Kant: It is Impossible to Prove God Exists as Real

[Veritas Aequitas]

Reference mean the page number from the CRP usually in the form of [A... B...] so I can refer to the CPR myself.

For reasons of convenience, Gutenberg publishes the text in one long text file:

https://www.gutenberg.org/files/4280/4280-h/4280-h.htm

Page numbers depend on the publication format. They are not a stable referencing mechanism because the number of pages depends on the publication size and format.

Re the CPR I had spent 3 years full time reading and analyzing it since long ago and continuously reading it to the present.

I have only read it to see what Kant said about mathematics. Fundamentally, I am not much impressed with his classification of statements using the (analytic,synthetic) and (a priori,a posteriori) dichotomies. Even though it is not wrong, nobody has built anything on top of that. In mathematics, the dichotomy (analytic,synthetic) corresponds to (axiom, theorem). I have never run into a mathematical publication that argued that we should switch to Kant's vocabulary.

I have 7 English translation of Kant's CPR. The one you refer to by J. M. D. Meiklejohn is not very accurate compared to the Smith, Guyer & Wood translation.
The Kant's CPR reference [A../B...] refer to the pages on the original German Edition so it it the same throughout all other translations. I will try to find the reference.

Since Godel's argument is an ontological argument,
therefore it is impossible for Godel's argument, to prove God exists as real.

This is certainly not any counterargument mentioned in the page on Gödel's ontological proof:

https://en.wikipedia.org/wiki/G%C3%B6de ... ical_proof

Kant's alleged impossibility is simply not even mentioned in this page. His work is just not considered relevant enough for that purpose. The critics deemed relevant enough are: Sobel, Koons, Anderson, Gettings, Oppy, Spitzer, and Fuhrmann. For historical reasons, Anselm and Leibniz are also mentioned, mostly because they attempted something similar. It is obvious why Kant is not mentioned in this page. There is no mention of Kant because his impossibility proof is considered worthless nonsense.

You think WIKI reference is highly authoritative?

There is no mention of Kant because his impossibility proof is considered worthless nonsense.

Your statement above merely insults your own intellectual integrity especially when you have not read Kant's CPR thoroughly.

[godelian]

You think WIKI reference is highly authoritative?

The page's list of supporting references is certainly impressive:

Wang, Hao. A Logical Journey: From Gödel to Philosophy. A Bradford Book, 1997. Print. p.316.
Quoted in Gödel 1995, p. 388. The German original is quoted in Dawson 1997, p. 307. The nested parentheses are in Morgenstern's original diary entry, as quoted by Dawson.
The publication history of the proof in this paragraph is from Gödel 1995, p. 388
Dawson 1997, pp. 6.
Dawson 1997, pp. 210–212.
Wang 1996, p. 317. The ellipsis is Wikipedia's.
Wang 1996, p. 51.
Gödel's proof is reprinted on p.403-404,429-437 of: Kurt Gödel (Mar 1995). Solomon Feferman and John W. Dawson jr. and Warren Goldfarb and Charles Parsons and Robert M. Solovay (ed.). Unpublished Essays and Lectures (PDF). Collected Works. Vol. III (1st ed.). Oxford: Oxford University Press. ISBN 0-19-507255-3.
Robert C. Koons (Jul 2005). Sobel on Gödel's Ontological Proof (PDF) (Unpublished Paper). University of Texas at Austin. Archived from the original (PDF) on 2020-08-02.
The presentation below follows that in Koons (2005),[9] p.3-7.
Fitting, 2002, p. 139
Jordan Howard Sobel (Nov 1987). "Gödel's ontological proof". In Judith Jarvis Thomson (ed.). On Being and Saying: Essays for Richard Cartwright. Cambridge/MA & London, England: MIT Press. pp. 241–261. ISBN 978-0262200639.
Kurt Gödel (Mar 1995). "Texts Relating to the Ontological Proof (App. B)". In Solomon Feferman; John W. Dawson jr.; Warren Goldfarb; Charles Parsons; Robert M. Solovay (eds.). Unpublished Essays and Lectures (PDF). Collected Works. Vol. III (1st ed.). Oxford: Oxford University Press. pp. 429–437. ISBN 0-19-507255-3. Here: p.435; probably, Sobel referred to Gödel's note 4.: "... If φ ( x ) ⇒ ◻ φ ( x ) {\displaystyle \varphi (x)\Rightarrow \Box \varphi (x)} is assumed [as following from the essence of x {\displaystyle x}], ... but that is the inferior way. Rather, φ ( x ) ⇒ ◻ φ ( x ) {\displaystyle \varphi (x)\Rightarrow \Box \varphi (x)} should follow first from the existence of God." The note might indicate that Gödel was aware of his axioms implying modal collapse.
Curtis Anthony Anderson (Jul 1990). "Some Emendations of Gödel's Ontological Proof" (PDF). Faith and Philosophy. 7 (3): 291–303. doi:10.5840/faithphil19907325. Archived (PDF) from the original on 2015-06-04.
Curtis Anthony Anderson and Michael Gettings (Aug 1996). "Gödel's ontological proof revisited". In Petr Hájek (ed.). Proc. Gödel '96: Logical Foundations of Mathematics, Computer Science and Physics — Kurt Gödel's Legacy. Lecture Notes in Logic. Vol. 6. Springer. pp. 167–172.
Graham Oppy (Oct 1996). "Godelian ontological arguments". Analysis. 54 (4): 226–230. doi:10.1093/analys/56.4.226. — Longer version (2005)
Gettings Michael (1999). "Gödel's ontological argument: a reply to Oppy". Analysis. 59 (264): 309–313. doi:10.1111/1467-8284.00184 (inactive 2024-01-23).
"Godel's Theorem and the Existence of God". Magis Center. 2017-04-26. Retrieved 2018-05-23.
André Fuhrmann (2005). "Existenz und Notwendigkeit — Kurt Gödels axiomatische Theologie" [Existence and Necessity — Kurt Gödel's Axiomatic Theology] (PDF). In W. Spohn (ed.). Logik in der Philosophie [Logic in Philosophy] (in German). Heidelberg: Synchron. pp. 349–374. Archived (PDF) from the original on 2016-05-18.
"FormalTheology/GoedelGod". GitHub. 28 June 2021.
Knight, David (23 October 2013). "Scientists Use Computer to Mathematically Prove Gödel's God Theorem". Der Spiegel. Retrieved 28 October 2013.
Christoph Benzmüller and Bruno Woltzenlogel-Paleo (2014). "Automating Gödel's Ontological Proof of God's Existence with Higher-Order Automated Theorem Provers" (PDF). Proc. European Conference on Artificial Intelligence. Frontiers in Artificial Intelligence and Applications. Vol. 263. IOS Press. pp. 93–98. Archived (PDF) from the original on 2014-07-14.
D. Scott (2004). "Appendix B: Notes in Dana Scott's Hand [1972]". In J.H. Sobel (ed.). Logic and Theism: Arguments for and Against Beliefs in God. Cambridge: Cambridge University Press. pp. 145–146. ISBN 978-0511497988.
Christoph Benzmüller and Bruno Woltzenlogel-Paleo (Jul 2016). "The Inconsistency in Gödel's Ontological Argument: — A Success Story for AI in Metaphysics" (PDF). In Subbarao Kambhampati (ed.). Proc. 25th International Joint Conference on Artificial Intelligence. AAAI Press. pp. 936–942. Archived (PDF) from the original on 2016-11-13.
Christoph Benzmüller and David Fuenmayor (May 2017). "Types, Tableaus and Gödel's God in Isabelle/HOL". Archive of Formal Proofs. ISSN 2150-914X.
Quentin Canterel (2015). The Jolly Coroner: A Picaresque Novel. Acorn Independent Press.
Jeffrey Kegler (2007), The God Proof, full text online.

Are these references inappropriate or irrelevant? Do they fail to support the content of the page? What exactly is your problem with them, one by one?

There is no mention of Kant because his impossibility proof is considered worthless nonsense.

Your statement above merely insults your own intellectual integrity especially when you have not read Kant's CPR thoroughly.

The page for Gödel's proof mentions 27 references. Kant's impossibility may seemingly be relevant but was not deemed worthy of being referenced. Hence, I can only conclude that Kant's argument is deemed worthless nonsense by the community that specializes in dealing with ontological proofs.

[Veritas Aequitas]

You think WIKI reference is highly authoritative?

The page's list of supporting references is certainly impressive:
.....

Are these references inappropriate or irrelevant? Do they fail to support the content of the page? What exactly is your problem with them, one by one?

There is no mention of Kant because his impossibility proof is considered worthless nonsense.

Your statement above merely insults your own intellectual integrity especially when you have not read Kant's CPR thoroughly.

