Philosophy Now Forum

Veritas Aequitas wrote: ↑Mon Apr 01, 2024 7:42 am

godelian wrote: ↑Mon Apr 01, 2024 6:04 am

Veritas Aequitas wrote: ↑Mon Apr 01, 2024 5:36 am I find it very weird you are insisting using mathematics as a final judgment.

As I clearly wrote already, I agree with the critics of Gödel's otherwise mathematically unobjectionable proof on grounds of the limitations that Aristotle expounded at length in Posterior Analytics. Hence, I consider the final word to be Aristotle's concern, which I certainly share.

The point is Aristotle's ontology was squashed by Kant in that he argued the ontological thing-in-itself, Aristotle's mind-independent 'substance' is an illusion.

Aristotelian realism is a minority view in the ontology of mathematics. Platonism is much more important. I am only referring to Aristotle's posterior analytics, of which the findings are foundational for the axiomatic systems in mathematics. The following is what it is about:

https://iep.utm.edu/foundationalism-in-epistemology/

Foundationalism has a long history. Aristotle in the Posterior Analytics argues for foundationalism on the basis of the regress argument. Aristotle assumes that the alternatives to foundationalism must either endorse circular reasoning or land in an infinite regress of reasons. Because neither of these views is plausible, foundationalism comes out as the clear winner in an argument by elimination.

In Aristotle's own words:

https://classics.mit.edu/Aristotle/posterior.1.i.html

Our own doctrine is that not all knowledge is demonstrative: on the contrary, knowledge of the immediate premisses is independent of demonstration. (The necessity of this is obvious; for since we must know the prior premisses from which the demonstration is drawn, and since the regress must end in immediate truths, those truths must be indemonstrable.)

An axiomatic system has a foundation of immediate premisses is independent of demonstration, i.e. axioms. Proving axioms merely leads to infinite regress. This concern has turned out to be essential to the epistemology of mathematics.

godelian wrote: ↑Mon Apr 01, 2024 8:45 am

Veritas Aequitas wrote: ↑Mon Apr 01, 2024 7:42 am

godelian wrote: ↑Mon Apr 01, 2024 6:04 am
As I clearly wrote already, I agree with the critics of Gödel's otherwise mathematically unobjectionable proof on grounds of the limitations that Aristotle expounded at length in Posterior Analytics. Hence, I consider the final word to be Aristotle's concern, which I certainly share.

The point is Aristotle's ontology was squashed by Kant in that he argued the ontological thing-in-itself, Aristotle's mind-independent 'substance' is an illusion.

Aristotelian realism is a minority view in the ontology of mathematics. Platonism is much more important. I am only referring to Aristotle's posterior analytics, of which the findings are foundational for the axiomatic systems in mathematics. The following is what it is about:

https://iep.utm.edu/foundationalism-in-epistemology/

Foundationalism has a long history. Aristotle in the Posterior Analytics argues for foundationalism on the basis of the regress argument. Aristotle assumes that the alternatives to foundationalism must either endorse circular reasoning or land in an infinite regress of reasons. Because neither of these views is plausible, foundationalism comes out as the clear winner in an argument by elimination.

In Aristotle's own words:

https://classics.mit.edu/Aristotle/posterior.1.i.html

Our own doctrine is that not all knowledge is demonstrative: on the contrary, knowledge of the immediate premisses is independent of demonstration. (The necessity of this is obvious; for since we must know the prior premisses from which the demonstration is drawn, and since the regress must end in immediate truths, those truths must be indemonstrable.)

An axiomatic system has a foundation of immediate premisses is independent of demonstration, i.e. axioms. Proving axioms merely leads to infinite regress. This concern has turned out to be essential to the epistemology of mathematics.

Your claim is that Godel's proof based on mathematics has a final say that God exists.

I do not agree with the above.
One point is Mathematics based on axioms are grounded upon a human-based mathematic framework and system.
Axioms are based on the consensus of humans, i.e. no humans, no axioms.
Kant had proven Platonic realism is illusory, so are platonic axioms.
The mathematical FS cannot be absolutely independent of the human conditions.

Godel is relying on a human-based mathematical FS to prove God exists.
This is at best a human-made proof.
Humans are fallible.
God is infallible
Fallible humans proofs cannot confirm the infallible God.

