Logical arguments for the death of God.

[Age]

Which is why I, again, do not do 'evidence', and I only do 'proof', only, and instead.

With the example of a proof, i.e. the digital signature protocol, in which the prover convinces the verifier, I just wanted to point out that you may believe that your kind of arguments would constitute proof, but they never do.

Are you some kind of imbecile?

If no, then why would you even begin to assume that 'my kind of arguments' would 'constitute proof'?

Also, what even are 'my kind of arguments', exactly?

And furthermore, did you miss the part where I talked about that only sound and valid arguments, only, provide, and are, proof?

The verifier may very well be a machine. It will never accept any of your arguments as incontrovertible.

I do not even know what you are trying to say and claim, here.

It is not that you "only do proof". The real situation is that you absolutely never do proof.

Is 'this' an irrefutable Fact?

Every proof is a computation. Where are your computations?

Why do you believe, absolutely, that 'every proof' is a computation?

Do you have any 'actual proof' that you are basing this belief and claim of yours on, here, exactly?

If yes, then where is 'that proof', exactly?

[Age]

If any one would like 'the proof' of what 'proof' and 'evidence' are, exactly, then, like always, let 'us' have a discussion.

[godelian]

Why do you believe, absolutely, that 'every proof' is a computation?
Do you have any 'actual proof' that you are basing this belief and claim of yours on, here, exactly?
If yes, then where is 'that proof', exactly?

The proof is itself obviously also a computation.

ChatGPT: Every proof is a computation

The statement "Every proof is a computation" reflects a deep and widely studied idea in logic, computer science, and the philosophy of mathematics. It's most famously associated with the Curry–Howard correspondence, also called the proofs-as-programs paradigm.

Here's a breakdown:

1. Curry–Howard Correspondence

This is a formal analogy between:
Proofs in logic ↔ Programs in computation
Propositions (logical statements) ↔ Types (in type theory)
In this view:
A proof of a proposition is like a program of a corresponding type.
Proving a theorem corresponds to writing a program.
Checking a proof is like type checking a program.

2. Implications of the Statement

A proof can be interpreted as a constructive algorithm: if you can prove that a solution exists, you can compute it.
Formal systems like Coq or Agda treat proofs as executable programs.
This shifts the focus from truth alone to constructibility or computability.

3. Limitations

While many formal proofs can be expressed as computations, some branches of classical mathematics rely on non-constructive proofs (e.g., existence proofs without explicit construction). In such cases, not every classical proof corresponds directly to a computation unless you reinterpret them constructively.

ChatGPT: proof of the Curry-Howard correspondence

How It Works: Sketch of the Proof

We'll outline how to establish the correspondence between natural deduction for implication and simply-typed lambda calculus.

Step 1: Propositions-as-Types

Each proposition in logic corresponds to a type in lambda calculus.
The implication A → B in logic corresponds to the function type A → B.

Step 2: Proofs-as-Programs

Each proof of a proposition corresponds to a lambda term of the corresponding type.
A proof of A → B is a function that, given a proof of A, returns a proof of B.
This matches the meaning of a lambda abstraction λx:A. M, where M is a term of type B.

...

Conclusion

So, the proof of the Curry–Howard correspondence is a mapping that shows:
Every constructive proof rule in natural deduction corresponds to a type rule or construct in lambda calculus.
Every normalization step in logic corresponds to a computation step in a program.

Maybe you should consider the following fact. It is not because you are not familiar with the Curry-Howard correspondence or that you do not understand any other formal argument involved that such argument would be wrong. It is obvious that if your understanding would be the benchmark for knowledge, that 99.999% of all knowledge would be deemed wrong. Hence, you really need to firmly reprogram yourself around the idea that there is a hell of a lot that you do not know.

[godelian]

Are you some kind of imbecile?

According to the Dunning-Kruger research on the matter, stupidity amounts to believing that you know when in fact you don't.

ChatGPT:

The Dunning–Kruger effect is a cognitive bias where people with low ability, knowledge, or experience in a domain overestimate their own competence.
It was first identified by psychologists David Dunning and Justin Kruger in a 1999 study. In short:
Incompetent individuals fail to recognize their own lack of skill.
They fail to recognize genuine skill in others.
They fail to accurately gauge the extremity of their inadequacy.
When their lack of skill is addressed through training or feedback, they can recognize and accept their previous incompetence.

