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 questionable. A proof does not necessitate that the conclusion be correct, but rather that by accepting the axioms, the conclusion follows logically.

Many philosophers have called the axioms into question. The first layer of criticism is simply that there are no arguments presented that give reasons why the axioms are true. A second layer is that these particular axioms lead to unwelcome conclusions. This line of thought was argued by Jordan Howard Sobel,[9] showing that if the axioms are accepted, they lead to a "modal collapse" where every statement that is true is necessarily true, i.e. the sets of necessary, of contingent, and of possible truths all coincide (provided there are accessible worlds at all).[note 6] According to Robert Koons,[10]:9 Sobel suggested that Gödel might have welcomed modal collapse.[11]

There are suggested amendments to the proof, presented by C. Anthony Anderson,[12] but argued to be refutable by Anderson and Michael Gettings.[13] Sobel's proof of modal collapse has been questioned by Koons,[10][note 7] but a counter-defence by Sobel has been given.[citation needed]

Gödel's proof has also been questioned by Graham Oppy,[14] asking whether lots of other almost-gods would also be "proven" by Gödel's axioms. This counter-argument has been questioned by Gettings,[15] who agrees that the axioms might be questioned, but disagrees that Oppy's particular counter-example can be shown from Gödel's axioms.

Religious scholar Fr. Robert J. Spitzer accepted Gödel's proof, calling it "an improvement over the Anselmian Ontological Argument (which does not work)."[16]

There are, however, many more criticisms, most focusing on the philosophically interesting question of whether these axioms must be rejected to avoid odd conclusions. The broader criticism is that even if the axioms cannot be shown to be false, that does not mean that they are true. Hilbert's famous remark about interchangeability of the primitives' names applies to those in Gödel's ontological axioms ("positive", "god-like", "essence") as well as to those in Hilbert's geometry axioms ("point", "line", "plane"). According to André Fuhrmann (2005) it remains to show that the dazzling notion prescribed by traditions and often believed to be essentially mysterious satisfies Gödel's axioms. This is not a mathematical, but merely a theological task.[17]:364–366 It is this task which decides which religion's god has been proven to exist.

Svartalf wrote:I'd say . I've known the ontological proof to be bunk for 35 years. Philosophy teacher in high school walked us through that one.
So I don't guess that, however great a logician Gödel may have been, couching it in the trappings of formal mathematical logic change that fact any.

Cito di Pense wrote:This is of interest to people developing automated theorem-provers, and not otherwise to be taken seriously.

aban57 wrote:

Cito di Pense wrote:This is of interest to people developing automated theorem-provers, and not otherwise to be taken seriously.

Indeed, it has no use in usual debates over gods' existence, pretty much like presup apologetics. I found the contrast between his work and his death to be rather noticeable though.

Cito di Pense wrote:

Svartalf wrote:I'd say . I've known the ontological proof to be bunk for 35 years. Philosophy teacher in high school walked us through that one.
So I don't guess that, however great a logician Gödel may have been, couching it in the trappings of formal mathematical logic change that fact any.

As usual, you don't have a fucking clue what you're talking about, but don't take that to mean that the trappings of mathematical logic are the root problem here. As already pointed out, it's the definitions that are questionable. Definitions are statements we accept without proof. We don't have to accept them, but then we can't prove anything with them, even if they're OK. This is elementary stuff, like the link between mitochondria and ATP.

Svartalf wrote:
I did say that the ontologic proof is a turd, and that nothing can change that.