Godel's Argument For God is Not Realistic

[Skepdick]

I don't understand your point in relation to my claim;

Numbers by themselves are not mathematics per se.

Numbers by themselves are absolutely Mathematics.

1, 2, 3, 4.

Numbers paired WITH UNITS are not Mathematics.
1 APPLE
2 APPLES

Here's AI's [wR] views.

No, numbers by themselves are not considered mathematics. Mathematics is the study of concepts like numbers, their properties, relationships, and structures.
Just seeing individual numbers is like having building blocks; mathematics is what you do with those blocks to build something.
Just seeing the digits 1, 2, 3, 4 doesn't involve any mathematical concepts.

Here's an analogy: Imagine having a bunch of Legos. The Legos themselves aren't what make something mathematical. But, if you start to follow instructions to build a complex structure, or if you use the Legos to explore ideas like symmetry or angles, then that's getting into the realm of mathematics.


Numbers are fundamental abstractions that represent quantities.
Mathematics explores how these numbers behave, how they relate to each other, and how they can be used to solve problems.
For instance, knowing the number 3 doesn't involve any mathematics. But understanding that 3 + 1 = 4 or that 3 is a prime number does involve mathematical concepts.

Neither you, nor the AI seem to understand the difference between numbers and numerals.

In the same way that philosophers can't agree what philosophy is - Mathematicians can't agree what Mathematics is.

Because "What is X?" is a metaphysical question. It has no good answers - pay attention and you'll develop some intuition.

[godelian]

If the problem is undecidable, i.e. the search algorithm does not halt, the situation is still fine. The real poison pill is the actual witness. If you find it, it is game over.

This amounts to nothing more than self-justification for the paradigm of axiomatics. But that's precisely the problem!

Example: Assume a fair coin. You flip it N times - you get a streak of N tails.

What's the witness, the smallest N sufficient to reject the fairness axiom?

Nobody can find a witness that you can't even specify. Even if the witness is guaranteed to exist - how would I know that I've found it?

Here's a lesson worth learning/remembering: Ask an unbounded question, get an uncomputable answer

An inconsistency is easy to specify. For example, if you manage to prove that 0=1, then you have your witness, which is simply the proof. All you need to do is to discover a poison-pill statement P, prove "P", and then prove "not P". If you manage to do that from PA, then PA is simply dead. Any logic sentence P in the language of PA will do.

You will perfectly well know when you have discovered P, because you will have proof for "P and not P".

[Skepdick]

An inconsistency is easy to specify. For example, if you manage to prove that 0=1, then you have your witness, which is simply the proof. All you need to do is to discover a poison-pill statement P, prove "P", and then prove "not P". If you manage to do that from PA, then PA is simply dead. Any logic sentence P in the language of PA will do.

You will perfectly well know when you have discovered P, because you will have proof for "P and not P".

He says it's easy to specify. And then he fails to specify it.

I mean - specify what an inconsistency is in the language of PA, stupid.

If you can't encode it in the system - how do you expect to find it in the system?

[godelian]

An inconsistency is easy to specify. For example, if you manage to prove that 0=1, then you have your witness, which is simply the proof. All you need to do is to discover a poison-pill statement P, prove "P", and then prove "not P". If you manage to do that from PA, then PA is simply dead. Any logic sentence P in the language of PA will do.

You will perfectly well know when you have discovered P, because you will have proof for "P and not P".

He says it's easy to specify. And then he fails to specify it.

I mean - specify what an inconsistency is in the language of PA, stupid.

If you can't encode it in the system - how do you expect to find it in the system?

1) Enumerate a whole bunch of arbitrarily-chosen candidate logic sentences P.
2) Try to prove P.
3) Try to prove not P.

isProvable(P) can be encoded. Obviously, isProvable(not P) can be encoded too.

So, you can encode this. I did not say that you will find P, but you can clearly try to.

[Skepdick]

1) Enumerate a whole bunch of arbitrarily-chosen candidate logic sentences P.
2) Try to prove P.
3) Try to prove not P.

isProvable(P) can be encoded. Obviously, isProvable(not P) can be encoded too.

So, you can encode this. I did not say that you will find P, but you can clearly try to.

Is there are reason you are refusing to specify P (the contradiction) in a PA encoding?

Also, why are you assuming LEM again? isProvable(P) or isProvable(not P)

[Skepdick]

An inconsistency is easy to specify. For example, if you manage to prove that 0=1, then you have your witness, which is simply the proof.