Important: It's not just arrogance; it's a lack of metacognition — the ability to think about one’s own thinking and skill level.

When I write that "every proof is a computation", you are convinced that this is not true. You do not write this because you know anything about the subject but because of arrogance and a lack of metacognition, related to the known phenomenon that Incompetent individuals fail to recognize their own lack of skill.

The Dunning–Kruger effect explains that you call other people imbeciles mostly because you are in fact yourself one.

[godelian]

If any one would like 'the proof' of what 'proof' and 'evidence' are, exactly, then, like always, let 'us' have a discussion.

You have already demonstrated at length that you do not know what "proof" means.

[Age]

Why do you believe, absolutely, that 'every proof' is a computation?
Do you have any 'actual proof' that you are basing this belief and claim of yours on, here, exactly?
If yes, then where is 'that proof', exactly?

The proof is itself obviously also a computation.

What do you 'now' mean by, 'also'?

ChatGPT: Every proof is a computation

The statement "Every proof is a computation" reflects a deep and widely studied idea in logic, computer science, and the philosophy of mathematics. It's most famously associated with the Curry–Howard correspondence, also called the proofs-as-programs paradigm.

Here's a breakdown:

1. Curry–Howard Correspondence

This is a formal analogy between:
Proofs in logic ↔ Programs in computation
Propositions (logical statements) ↔ Types (in type theory)
In this view:
A proof of a proposition is like a program of a corresponding type.
Proving a theorem corresponds to writing a program.
Checking a proof is like type checking a program.

2. Implications of the Statement

A proof can be interpreted as a constructive algorithm: if you can prove that a solution exists, you can compute it.
Formal systems like Coq or Agda treat proofs as executable programs.
This shifts the focus from truth alone to constructibility or computability.

3. Limitations

While many formal proofs can be expressed as computations, some branches of classical mathematics rely on non-constructive proofs (e.g., existence proofs without explicit construction). In such cases, not every classical proof corresponds directly to a computation unless you reinterpret them constructively.

ChatGPT: proof of the Curry-Howard correspondence

How It Works: Sketch of the Proof

We'll outline how to establish the correspondence between natural deduction for implication and simply-typed lambda calculus.

Step 1: Propositions-as-Types

Each proposition in logic corresponds to a type in lambda calculus.
The implication A → B in logic corresponds to the function type A → B.

Step 2: Proofs-as-Programs

Each proof of a proposition corresponds to a lambda term of the corresponding type.
A proof of A → B is a function that, given a proof of A, returns a proof of B.
This matches the meaning of a lambda abstraction λx:A. M, where M is a term of type B.

...

Conclusion

So, the proof of the Curry–Howard correspondence is a mapping that shows:
Every constructive proof rule in natural deduction corresponds to a type rule or construct in lambda calculus.
Every normalization step in logic corresponds to a computation step in a program.

Maybe you should consider the following fact. It is not because you are not familiar with the Curry-Howard correspondence or that you do not understand any other formal argument involved that such argument would be wrong. It is obvious that if your understanding would be the benchmark for knowledge, that 99.999% of all knowledge would be deemed wrong. Hence, you really need to firmly reprogram yourself around the idea that there is a hell of a lot that you do not know.

Again, what are you even on about now, here, exactly?

Look, it is very, very simple;

you made the claim, 'Proof is exclusively the product of pure reason, which is deaf and blind. You cannot produce proof by observing anything.'

To wit I then went on to show one example, out of countless other examples, of when 'observing' can be and is a so-called 'product of' 'proof', and thus 'a proof', itself. Now, obviously so-called 'pure reason', backed up with and supported by a 'sound and valid argument', is also a so-called 'product of' 'proof'.

Once more if you really want to believe that 'proof', itself, can not be produced by 'observing', itself, then go on ahead and keep believing this, already proved, False, Wrong, Inaccurate, and Incorrect belief and claim, of yours alone, here.

[godelian]

you made the claim, 'Proof is exclusively the product of pure reason, which is deaf and blind. You cannot produce proof by observing anything.'

Yes, a proof is a computation.
Computations are deaf and blind.

To wit I then went on to show one example, out of countless other examples, of when 'observing' can be and is a so-called 'product of' 'proof', and thus 'a proof', itself.

Impossible.

Seeing something in front of you, is not equivalent to proof that it is in front of you.