As I had stated, to prove God is real, you need to provide evidence of God directly of itself for verification and justification God is really real.

Veritas Aequitas wrote: ↑Mon Apr 01, 2024 9:28 am Your claim is that Godel's proof based on mathematics has a final say that God exists.

I did not write that. You did

Godel translates the idea that God exists into five new axioms. Aristotle warned that doing this would only lead to regress in the form of a request to prove these five new axioms. Ad nauseam.

But then again, since Godel did it in mathematically unobjectionable manner, his proof is worth discussing.

It is definitely of superior value to what Kant wrote. Kant claims that the exists(n) predicate is undefinable without providing mathematically unobjectionable proof.

godelian wrote: ↑Mon Apr 01, 2024 1:49 am

Sculptor wrote: ↑Sun Mar 31, 2024 12:12 pm "God Exists"

Really?
WTF does that even mean?

Tarski successfully proves the undefinability of the truth. Kant does not manage to prove the undefinability of existence.

Therefore, Kant's views are unsubstantiated when he argues that existence is undefinable. Unlike Tarski, Kant's argument simply does not meet the standards of proof. Kant has failed to proceed in a mathematically unobjectionable manner.

Why don't you answer the question?

Sculptor wrote: ↑Mon Apr 01, 2024 11:22 am

godelian wrote: ↑Mon Apr 01, 2024 1:49 am

Sculptor wrote: ↑Sun Mar 31, 2024 12:12 pm "God Exists"

Really?
WTF does that even mean?

Tarski successfully proves the undefinability of the truth. Kant does not manage to prove the undefinability of existence.

Therefore, Kant's views are unsubstantiated when he argues that existence is undefinable. Unlike Tarski, Kant's argument simply does not meet the standards of proof. Kant has failed to proceed in a mathematically unobjectionable manner.

Why don't you answer the question?

Whether God exists? That is a belief. You either do or you don't.

godelian wrote: ↑Mon Apr 01, 2024 12:09 pm

Sculptor wrote: ↑Mon Apr 01, 2024 11:22 am

godelian wrote: ↑Mon Apr 01, 2024 1:49 am
Tarski successfully proves the undefinability of the truth. Kant does not manage to prove the undefinability of existence.

Therefore, Kant's views are unsubstantiated when he argues that existence is undefinable. Unlike Tarski, Kant's argument simply does not meet the standards of proof. Kant has failed to proceed in a mathematically unobjectionable manner.

Why don't you answer the question?

Whether God exists? That is a belief. You either do or you don't.

no, I asked what does the sentence; " God exists" mean?

Sculptor wrote: ↑Mon Apr 01, 2024 12:26 pm no, I asked what does the sentence; " God exists" mean?

Godel's definition goes as following:

https://en.m.wikipedia.org/wiki/G%C3%B6 ... ical_proof

.First, Gödel axiomatizes the notion of a "positive property":[note 2] for each property φ, either φ or its negation ¬φ must be positive, but not both (axiom 2). If a positive property φ implies a property ψ in each possible world, then ψ is positive, too (axiom 1).[note 3] Gödel then argues that each positive property is "possibly exemplified", i.e. applies at least to some object in some world (theorem 1). Defining an object to be Godlike if it has all positive properties (definition 1),[note 4] and requiring that property to be positive itself (axiom 3),[note 5] Gödel shows that in some possible world a Godlike object exists (theorem 2), called "God" in the following.[note 6] Gödel proceeds to prove that a Godlike object exists in every possible world.

So, his approach is to define a God-like entity as having all positive properties. This is very much in line with the 99 attributes/names of Allah in Islam.

https://en.m.wikipedia.org/wiki/Names_of_God_in_Islam

Next, Godel introduces 5 axioms from which the existence of God necessarily follows:

□∃x G(x)

("There exists a God-like object "x")

So, "exists" is expressed by the standard first-order logic's existential quantifier ∃, while the modal modifier (it's higher-order "modal logic") for "necessity" is expressed by the symbol □.

