?

No. Truth is deduction from true premises to true conclusions as expressed
as the valid use of rules-of-inference to theorem consequences.

So when the input is true then the output is true and that is all there is to the essence of truth.