The expression of a proof is a document, i.e. a finite, structured object made of symbols according to the rules of a formal language, designed so that a verifier can check the validity of the reasoning. For any immediate perception P, there does not exist a finite sequence of statements S1,S2,...,Sn such that Sn=P and each Si​ follows from earlier Sj​ (for j<i) by purely logical inference rules starting from a set of axioms independent of sensory experience.

You cannot provide such document to a verifier, that proves that you can see what you see in front of you.

The visible reality in front of you, is true (to you) but unprovable (to others).

Once more if you really want to believe that 'proof', itself, can not be produced by 'observing', itself, then go on ahead and keep believing this, already proved, False, Wrong, Inaccurate, and Incorrect belief and claim, of yours alone, here.

It is standard knowledge that no proof can come from physical observation:

ChatGPT: Can mathematical proof be obtained by physical observation?

Good question. The short answer is: no, not in the strict sense.

Mathematical proof, by its traditional definition, is a sequence of purely logical deductions from axioms and previously proven theorems. It's formal, symbolic, and independent of the physical world. Proof guarantees absolute certainty (within the system), whereas physical observation only gives empirical evidence, which is always subject to error, measurement limits, and interpretation.

[Age]

Are you some kind of imbecile?

According to the Dunning-Kruger research on the matter, stupidity amounts to believing that you know when in fact you don't.

1. A 'Yes', or, a 'No' was only required for 'that question'.

2. Why are you just providing 'this information', which you did, here, exactly?

3. I used the word 'imbecile', but you thought it was appropriate to mention and talk about 'stupidity'.

4. Why do you keep presuming that I am meaning and/or assuming some thing when all I am essentially doing is just asking you questions, for clarity sake, from a Truly open perspective.

5. There were two parts to my questions in that post. If the answer was 'No' you are not an imbecile, then there was the 'next part' following on. Did you manage to comprehend and understand 'this'?

ChatGPT:

The Dunning–Kruger effect is a cognitive bias where people with low ability, knowledge, or experience in a domain overestimate their own competence.
It was first identified by psychologists David Dunning and Justin Kruger in a 1999 study. In short:
Incompetent individuals fail to recognize their own lack of skill.
They fail to recognize genuine skill in others.
They fail to accurately gauge the extremity of their inadequacy.
When their lack of skill is addressed through training or feedback, they can recognize and accept their previous incompetence.

Important: It's not just arrogance; it's a lack of metacognition — the ability to think about one’s own thinking and skill level.

When I write that "every proof is a computation", you are convinced that this is not true.

But I am not 'convinced'. I 'know' that 'proof' can be provided by and/or in;

Actual physical form, and thus can be 'observed'. Which is obviously contrary to your belief and claim, here.

Reason form, in and through sound and valid arguments. And,

Computation form, as you have said.

You do not write this because you know anything about the subject but because of arrogance and a lack of metacognition, related to the known phenomenon that Incompetent individuals fail to recognize their own lack of skill.

If you this is what you want to believe is true, then this is perfectly fine and okay, with me.

But, have you considered that you could be going off track, here, because your own thinking could be somewhat scattered, and/or could your level of cognitive skill, here, not be as good, nor great, as you think or believe it is? Or, is this not a possibility to you.

The Dunning–Kruger effect explains that you call other people imbeciles mostly because you are in fact yourself one.

But, I never ever called absolutely any one an imbecile, here.

Once again, here is further proof of just how often the actual words that i write and present, here, are not read, and understood, in the actual way that they are presented, and meant, exactly.

[Age]

If any one would like 'the proof' of what 'proof' and 'evidence' are, exactly, then, like always, let 'us' have a discussion.

You have already demonstrated at length that you do not know what "proof" means.

If this is what you believe is absolutely true, then okay.

Now, from what you have just said and written, here, it appears that you believe that you know what 'proof' is, exactly. So, what is 'proof', exactly, to you "godelian'"?

Let 'us' see if 'this one' really does 'know'.

But, of course, if it shows that it does not know, then it, again, is providing another great example of the "dunning-kruger" effect.

So, again, let 'us' see if 'this one' can show 'us' that it actually knows what 'proof' is, exactly.

[godelian]

So, again, let 'us' see if 'this one' can show 'us' that it actually knows what 'proof' is, exactly.

ChatGPT: Does proof, i.e. incontrovertible evidence, exist outside mathematics?

In most fields outside mathematics and formal logic, "proof" in the strict, absolute sense—meaning incontrovertible, deductive certainty—does not exist.