I think the crux of the matter here, is that you have no actual idea what the "=" operator means.

The 2nd Peano axiom literally states: For every natural number x, x = x.

OK, great! So what does that mean in computational terms? Does x=x mean the computation Equals(x,x) always halts; or never halts?
Which computational behaviour are you encoding as "true" and which as "false" ?

If halting is "True" and failure to halt is "False" then then 1=1 halts and 1=2 doesn't halt?

[godelian]

OK, great! So what does that mean in computational terms? Does x=x mean the computation Equals(x,x) always halts; or never halts?

I assume that it halts for finite numbers. It may halt or not halt when dealing with nonstandard models of arithmetic, but I assume the standard model here.

This will have to computed on a real-world computer and not an abstract one, because we need an actual witness here and not just a computation method for one.

[Skepdick]

OK, great! So what does that mean in computational terms? Does x=x mean the computation Equals(x,x) always halts; or never halts?

I assume that it halts for finite numbers. It may halt or not halt when dealing with nonstandard models of arithmetic, but I assume the standard model here.

This will have to computed on a real-world computer and not an abstract one, because we need an actual witness here and not just a computation method for one.

You failed to answer the question. What does halting amount to? Truth or Falsehood?

The actual witness is the actual computer program. Such as the program Equals() which takes two arguments.

The program Equals(1,1) either halts or doesn't.
The program Equals(1,2) either halts or doesn't.

I am asking you to explain what such a program is actually witnessing. If the program halts does it mean it's witnessing equality or non-equality?

This thing you don't seem to grasp about the subtle difference between Mathematics and Computation. Computational functions need to return some result; or at the very least - they simply need to return/halt. Mathematical functions don't.

How do you return (signal?) "True" and "False" in the language of PA? How do you signal the difference between (1=1) and (0=1)?

You can't use 0 and 1. Those names are taken...

So you have yourself a super serious Mathematical problem.

Either equality is decidable (0=0); or non-equality is decidable (0=1).
Iff PA can prove both equality and non-equality then PA can prove both P and not-P.

[godelian]

Godelian's claimed;
Godel's God is true, thus real.

My practical view on the matter is rather that there is now mathematically unobjectionable proof for religion while there isn't one for atheism.

Secondly, Godel's proof raises the bar because all criticism must be directed at its axioms, which are expressed in higher-order modal logic, which I do not expect most atheist to be able to master.

By raising the bar and forcibly removing and excluding most atheists from the debate, Godel did again a great job.

So, yes, Godel's proof is socially very useful. It is indeed an excellent piece of mathematical work.

[Skepdick]

My practical view on the matter is rather that there is now mathematically unobjectionable proof for religion while there isn't one for atheism.

Atheism has always been epistemologically and methodologically untenable. It's just that atheists don't seem to have any grasp on logic; or reason.

Picture a balancing scale leaning neither way. That's the default position: agnosticism.

What could possibly amount to positive evidence for God's non-existence?
What could possibly tip the scale from agnosticism towards atheism?

Any prover who can prove the non-existence of God is necessarily an omniscient prover. Irony ensues.

[godelian]

My practical view on the matter is rather that there is now mathematically unobjectionable proof for religion while there isn't one for atheism.

Atheism has always been epistemologically and methodologically untenable. It's just that atheists don't seem to have any grasp on logic; or reason.

Picture a balancing scale leaning neither way. That's the default position: agnosticism.

What could possibly amount to positive evidence for God's non-existence?
What could possibly tip the scale from agnosticism towards atheism?

Veritas Aequitas seems to be convinced that God must either exist as a physical object in the physical universe or else not at all. The problem with this view is that the creator of the universe being a physical object in the physical universe that he created, is essentially circular.

Agnosticism, on the other hand, is indeed much more reasonable. It is indeed the default position. The evidence tipping the scale from agnosticism to belief in God is actually quite subtle. Not everybody will be swayed by it. I would never argue against agnosticism because I consider it a reasonable point of view.

But then again, since religious belief is so universal across the globe and across history, I somehow suspect that it is subtly built into our biological firmware, weakly tipping the scale towards it. The individual can easily overrule it, though.

Any prover who can prove the non-existence of God is necessarily an omniscient prover. Irony ensues.

Agreed. He would need to have perfect theoretical knowledge on how the universe came about, and prove it from there. Unlike agnosticism, atheism is clearly unreasonable.

[Veritas Aequitas]

Godelian's claimed;
Godel's God is true, thus real.

My practical view on the matter is rather that there is now mathematically unobjectionable proof for religion while there isn't one for atheism.