The page for Gödel's proof mentions 27 references. Kant's impossibility may seemingly be relevant but was not deemed worthy of being referenced. Hence, I can only conclude that Kant's argument is deemed worthless nonsense by the community that specializes in dealing with ontological proofs.

That WIKI's focus on Godel's Argument is not on the ontological proof specifically.
Regardless, whatever of WIKI we cannot claim it is by default authoritative.
The number of references therein is not the point but rather the actual contents of each reference provided.

Here is the proper article on the Ontological Argument where Kant is mentioned;

https://en.wikipedia.org/wiki/Ontological_argument
Immanuel_Kant's Criticism
https://en.wikipedia.org/wiki/Ontologic ... anuel_Kant
Here I would not consider the point re Kant as highly authoritative, rather we need to refer to Kant's CPR.

Re your earlier reference to mathematics and Kant;
It has no relevant to the topic at all;

This is your quote [without the blue portion] with the specific CPR Reference:

A160 B199
Such principles mathematical science possesses, but their application to experience, consequently their objective validity, nay the possibility of such a priori synthetical cognitions (the deduction thereof) rests entirely upon the pure understanding.
On this account, I shall not reckon among my principles those of mathematics;
though I shall include those upon the possibility and objective validity à priori, of principles of the mathematical science, which, consequently, are to be looked upon as the principle of these, and which proceed from conceptions to intuition, and not from intuition to conceptions.
Mickeljohn's Translation

This is the NK Smith's translation;

For though they [Faculty of Concepts] are mediated by the Understanding, they are not derived from Pure Concepts but from Pure Intuitions. A160 B199
We find such Principles in Mathematics.
The question, however, of their application to Experience, that is, of their Objective Validity,
nay, even the Deduction of the Possibility of such Synthetic a priori Knowledge, must always carry us back to the Pure Understanding.

While, therefore, I leave aside the Principles of Mathematics, I shall none the less include those [more fundamental] Principles upon which the Possibility and a priori Objective Validity of Mathematics are grounded.
These latter [fundamental principles re Mathematics] must be regarded as the foundation 2 of all Mathematical Principles.
They proceed from Concepts to Intuition, not from Intuition to Concepts.

It has no relevant to the topic at all; I don't want to go into the details of the above in their context to the whole section and whole CPR.

Your refutation should be based on the following;
A summary of Kant's argument is this;
1. It is impossible to prove God exists as real based on the Ontological Argument,
2. All arguments for the existence of God are reducible to the Ontological Argument,
3. It is impossible to prove God exists as real at all.

You should prove Kant's premise 1 is wrong based on general principles of the Ontological Proof which would include Godel's amongst others.

[godelian]

You should prove Kant's premise 1 is wrong based on general principles of the Ontological Proof which would include Godel's amongst others.

Apparently, Kant argues his impossibility as following:

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

Immanuel Kant's critique was based on what he saw as the false premise that existence is a predicate, arguing that "existing" adds nothing (including perfection) to the essence of a being. Thus, a "supremely perfect" being can be conceived not to exist.

We know that truth is not a legitimate predicate, from Tarski's undefinability of the truth:

https://en.m.wikipedia.org/wiki/Tarski% ... ty_theorem

This result trivially follows from Carnap's diagonal lemma.

So, true() cannot be defined. On what grounds can exists() not be defined? It certainly does not follow from Carnap's diagonal lemma.

So, how does Kant argue in a mathematically unobjectionable way that exists() is not a legitimate predicate? Unlike Tarski, Kant simply does not provide proof for that.

Furthermore, the exists() predicate does not even appear anywhere in Godel's proof. He only makes use of the existential quantifier (∃).

I can only conclude the impossibility that Kant argues is unsubstantiated. There is nothing wrong in Godel's proof because Kant does not only fail to prove that exists() is undefinable as a predicate but Godel does not even use an exists() predicate, to begin with.

[Sculptor]

"God Exists"

Really?
WTF does that even mean?

[godelian]

"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.

[Veritas Aequitas]

You should prove Kant's premise 1 is wrong based on general principles of the Ontological Proof which would include Godel's amongst others.

Apparently, Kant argues his impossibility as following:

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

Immanuel Kant's critique was based on what he saw as the false premise that existence is a predicate, arguing that "existing" adds nothing (including perfection) to the essence of a being. Thus, a "supremely perfect" being can be conceived not to exist.