Mathematics operates within formal systems where proofs are constructed from axioms using strict rules of logic, making them airtight within that system. In contrast, fields like science, history, or law rely on evidence and inference, which can be extremely strong but are always open to revision or reinterpretation if new information comes to light.

For example:

Science deals with theories supported by overwhelming empirical evidence, but any theory can, in principle, be overturned by new observations.

History relies on documents, artifacts, and accounts, which can be misinterpreted or incomplete.

Law talks about "proof beyond a reasonable doubt," which is a high standard but still not absolute.

There is no proof outside pure reason. By definition, pure reason is deaf and blind. Otherwise, it would not be pure.

[Age]

you made the claim, 'Proof is exclusively the product of pure reason, which is deaf and blind. You cannot produce proof by observing anything.'

Yes, a proof is a computation.
Computations are deaf and blind.

And, as I just showed, and proved, very clearly, you can actually produce 'proof' by observing things.

Now, are you, still, 'trying to' claim that you can not produce 'proof' by observing absolutely any thing at all?

If you are, then you really are not comprehending and understanding, here.

To wit I then went on to show one example, out of countless other examples, of when 'observing' can be and is a so-called 'product of' 'proof', and thus 'a proof', itself.

Impossible.

So, when I provide an actual example of when 'proof' can be produced by and through observing, you are convinced that it is not true, right?

And, like always, your open and honest answer and clarification would be and will be much appreciated.

Seeing something in front of you, is not equivalent to proof that it is in front of you.

The expression of a proof is a document, i.e. a finite, structured object made of symbols according to the rules of a formal language, designed so that a verifier can check the validity of the reasoning.

Once again, 'we' have 'another one', here, who actually believes that the one and only definition that it uses for 'a word' is the one and only definition for 'that word'.

For any immediate perception P, there does not exist a finite sequence of statements S1,S2,...,Sn such that Sn=P and each Si​ follows from earlier Sj​ (for j<i) by purely logical inference rules starting from a set of axioms independent of sensory experience.

And, the sun rays on earth are 'proof' that the sun is 'shining light on earth'. Well to 'us' anyway, but not to you, right?

You cannot provide such document to a verifier, that proves that you can see what you see in front of you.

Again, you seem to be going off on some random topic and track, here.

Once more, you claimed that you can not produce proof by observing absolutely any thing at all. However, I have now produced two examples of when 'proof' is provided with, through, and by observing things.

Now, you are 'trying' your hardest to not acknowledge and accept these two examples, which prove that observing things can produce proof. Obviously you can keep refusing to 'see' and accept Facts, themselves, but others are seeing your denial, here.

The visible reality in front of you, is true (to you) but unprovable (to others).

Which is exactly why I allow others to acknowledge and accept 'proof/s' themselves. In my first example I just 'led' them to 'the tree', and it was up to them, completely, to accept 'that' as 'proof', or not.

And, just like you will not accept that the example I gave is 'proof' that one can actually produce 'proof' through and by observing things, you, and everyone else, are absolutely free to choose to accept and not accept absolutely any thing one wants to. But, as I have been continually saying, and stating, having and/or holding pre-existing views, beliefs, or assumptions will affect 'the way' one 'looks at' and 'sees' things.

Once more if you really want to believe that 'proof', itself, can not be produced by 'observing', itself, then go on ahead and keep believing this, already proved, False, Wrong, Inaccurate, and Incorrect belief and claim, of yours alone, here.

It is standard knowledge that no proof can come from physical observation:

So-called 'standard knowledge' to who and/or what, exactly?

ChatGPT: Can mathematical proof be obtained by physical observation?

Good question. The short answer is: no, not in the strict sense.

Why would any one want to add the 'mathematical' word in, here, other than to just 'try to' trick and deceive others, here?

Not once has 'mathematical proof' been talked about nor mentioned, but you 'now' 'try to' use those words as though they have any thing at all to do, here, with any thing at all.

Again, you claimed that one can not produce 'proof' by observing any thing at all.

Mathematical proof, by its traditional definition, is a sequence of purely logical deductions from axioms and previously proven theorems. It's formal, symbolic, and independent of the physical world. Proof guarantees absolute certainty (within the system), whereas physical observation only gives empirical evidence, which is always subject to error, measurement limits, and interpretation.

Once more, what are you even on about, here?

'Mathematical proof', itself, has nothing at all to do with 'proof', itself, here.