In fact, to fully understand Godel's conclusion, it is necessary to fully understand the axioms upon which his argument rests.

godelian wrote: ↑Mon Apr 01, 2024 1:05 pm

Sculptor wrote: ↑Mon Apr 01, 2024 12:26 pm no, I asked what does the sentence; " God exists" mean?

Godel's definition goes as following:

https://en.m.wikipedia.org/wiki/G%C3%B6 ... ical_proof

.First, Gödel axiomatizes the notion of a "positive property":[note 2] for each property φ, either φ or its negation ¬φ must be positive, but not both (axiom 2). If a positive property φ implies a property ψ in each possible world, then ψ is positive, too (axiom 1).[note 3] Gödel then argues that each positive property is "possibly exemplified", i.e. applies at least to some object in some world (theorem 1). Defining an object to be Godlike if it has all positive properties (definition 1),[note 4] and requiring that property to be positive itself (axiom 3),[note 5] Gödel shows that in some possible world a Godlike object exists (theorem 2), called "God" in the following.[note 6] Gödel proceeds to prove that a Godlike object exists in every possible world.

So, his approach is to define a God-like entity as having all positive properties. This is very much in line with the 99 attributes/names of Allah in Islam.

https://en.m.wikipedia.org/wiki/Names_of_God_in_Islam

Next, Godel introduces 5 axioms from which the existence of God necessarily follows:

□∃x G(x)

("There exists a God-like object "x")

So, "exists" is expressed by the standard first-order logic's existential quantifier ∃, while the modal modifier (it's higher-order "modal logic") for "necessity" is expressed by the symbol □.

In fact, to fully understand Godel's conclusion, it is necessary to fully understand the axioms upon which his argument rests.

That's one idea,
There are many verions of god, and various claims about the manner of its existence.
WHy is your one more valid than others?

Veritas Aequitas wrote: ↑Mon Apr 01, 2024 9:28 am As I had stated, to prove God is real, you need to provide evidence of God directly of itself for verification and justification God is really real.

And what if God does not want to be proven to be real?

Do you actually believe that a Being who is capable of creating the vast order of the universe out of the living fabric of its very own being, couldn't attenuate our awareness in such a way as to keep us from discovering the truth?

I know this question means nothing to you, but how many times do I have to point out the possibility that if God were to reveal itself (along with the truth of our ultimate and eternal destiny), that it could jeopardize the very purpose and reason for why the universe was created in the first place?

And lastly, even though the answer to the following question is implicit within the question itself,...

...if it is indeed possible that God truly does exist as a real (yet transcendent) Entity, then where do you find the gall to question the motives of a Being that is as far above us humans in scope and consciousness, as humans are above amoebas?
_______

Sculptor wrote: ↑Mon Apr 01, 2024 4:27 pm

godelian wrote: ↑Mon Apr 01, 2024 1:05 pm

Sculptor wrote: ↑Mon Apr 01, 2024 12:26 pm no, I asked what does the sentence; " God exists" mean?

Godel's definition goes as following:

https://en.m.wikipedia.org/wiki/G%C3%B6 ... ical_proof

.First, Gödel axiomatizes the notion of a "positive property":[note 2] for each property φ, either φ or its negation ¬φ must be positive, but not both (axiom 2). If a positive property φ implies a property ψ in each possible world, then ψ is positive, too (axiom 1).[note 3] Gödel then argues that each positive property is "possibly exemplified", i.e. applies at least to some object in some world (theorem 1). Defining an object to be Godlike if it has all positive properties (definition 1),[note 4] and requiring that property to be positive itself (axiom 3),[note 5] Gödel shows that in some possible world a Godlike object exists (theorem 2), called "God" in the following.[note 6] Gödel proceeds to prove that a Godlike object exists in every possible world.

So, his approach is to define a God-like entity as having all positive properties. This is very much in line with the 99 attributes/names of Allah in Islam.

https://en.m.wikipedia.org/wiki/Names_of_God_in_Islam

Next, Godel introduces 5 axioms from which the existence of God necessarily follows:

□∃x G(x)

("There exists a God-like object "x")

So, "exists" is expressed by the standard first-order logic's existential quantifier ∃, while the modal modifier (it's higher-order "modal logic") for "necessity" is expressed by the symbol □.