We know that truth is not a legitimate predicate, from Tarski's undefinability of the truth:

https://en.m.wikipedia.org/wiki/Tarski% ... ty_theorem

This result trivially follows from Carnap's diagonal lemma.

So, true() cannot be defined. On what grounds can exists() not be defined? It certainly does not follow from Carnap's diagonal lemma.

So, how does Kant argue in a mathematically unobjectionable way that exists() is not a legitimate predicate? Unlike Tarski, Kant simply does not provide proof for that.

Furthermore, the exists() predicate does not even appear anywhere in Godel's proof. He only makes use of the existential quantifier (∃).

I can only conclude the impossibility that Kant argues is unsubstantiated. There is nothing wrong in Godel's proof because Kant does not only fail to prove that exists() is undefinable as a predicate but Godel does not even use an exists() predicate, to begin with.

First, you have highlighted this yourself, i.e. Godel's proof is questionable.

Most criticism of Gödel's proof is aimed at its axioms: as with any proof in any logical system, if the axioms the proof depends on are doubted, then the conclusions can be doubted. It is particularly applicable to Gödel's proof – because it rests on five axioms, some of which are considered questionable. A proof does not necessitate that the conclusion be correct, but rather that by accepting the axioms, the conclusion follows logically.
https://en.wikipedia.org/wiki/G%C3%B6de ... #Criticism

Even if Godel's proof is accepted as God exists.

Kant argued, 'existence' is not a predicate.

For example,
That apple [on the table] exists.
In this case 'exist' is not a predicate, but the predicate is implied, i.e.
1. The apple exists as a fruit which can be verified and justified via the human-based science-biology framework and system [FS] or the common sense [FS].
2. The apple exists as a cluster of certain molecules, atoms, particles which can be verified and justified via the science-physics framework and system [FS].

From the above 'exist' is not a predicate, but rather the predicate is what is verified and justified based on the specific human-based FS.

The above is based on scientific-antirealism and not scientific-realism.

Therefore, even if Godel's proof 'God exists' is acceptable, then, that God exists as what [predicate ??] that can be verified and justified as real via the science FS as the gold standard of credibility and objectivity.

Btw, Kant refuted the ontological argument based a few arguments other than 'existence is not a predicate'.

[godelian]

First, you have highlighted this yourself, i.e. Godel's proof is questionable.

Even though Godel did proceed in a mathematically unobjectionable manner, his work is nonetheless still subject to the limitations expounded by Aristotle in Posterior analytics.

Kant argued, 'existence' is not a predicate.

Unlike Tarski, who argued in a mathematically unobjectionable manner that 'truth' is not a predicate, Kant failed to do so for 'existence'.

Btw, Kant refuted the ontological argument based a few arguments other than 'existence is not a predicate'.

That is not what the page on ontological proofs says about Kant's arguments. Furthermore, has Kant actually ever argued anything in a mathematically unobjectionable manner?

[Veritas Aequitas]

First, you have highlighted this yourself, i.e. Godel's proof is questionable.

Even though Godel did proceed in a mathematically unobjectionable manner, his work is nonetheless still subject to the limitations expounded by Aristotle in Posterior analytics.

Kant argued, 'existence' is not a predicate.

Unlike Tarski, who argued in a mathematically unobjectionable manner that 'truth' is not a predicate, Kant failed to do so for 'existence'.

Btw, Kant refuted the ontological argument based a few arguments other than 'existence is not a predicate'.

That is not what the page on ontological proofs says about Kant's arguments. Furthermore, has Kant actually ever argued anything in a mathematically unobjectionable manner?

Kant failed to do so for 'existence'.

That is the problem when you have not read Kant's CPR and understood [not agree with] it thoroughly.
Kant recognized Mathematics is merely a tool used in science and other fields of knowledge.

One can prove mathematically 'one apple plus one apple = two apples' on paper, but where and how do one verified and justified the real apples. This of course can be done via the human-based [note 'human-based'] science-biology FS.

So suppose, one can mathematically prove God exist, where is the predicate related to God to be verified and justified as real and not illusory.

Somebody near you can prove 'you exists' as real [not illusory or a hallucination].
But 'exist' is not a predicate.
So, that person will have to predicate you as a real human being.
You as a real human being as predicated can be verified and justified by the science-biology FS and other scientific FS.

As with the above, what is the predicate for God exists as real?
And what FS can you verify and justify God exists as real.

[godelian]

But 'exist' is not a predicate.

As I have mentioned previously, we can argue in a mathematically unobjectionable manner that 'truth' is not a predicate.