Secondly, Godel's proof raises the bar because all criticism must be directed at its axioms, which are expressed in higher-order modal logic, which I do not expect most atheist to be able to master.

By raising the bar and forcibly removing and excluding most atheists from the debate, Godel did again a great job.

So, yes, Godel's proof is socially very useful. It is indeed an excellent piece of mathematical work.

First you misunderstood the basic meaning of 'atheism'.
Atheism basically mean, one is not-a-theist or do not have a belief in theism.
There is NO onus on the atheist to provide proof God does not exist, i.e. a negative claim.
So, it is up to atheists' discretion to prove god does not exists, e.g. as what I have done here.
I addition I have provided reasons [tons of] why theists are desperately clinging to an illusory for psychological comforts based on an evolutionary default.

If you are a rational person and critical thinker, you MUST at least consider alternative views and understand [not necessary agree with] the reasons why you and theists believe in a God? Have you?

Godel's provided a mathematical proof for God which is ONLY valid within the mathematic framework and system [FS] as grounded on its man-made axioms.

I have argued the scientific FS is the gold standard [benchmark] on what-is-reality.
The mathematical FS which is grounded on man-made axioms is not as credible and objective in terms of what-is-real in comparison to the scientific FS.

If Godel's mathematical God is mathematical true but non-physical and is not real [in contrast to scientific reality] then it is illusory, imaginary, and fictitious.

[Veritas Aequitas]

Numbers by themselves are absolutely Mathematics.

1, 2, 3, 4.

Numbers paired WITH UNITS are not Mathematics.
1 APPLE
2 APPLES

Here's AI's [wR] views.

No, numbers by themselves are not considered mathematics. Mathematics is the study of concepts like numbers, their properties, relationships, and structures.
Just seeing individual numbers is like having building blocks; mathematics is what you do with those blocks to build something.
Just seeing the digits 1, 2, 3, 4 doesn't involve any mathematical concepts.

Here's an analogy: Imagine having a bunch of Legos. The Legos themselves aren't what make something mathematical. But, if you start to follow instructions to build a complex structure, or if you use the Legos to explore ideas like symmetry or angles, then that's getting into the realm of mathematics.


Numbers are fundamental abstractions that represent quantities.
Mathematics explores how these numbers behave, how they relate to each other, and how they can be used to solve problems.
For instance, knowing the number 3 doesn't involve any mathematics. But understanding that 3 + 1 = 4 or that 3 is a prime number does involve mathematical concepts.

Neither you, nor the AI seem to understand the difference between numbers and numerals.

In the same way that philosophers can't agree what philosophy is - Mathematicians can't agree what Mathematics is.

Because "What is X?" is a metaphysical question. It has no good answers - pay attention and you'll develop some intuition.

It is not AI's problem.
I asked AI re 'numbers-by-themselves' so it answer in terms of 'number'.

When I stated 'numbers-by-themselves' my intention was with reference to numerals or digits.
'numbers-by-themselves' i.e. without reference to any conceptual system, e.g. mathematics, music, etc.

[godelian]

Godelian's claimed;
Godel's God is true, thus real.

My practical view on the matter is rather that there is now mathematically unobjectionable proof for religion while there isn't one for atheism.

Secondly, Godel's proof raises the bar because all criticism must be directed at its axioms, which are expressed in higher-order modal logic, which I do not expect most atheist to be able to master.

By raising the bar and forcibly removing and excluding most atheists from the debate, Godel did again a great job.

So, yes, Godel's proof is socially very useful. It is indeed an excellent piece of mathematical work.

First you misunderstood the basic meaning of 'atheism'.
Atheism basically mean, one is not-a-theist or do not have a belief in theism.
There is NO onus on the atheist to provide proof God does not exist, i.e. a negative claim.
So, it is up to atheists' discretion to prove god does not exists, e.g. as what I have done here.
I addition I have provided reasons [tons of] why theists are desperately clinging to an illusory for psychological comforts based on an evolutionary default.

If you are a rational person and critical thinker, you MUST at least consider alternative views and understand [not necessary agree with] the reasons why you and theists believe in a God? Have you?

Godel's provided a mathematical proof for God which is ONLY valid within the mathematic framework and system [FS] as grounded on its man-made axioms.

I have argued the scientific FS is the gold standard [benchmark] on what-is-reality.
The mathematical FS which is grounded on man-made axioms is not as credible and objective in terms of what-is-real in comparison to the scientific FS.