One can produce 'proof' by observing things.

For example, if I claimed that if you are 'looking at' 'these words', here, 'now', then there is a screen in front of 'those eyes'. And, to 'prove' 'this', then I can do 'this' by producing 'the proof' by 'you' observing the 'very thing', which 'you' are 'looking at', right here, right now.

But, you are 'convinced' that 'this' is not true, right?

[Age]

So, again, let 'us' see if 'this one' can show 'us' that it actually knows what 'proof' is, exactly.

ChatGPT: Does proof, i.e. incontrovertible evidence, exist outside mathematics?

In most fields outside mathematics and formal logic, "proof" in the strict, absolute sense—meaning incontrovertible, deductive certainty—does not exist.

Mathematics operates within formal systems where proofs are constructed from axioms using strict rules of logic, making them airtight within that system. In contrast, fields like science, history, or law rely on evidence and inference, which can be extremely strong but are always open to revision or reinterpretation if new information comes to light.

For example:

Science deals with theories supported by overwhelming empirical evidence, but any theory can, in principle, be overturned by new observations.

History relies on documents, artifacts, and accounts, which can be misinterpreted or incomplete.

Law talks about "proof beyond a reasonable doubt," which is a high standard but still not absolute.

There is no proof outside pure reason. By definition, pure reason is deaf and blind. Otherwise, it would not be pure.

Here is another prime example of just how Truly closed one can and does become when they hold onto and maintain their 'currently' held onto belief.

[godelian]

For example, if I claimed that if you are 'looking at' 'these words', here, 'now', then there is a screen in front of 'those eyes'. And, to 'prove' 'this', then I can do 'this' by producing 'the proof' by 'you' observing the 'very thing', which 'you' are 'looking at', right here, right now.
But, you are 'convinced' that 'this' is not true, right?

You confuse truth and proof.

What you see, is true. However, you cannot prove that you have seen it. Two or more people can see it and know that it is true. They still cannot prove that they saw it.

The verifier did not see it. He just wants a copy of your proof in order to verify it. Please, give him a copy.

[godelian]

Here is another prime example of just how Truly closed one can and does become when they hold onto and maintain their 'currently' held onto belief.

There are two documents: (1) the claim (2) the proof.

In the first document, the claim, you write, "I saw a car in the street this afternoon. At least five other people saw it too." What exactly are you going to write in the second document, the proof, that will render the truth in your first document incontrovertible?

[Age]

For example, if I claimed that if you are 'looking at' 'these words', here, 'now', then there is a screen in front of 'those eyes'. And, to 'prove' 'this', then I can do 'this' by producing 'the proof' by 'you' observing the 'very thing', which 'you' are 'looking at', right here, right now.
But, you are 'convinced' that 'this' is not true, right?

You confuse truth and proof.

Considering that you will not present your own personal definition for the 'proof' word, here, why do you believe, absolutely, that 'I' confuse 'truth' and 'proof'.

Now, for you to 'prove' 'your' claim, here, that 'I' confuse 'truth' and 'proof', 'true', you will 'have to' provide what 'my definitions' are for these two words, and also provide 'your definitions' for these two words.

But, firstly, would you like to explain to 'the readers', here, how you already, supposedly, 'know', irrefutably, what 'my definitions' are for those two words, when 'i' have, obviously, not yet provided them, here.

What you see, is true.

So, 'now' 'this one' is 'trying to' claim that when one 'sees' hallucinations, for example, then what they 'see', is true.

Once more, what 'we' have, here, is another prime example of 'another one' 'looking for' and 'trying to' use any word/s, which it hopes will somehow back up and support its 'current' beliefs and/or claims.

Instead of just acknowledging and accepting that I just showed, and proved, that one can actually produce 'proof' from 'observing' things, 'this one' would rather spend so much unnecessary 'time' 'trying' its very hardest to 'hang onto' and keep maintaining its 'current' belief, although it has absolutely nothing, which could even begin to back up and support its belief and claim, here.

However, you cannot prove that you have seen it.

Did any one even 'think' 'this', let alone 'say' and/or 'claim' that you could?

Two or more people can see it and know that it is true. They still cannot prove that they saw it.

Have you heard of the expression, 'Clutching at straws', before?

The verifier did not see it. He just wants a copy of your proof in order to verify it. Please, give him a copy.

Please give 'some male' a copy of 'what', exactly?

And, also 'what for', exactly?