In fact, to fully understand Godel's conclusion, it is necessary to fully understand the axioms upon which his argument rests.

That's one idea,
There are many verions of god, and various claims about the manner of its existence.
WHy is your one more valid than others?

That wasn't my take on things. It's Godel's approach. I think that it has some merit. I have also pointed out, however, in previous comments, that the issue is indeed the five axioms with which Godel has replaced God as a basic belief.

godelian wrote: ↑Mon Apr 01, 2024 10:15 am

Veritas Aequitas wrote: ↑Mon Apr 01, 2024 9:28 am Your claim is that Godel's proof based on mathematics has a final say that God exists.

I did not write that. You did

Godel translates the idea that God exists into five new axioms. Aristotle warned that doing this would only lead to regress in the form of a request to prove these five new axioms. Ad nauseam.

But then again, since Godel did it in mathematically unobjectionable manner, his proof is worth discussing.

It is definitely of superior value to what Kant wrote. Kant claims that the exists(n) predicate is undefinable without providing mathematically unobjectionable proof.

As I had stated, Kant's refutation of God's existence as real is not based solely on 'existence is not a predicate'.

The Kant's argument I provided covers ALL arguments which would include any mathematical proofs [Godel's or any others].

Godel's proof is only qualified to a closed mathematical system with its qualified axioms within the system of reality.

Kant's counter is, while Godel's proof is valid within his qualified mathematical model, it cannot justify and prove God is real within reality.
I have already countered,
it is mathematically true, 1 + 1 = 2 say apples, but that itself does not prove apples are real.
To prove apples are real we need a scientific system, i.e. biology, physics or chemistry plus critical philosophy.

I mentioned many scientific speculated theories were proven to be true based mathematical proofs within the closed mathematical system, but these theories can only be confirmed to be real when verified and justified with empirical evidences and if extended to philosophy, then needs critical philosophy.

Note for example: the empirical confirmation of Einstein mathematical based theory:

The aim of the expeditions was to measure the gravitational deflection of starlight passing near the Sun.[1] The value of this deflection had been predicted by Albert Einstein in a 1911 paper; however, this initial prediction turned out not to be correct because it was based on an incomplete theory of general relativity. Einstein later improved his prediction after finalizing his theory in 1915 and obtaining the solution to his equations by Karl Schwarzschild. Following the return of the expeditions, the results were presented by Eddington to the Royal Society of London[2] and, after some deliberation, were accepted. Widespread newspaper coverage of the results led to worldwide fame for Einstein and his theories.
https://en.wikipedia.org/wiki/Eddington_experiment

Kant refutation would be,
one make whatever claim God exists based on whatever argument [mathematics, logic, pure reason, speculations, hypotheses], they all failed to prove God is real until empirical evidences are provided to test, verify and justify as real under the scientific framework and system.

seeds wrote: ↑Mon Apr 01, 2024 6:09 pm

Veritas Aequitas wrote: ↑Mon Apr 01, 2024 9:28 am As I had stated, to prove God is real, you need to provide evidence of God directly of itself for verification and justification God is really real.

And what if God does not want to be proven to be real?

Do you actually believe that a Being who is capable of creating the vast order of the universe out of the living fabric of its very own being, couldn't attenuate our awareness in such a way as to keep us from discovering the truth?

I know this question means nothing to you, but how many times do I have to point out the possibility that if God were to reveal itself (along with the truth of our ultimate and eternal destiny), that it could jeopardize the very purpose and reason for why the universe was created in the first place?

And lastly, even though the answer to the following question is implicit within the question itself,...

...if it is indeed possible that God truly does exist as a real (yet transcendent) Entity, then where do you find the gall to question the motives of a Being that is as far above us humans in scope and consciousness, as humans are above amoebas?
_______

Reality is an imperative 'hallmark' of sanity.
If you do not want to ground God on the basis of reality, then you are associating god with insanity from the start.

If you belief in God is out of reach of reality on a personal basis as confined to your own private thoughts and activities, there is no serious issue with it.
There are lots of usefulness for individual[s] to indulge in fiction while being aware the contents are fictions and not real.

