Logical arguments for the death of God.

[Age]

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.

Why do you refer to these 'two things' as 'documents' for, exactly?

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?

But, 'who' is saying 'the claim' is 'true'?

Obviously if one can not 'prove' some thing, then no one would say, 'it is true'.

Also, why would any one, "them" 'self', say, or worse still believe, some thing is true, if they do not even have the actual proof' for 'it/the claim'?

Furthermore, there is a huge difference between 'incontrovertible' and 'irrefutable', which you appear to have not yet considered, or are not yet aware of fully, at least.

[godelian]

Why do you refer to these 'two things' as 'documents' for, exactly?

A claim and its proof must be expressed in language. So, you could as well write them down. If you cannot express the proof in language, then you simply have no proof.

Claim: I am currently drinking a coffee.
Proof: ???

I can call lots of other people who can testify that it is true that I am drinking a coffee. None of us, however, can prove it. There is nothing that we can write in the second document to make the truth in the first document incontrovertible/irrefutable/whatever.

[Age]

Why do you refer to these 'two things' as 'documents' for, exactly?

A claim and its proof must be expressed in language.

But, the 'proof' part can not be observed 'in language', right?

So, you could as well write them down. If you cannot express the proof in language, then you simply have no proof.

But, it takes 'observation' to 'see' 'written language'. And, well according to you anyway, 'you cannot produce proof by observing anything'.

Claim: I am currently drinking a coffee.

Let 'us', here, not forget that 'this' is "godelian's" claim, as it certainly would not be 'my' claim, at all.

Proof: ???

Do 'you' have any proof that the 'i' drinks coffee, ever, let alone 'currently'?

By the way, who and/or what even is, or am, 'I', exactly?

I can call lots of other people who can testify that it is true that I am drinking a coffee. None of us, however, can prove it.

But,

1. Who can none of you, supposedly, prove it to, exactly?

2. How could lots of other people logically, and/or truthfully, testify that it is true that 'I' am 'currently' drinking a coffee, if none of you can even prove that 'i' am 'currently' drinking coffee?

'you' seem to have a really skewed and twisted view and perception of things, here. Well to 'me' anyway.

There is nothing that we can write in the second document to make the truth in the first document incontrovertible/irrefutable/whatever.

But, who is even claiming that 'it' is even true, anyway?

[godelian]

But, it takes 'observation' to 'see' 'written language'. And, well according to you anyway, 'you cannot produce proof by observing anything'.

A human will use his eyes to read a proof. A computer will typically not. A computer will read the proof from a file or another byte stream.

Language is not physically "observed". Language is "read". There may be an analog-digital conversion for that, but it is not essential.

Language is essentially not something physical. Pure reason only deals with language.

[Age]

But, it takes 'observation' to 'see' 'written language'. And, well according to you anyway, 'you cannot produce proof by observing anything'.

A human will use his eyes to read a proof. A computer will typically not. A computer will read the proof from a file or another byte stream.

Language is not physically "observed". Language is "read".

So, you, anyway, do not 'read', through 'physical observation'. So, how do 'you' 'read', exactly?

There may be an analog-digital conversion for that, but it is not essential.

Okay.

Language is essentially not something physical.

Yet, language is 'heard', physically, by the 'physical ears', and, 'seen', physically, by the 'physical eyes'.

Pure reason only deals with language.

Which is but just one of a few ways of gaining, and obtaining, 'actual proof/s'.

[godelian]

Yet, language is 'heard', physically, by the 'physical ears', and, 'seen', physically, by the 'physical eyes'.

That depends on the device that will verify the proof. It will typically just accept digital inputs.

Which is but just one of a few ways of gaining, and obtaining, 'actual proof/s'.

There is no physical proof possible. It is language only. Therefore, proof is always a document. The verifier verifies that document, and accepts or rejects it.

[Age]

Yet, language is 'heard', physically, by the 'physical ears', and, 'seen', physically, by the 'physical eyes'.

That depends on the device that will verify the proof. It will typically just accept digital inputs.

I am unclear as to what 'device' you are talking about or referring to, here, but I was talking about and referring to human beings, just in case you were unaware.

Which is but just one of a few ways of gaining, and obtaining, 'actual proof/s'.

There is no physical proof possible.

Once more, if 'this' is what you really want to keep on believing is absolutely true, here, then you are absolutely free to keep doing so.

It is language only.

Why do you not inform 'us' of how 'you' define the 'proof' word, exactly?

Therefore, proof is always a document. The verifier verifies that document, and accepts or rejects it.

if not through and by 'observation', then how, exactly?

[godelian]

I am unclear as to what 'device' you are talking about or referring to, here, but I was talking about and referring to human beings, just in case you were unaware.

Both humans and computers can act in the role of prover and verifier. If you say something about a prover or a verifier that is exclusively human, then I must reject that point of view because computers can also prove and/or verify.

I repeat, a proof is a computation. The verification of a proof is also a computation.

ChatGPT: Can computers prove or verify proof?