If Godel's mathematical God is mathematical true but non-physical and is not real [in contrast to scientific reality] then it is illusory, imaginary, and fictitious.

No, it is too late. The dictatorship of mathematics has now grabbed control. Again, mathematics is relentless.

https://github.com/FormalTheology/Goede ... oedelGod.v

(* Theorem T2: being God-like is an essence of any God-like being *)
Theorem theorem2: V (mforall x, (G x) m-> (G ess x)).
Proof.
intro.
intro y.
intro H1.
unfold Essence.
split.
exact H1.

intro q.
intro H2.
cut (box (Positive q) w).
intro H3.
intros w1 R1.
intro y0.
cut (Positive q w1).
intro H4.
intro H5.
cut (Positive q w1).
unfold G in H5.
apply H5.
...

It's not just higher-order modal logic that you need to master. Now you also need to become intimately familiar with the formalisms of the Coq or Isabelle proof assistants. Hence, it is simply game over for the atheist producers of nebulous rants, of a kind similar to Immanuel Kant. They will never be able to match this!

Seriously, you cannot counter this just with some word salad.

Does it compile properly?
Is it executable?
Does it run correctly?

If all you are bringing to the table, is a nebulous word salad, then you are simply no match. As Linus Torvalds so succinctly remarked, Talk is cheap. Show me the code.

I repeat again:

Resistance is futile.
You will be assimilated.

[Veritas Aequitas]

My practical view on the matter is rather that there is now mathematically unobjectionable proof for religion while there isn't one for atheism.

Secondly, Godel's proof raises the bar because all criticism must be directed at its axioms, which are expressed in higher-order modal logic, which I do not expect most atheist to be able to master.

By raising the bar and forcibly removing and excluding most atheists from the debate, Godel did again a great job.

So, yes, Godel's proof is socially very useful. It is indeed an excellent piece of mathematical work.

First you misunderstood the basic meaning of 'atheism'.
Atheism basically mean, one is not-a-theist or do not have a belief in theism.
There is NO onus on the atheist to provide proof God does not exist, i.e. a negative claim.
So, it is up to atheists' discretion to prove god does not exists, e.g. as what I have done here.
I addition I have provided reasons [tons of] why theists are desperately clinging to an illusory for psychological comforts based on an evolutionary default.

If you are a rational person and critical thinker, you MUST at least consider alternative views and understand [not necessary agree with] the reasons why you and theists believe in a God? Have you?

Godel's provided a mathematical proof for God which is ONLY valid within the mathematic framework and system [FS] as grounded on its man-made axioms.

I have argued the scientific FS is the gold standard [benchmark] on what-is-reality.
The mathematical FS which is grounded on man-made axioms is not as credible and objective in terms of what-is-real in comparison to the scientific FS.

If Godel's mathematical God is mathematical true but non-physical and is not real [in contrast to scientific reality] then it is illusory, imaginary, and fictitious.

No, it is too late. The dictatorship of mathematics has now grabbed control. Again, mathematics is relentless.

https://github.com/FormalTheology/Goede ... oedelGod.v

(* Theorem T2: being God-like is an essence of any God-like being *)
Theorem theorem2: V (mforall x, (G x) m-> (G ess x)).
Proof.
intro.
intro y.
intro H1.
unfold Essence.
split.
exact H1.

intro q.
intro H2.
cut (box (Positive q) w).
intro H3.
intros w1 R1.
intro y0.
cut (Positive q w1).
intro H4.
intro H5.
cut (Positive q w1).
unfold G in H5.
apply H5.
...

It's not just higher-order modal logic that you need to master. Now you also need to become intimately familiar with the formalisms of the Coq or Isabelle proof assistants. Hence, it is simply game over for the atheist producers of nebulous rants, of a kind similar to Immanuel Kant. They will never be able to match this!

Seriously, you cannot counter this just with some word salad.

Does it compile properly?
Is it executable?
Does it run correctly?

If all you are bringing to the table, is a nebulous word salad, then you are simply no match. As Linus Torvalds so succinctly remarked, Talk is cheap. Show me the code.

I repeat again:

Resistance is futile.
You will be assimilated.

In addition of my critique of the failure of Godel's argument, here is one with reference to Kant:

see:
The Soundness [???] of Godel's Argument for God
viewtopic.php?t=42170

Another:
Can God Be Proved Mathematically?
https://www.scientificamerican.com/arti ... matically/
Has mathematics now finally disproved the claims of all atheists?
As you probably already suspect, it has not.