That is not the case for 'existence'. On the contrary, existential quantification is even a mainstay in first-order predicate logic:

https://en.wikipedia.org/wiki/Existenti ... tification

In predicate logic, an existential quantification is a type of quantifier, a logical constant which is interpreted as "there exists", "there is at least one", or "for some". It is usually denoted by the logical operator symbol ∃, which, when used together with a predicate variable, is called an existential quantifier ("∃x" or "∃(x)" or "(∃x)"[1]).

It may conceivably be possible to argue that exists(n) is undefinable as a predicate -- even though it is perfectly definable as a quantifier -- but Kant certainly did not manage to argue his dubitable opinion in a mathematically unobjectionable manner.

[Veritas Aequitas]

But 'exist' is not a predicate.

As I have mentioned previously, we can argue in a mathematically unobjectionable manner that 'truth' is not a predicate.

That is not the case for 'existence'. On the contrary, existential quantification is even a mainstay in first-order predicate logic:

https://en.wikipedia.org/wiki/Existenti ... tification

In predicate logic, an existential quantification is a type of quantifier, a logical constant which is interpreted as "there exists", "there is at least one", or "for some". It is usually denoted by the logical operator symbol ∃, which, when used together with a predicate variable, is called an existential quantifier ("∃x" or "∃(x)" or "(∃x)"[1]).

It may conceivably be possible to argue that exists(n) is undefinable as a predicate -- even though it is perfectly definable as a quantifier -- but Kant certainly did not manage to argue his dubitable opinion in a mathematically unobjectionable manner.

From his CPR, it would be an insult for Kant to use mathematics for his refutations that it is impossible for God to exists as real.

For whatever is claimed as real it must be predicated so that it can be verified and justified as real using the science FS as the gold standard.

If you claim 'truth' is mathematically not a predicate and 'exist' is not a predicate, then there is no predicate to justify and verify your God is real, thus illusory.
Kant did prove the idea of God is an illusion, albeit a necessary critical useful illusion.

[godelian]

From his CPR, it would be an insult for Kant to use mathematics for his refutations that it is impossible for God to exists as real.

Well, Kant wrote in Critique of Pure Reason:

On this account, I shall not reckon among my principles those of mathematics;

That is clearly the reason why Kant was completely inept in the realm of mathematics. You see, Gödel and Tarski are grandees. Carnap is arguably also a grandee in mathematics. Kant, if only through his own admission, is obviously not.

Gödel, Tarski, and Carnap collectively proved in a mathematically unobjectionable manner that true(n) cannot be defined as a predicate. As far as I am concerned, Kant has no business arguing that exists(n) would not be a legitimate predicate. It does not necessarily follow from anything.

Kant does not stand a snowball's chance in hell against Gödel. There is a massive difference in class and capability between them. You fail to acknowledge the incontestable superiority of mathematics over Kant's blank-slate arguments. Kant's unmethodical opinions on the matter are simply worthless nonsense.

[Veritas Aequitas]

From his CPR, it would be an insult for Kant to use mathematics for his refutations that it is impossible for God to exists as real.

Well, Kant wrote in Critique of Pure Reason:

On this account, I shall not reckon among my principles those of mathematics;

That is clearly the reason why Kant was completely inept in the realm of mathematics. You see, Gödel and Tarski are grandees. Carnap is arguably also a grandee in mathematics. Kant, if only through his own admission, is obviously not.

Gödel, Tarski, and Carnap collectively proved in a mathematically unobjectionable manner that true(n) cannot be defined as a predicate. As far as I am concerned, Kant has no business arguing that exists(n) would not be a legitimate predicate. It does not necessarily follow from anything.

Kant does not stand a snowball's chance in hell against Gödel. There is a massive difference in class and capability between them. You fail to acknowledge the incontestable superiority of mathematics over Kant's blank-slate arguments. Kant's unmethodical opinions on the matter are simply worthless nonsense.

I find it very weird you are insisting using mathematics as a final judgment.

As I had stated mathematics is merely a tool.
All the scientific that relied up mathematics, e.g. Newtonian, Einsteinian, QM has to be verified and justified by empirical evidence to be recognized as real.
Otherwise they are merely empirically possible speculations or speculative theories.

There are many claims of reality that do not require mathematics but empirical evidence is imperative to justify the claim is real.

God does not have any empirical possibility at all.

[godelian]

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.

[Veritas Aequitas]

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.