Yes, computers can both prove and verify proofs, but with some important distinctions:

Proof Verification (Well Established)

Computers are very good at verifying proofs. Given a formal proof written in a logical system (like first-order logic), a computer can check step by step whether the logic is valid. This process is:

Deterministic: The computer follows precise rules.
Reliable: As long as the logic system and software are sound, verification is trustworthy.
Common Tools: Examples include proof assistants like:
Coq
Isabelle
Lean
HOL Light

These systems have been used to formally verify extremely complex proofs (e.g., the Four Color Theorem, or Feit–Thompson theorem).

Proof Discovery (Possible but Hard)

Computers can also find or generate proofs, but this is much more difficult and depends on the domain:

Automated Theorem Provers like E, Vampire, and Z3 use algorithms to discover proofs in logic or algebra.
AI-assisted tools like Lean’s GPT-based autoformalization tools or OpenAI’s Codex can suggest steps or even entire formal proofs, especially in structured systems.

However, for complex or creative mathematical proofs, humans still lead in discovering key insights or strategies.

Hence, everything you say about proof, proving, or verifying proof that only applies to humans, is necessarily wrong.

[Age]

I am unclear as to what 'device' you are talking about or referring to, here, but I was talking about and referring to human beings, just in case you were unaware.

Both humans and computers can act in the role of prover and verifier.

I do not do so-called 'prover' nor 'verifier'. Just so you become aware.

If you say something about a prover or a verifier that is exclusively human, then I must reject that point of view because computers can also prove and/or verify.

Again, I do not 'do' 'prover' nor 'verifier', so I will never say absolutely any thing about any so-called 'provers' nor 'verifiers'.

I repeat, a proof is a computation. The verification of a proof is also a computation.

But, I will also repeat, What is 'proof', itself, to you, exactly?

ChatGPT: Can computers prove or verify proof?

Yes, computers can both prove and verify proofs, but with some important distinctions:

Proof Verification (Well Established)

Computers are very good at verifying proofs. Given a formal proof written in a logical system (like first-order logic), a computer can check step by step whether the logic is valid. This process is:

Deterministic: The computer follows precise rules.
Reliable: As long as the logic system and software are sound, verification is trustworthy.
Common Tools: Examples include proof assistants like:
Coq
Isabelle
Lean
HOL Light

These systems have been used to formally verify extremely complex proofs (e.g., the Four Color Theorem, or Feit–Thompson theorem).

Proof Discovery (Possible but Hard)

Computers can also find or generate proofs, but this is much more difficult and depends on the domain:

Automated Theorem Provers like E, Vampire, and Z3 use algorithms to discover proofs in logic or algebra.
AI-assisted tools like Lean’s GPT-based autoformalization tools or OpenAI’s Codex can suggest steps or even entire formal proofs, especially in structured systems.

However, for complex or creative mathematical proofs, humans still lead in discovering key insights or strategies.

Hence, everything you say about proof, proving, or verifying proof that only applies to humans, is necessarily wrong.

Okay, so absolutely every thing that 'I' say about 'proof', 'proving', or 'verifying proof', which applies to human beings, to you, is 'necessarily wrong'.

And, to you, it takes a computer to 'prove', to you, that, for example, there is 'a tree' 'over there' behind 'that mountain', or, that there are words in front of the screen that you are looking at and observing right now, right? Because, to you, human beings can not have things proved, to them, through observation, at all, correct?

[godelian]

And, to you, it takes a computer to 'prove', to you, that, for example, there is 'a tree' 'over there' behind 'that mountain', or, that there are words in front of the screen that you are looking at and observing right now, right?

These things cannot be proved, neither by a human, nor by a computer.

Because, to you, human beings can not have things proved, to them, through observation, at all, correct?

Correct. Neither humans nor computers can prove anything by means of observation.

ChatGPT: Can a claim be proved irrefutably by means of empirical observation?

No, a claim cannot be proved irrefutably by means of empirical observation.

Empirical observation always involves some degree of uncertainty due to:

1. Limited scope – We can't observe everything, only a subset of all possible instances.

2. Measurement error – Observations can be imprecise or affected by instruments or conditions.

3. Theory-ladenness – Observations are often interpreted through existing theories or assumptions.

4. Problem of induction – Just because something has always been observed doesn't guarantee it always will (e.g., the sun rising every day).

Scientific knowledge is provisional—based on the best available evidence, but always open to revision. So, while empirical evidence can strongly support a claim, it cannot make it absolutely irrefutable.

Would you like to explore how this relates to scientific theories or falsifiability?

[godelian]

Okay, so absolutely every thing that 'I' say about 'proof', 'proving', or 'verifying proof', which applies to human beings, to you, is 'necessarily wrong'.

That is not what I have said. The following is what I have said:

If what you say about proof only applies to humans and cannot apply to computers, then it is wrong.

Humans and computers are substitutes for each other as provers and verifiers. There is, of course, the sidenote that humans are noticeably better at discovering proof. Computers, on the other hand, are noticeably faster at verifying proof.

This invariant -- humans and computers are interchangeable in the context of proof -- is very important when discussing proof. If a computer cannot possibly verify your proof, then it is not even a proof to begin with.

This emphasizes an important property of proof. It is both produced and verified by pure reason alone. Computers are blind and deaf. They must still be able to verify your proof. Otherwise, it is not proof.