One example of the usefulness of the unreal is 'sexual fantasies'

A sexual fantasy or erotic fantasy is an autoerotic mental image or pattern of thought that stirs a person's sexuality and can create or enhance sexual arousal.[1] A sexual fantasy can be created by the person's imagination or memory, and may be triggered autonomously or by external stimulation such as erotic literature or pornography, a physical object, or sexual attraction to another person. Anything that may give rise to a sexual arousal may also produce a sexual fantasy, and sexual arousal may in turn give rise to fantasies.
https://en.wikipedia.org/wiki/Sexual_fantasy#:~:text

Also, Einstein stated "imagination is more important than knowledge."

Thus, if your admit your belief in God is not grounded on reality, then I am not interested in refuting your claim. You can carry on with your private thoughts as much as you like.

I have always stated along with Kant, God is not real but any one can think of God albeit recognizing God is an illusion that is useful for unavoidable psychological & therapeutic reasons.

However, any argument and belief that God exists as real must be taken seriously and be refuted because such a belief have serious dangerous impact of evil that is detrimental to humanity.

It is so evident that theists claim their god to be really real to the extent;
- god sent his sons, messenger, prophets, agents, etc. to deliver his holy commands to human beings that they must obey his commands absolutely [to the best of their abilities] in exchange with a promise of salvation in heaven which result in theists;
-killing non-believers from individual[s] to genocidal scale.
-suppress the freedom of non-believers
-burnt abortion clinics
-hinder knowledge with their creationist theories
-pose a threat to the extinction of the human species -their disregard for MAD - X
-all sort of evil acts as sanction within God holy book.

As a fool-proof measure to avoid X [plus all other god driven evil acts], it is effective to gradually wean off and ultimately eliminate the belief of God as real in the future [not possible now].
However, due to unavoidability, it is acceptable for theists to believe in God for some 'salvation' and other purposes, but only on the basis that God is not a real entity but merely an illusion, i.e. a useful illusion like other fantasies.

Veritas Aequitas wrote: ↑Tue Apr 02, 2024 4:18 am As I had stated, Kant's refutation of God's existence as real is not based solely on 'existence is not a predicate'.

https://en.wikipedia.org/wiki/Ontological_argument

Kant goes on to write ...

He proposes that existence is not a predicate, or quality. He argues that the ontological argument works only if existence is a predicate; if this is not so, he claims the ontological argument is invalidated

Kant's other arguments are so confused that they do not commit him to anything.

godelian wrote: ↑Tue Apr 02, 2024 5:09 am

Veritas Aequitas wrote: ↑Tue Apr 02, 2024 4:18 am As I had stated, Kant's refutation of God's existence as real is not based solely on 'existence is not a predicate'.

https://en.wikipedia.org/wiki/Ontological_argument

Kant goes on to write ...

He proposes that existence is not a predicate, or quality. He argues that the ontological argument works only if existence is a predicate; if this is not so, he claims the ontological argument is invalidated

Kant's other arguments are so confused that they do not commit him to anything.

The whole of Kant's CPR [except the penultimate and last part] is on long argument culminating in the above claims in the OP.
Have you understood [not agree with] Kant's CPR to make the above critiques and refutations?

Veritas Aequitas wrote: ↑Tue Apr 02, 2024 5:31 am

godelian wrote: ↑Tue Apr 02, 2024 5:09 am

Veritas Aequitas wrote: ↑Tue Apr 02, 2024 4:18 am As I had stated, Kant's refutation of God's existence as real is not based solely on 'existence is not a predicate'.

https://en.wikipedia.org/wiki/Ontological_argument

Kant goes on to write ...

He proposes that existence is not a predicate, or quality. He argues that the ontological argument works only if existence is a predicate; if this is not so, he claims the ontological argument is invalidated

Kant's other arguments are so confused that they do not commit him to anything.

The whole of Kant's CPR [except the penultimate and last part] is on long argument culminating in the above claims in the OP.
Have you understood [not agree with] Kant's CPR to make the above critiques and refutations?

Pretty much nothing of what Kant says, is actionable. It is just nebulous nonsense. The only claim that truly commits him, is his opinion that exists(n) is not definably as a predicate. Kant is wrong about that. There is absolutely nothing wrong with the existential quantifier in first-order predicate logic. Kant's views are simply in violation of the definition of standard logic.