The Curry-Howard correspondence is adamant about the following:

A proof is a computation.

[Skepdick]

I would like to present some arguments for the death of God as a logical construct.

Who even believes in such a God? God is not a logical construct any more than the blacksmith is a construct of the hammers he makes.

3 Creation from nothing is impossible, as ex nihilo nihil fit holds—God, too, can’t defy reason to shape something from nothing.

4 The universe arises from God’s substance, a self-existent reality holding the full scope of being.

5 God’s absolute simplicity—structureless and timeless—marks Him as the universe’s sole source.

6 With no parts, His seamless unity requires His complete transformation into creation.

7 God became the universe entirely, leaving no trace of His transcendence.

This is where the Kalam sleight of hand really happens. Kalamists deny " ex nihilio", but then default to apophatic statements like "The creator of time, space, matter and structure is timeless, spaceless, immaterial and structurless."

You can't reconcile acceptance of ex nihilio nihil fit while arguing that space, time matter and structure follows from a spaceless, timeless, immaterial structurless God.

It's akin to getting color from something colorless; or truth from something truthless. Take the logical form "X -> Y" to represent the process of creation "God -> Universe" - by the principle "nemo dat quod non habet" the universe cannot have any properties God lacks.

If you are trying to approach God via logic your faith is misguided - the mystics were right. Logical/systematic thought simply lacks the tools to navigate paradox/contradictions.

[Skepdick]

Both humans and computers can act in the role of prover and verifier. If you say something about a prover or a verifier that is exclusively human, then I must reject that point of view because computers can also prove and/or verify.

I repeat, a proof is a computation. The verification of a proof is also a computation.

You still haven't figured out the implications of the symbol-grounding problem.

Prove or verify that the color of this sentence is red.

What grounds the symbol "red"?

[Age]

And, to you, it takes a computer to 'prove', to you, that, for example, there is 'a tree' 'over there' behind 'that mountain', or, that there are words in front of the screen that you are looking at and observing right now, right?

These things cannot be proved, neither by a human, nor by a computer.

Are you, here, speaking for:

1. you, only.

2. Some. Or,

3. Everyone.

Because, to you, human beings can not have things proved, to them, through observation, at all, correct?

Correct. Neither humans nor computers can prove anything by means of observation.

So, what 'this one', personally, believes is absolutely true, and right, here is 'now' absolutely clear.

ChatGPT: Can a claim be proved irrefutably by means of empirical observation?

No, a claim cannot be proved irrefutably by means of empirical observation.

To 'who', exactly?

1. The 'observer'.

2. Some people.

3. Everyone.

4. Artificial intelligence. Or,

5 A computer.

Also, what 'this' means is that to some human being made up so-called 'artificial intelligence', anyway, that if there are 'trees' 'on earth', or not, neither way can be, 'proved irrefutably so', by 'empirical observation', correct/

Empirical observation always involves some degree of uncertainty

you have really absolutely completely missed or misunderstood what I was actually saying and pointing out in the example I provided above, here.

due to:

1. Limited scope – We can't observe everything, only a subset of all possible instances.

2. Measurement error – Observations can be imprecise or affected by instruments or conditions.

3. Theory-ladenness – Observations are often interpreted through existing theories or assumptions.

4. Problem of induction – Just because something has always been observed doesn't guarantee it always will (e.g., the sun rising every day).

And, it is because of these things, here, why you completely and utterly missed and misunderstood what I was actually saying and meaning in the example I have provided so far.

And, because you have absolutely no interest at all in learning and/or understanding any thing further, more, or even at all, here, this is why you will keep on believing only what you have been and will keep on doing, here.

Scientific knowledge is provisional—based on the best available evidence, but always open to revision. So, while empirical evidence can strongly support a claim, it cannot make it absolutely irrefutable.

Exactly, and as I have continually been pointing out, it is for what you just said and wrote, here, why 'I' do not 'do evidence', and thus 'do proof' only, and instead.

Like you rightly pointed out, here, 'science' does not deal with what is actually True at all, 'science' only deals with what maybe, only.

Would you like to explore how this relates to scientific theories or falsifiability?

[/quote]

I am still trying to get you to comprehend and understand that, contrary to your absolute belief, here, you can actually produce proof through observations. But, 'we' are not really moving along, here, at all, correct?

[Age]

Both humans and computers can act in the role of prover and verifier. If you say something about a prover or a verifier that is exclusively human, then I must reject that point of view because computers can also prove and/or verify.

I repeat, a proof is a computation. The verification of a proof is also a computation.

You still haven't figured out the implications of the symbol-grounding problem.

How do you prove; or verify that any given object is the color red? What grounds the symbol "red"?

The exact same way that all 'truth' is found, and known.

Prove or verify that the color of this sentence is red.

Okay. But, once again, it is an absolute impossibility to 'prove' some thing to some one while they are believing the exact opposite is 'the truth'.

For example if and while you are believing that it is impossible to prove or verify that the color of 'that sentence' is 'red', then it is impossible to prove and/or verify, to you, that 'that sentence' is, in fact, actually red.