There are only three kinds of proof for the existence of God possible from speculative reason.
All paths on which one may set forth with this aim either begin from determinate experience and the special constitution of our world of sense known a through it, and ascend from that by means of laws of causality to the highest cause outside the world; or else they are empirically grounded on an experience that is only indeterminate, i.e., on some existence; or, finally, they abstract from all experience and infer the existence of a highest cause entirely a priori from mere concepts. The first proof is the physico-theological, the second the cosmological, and the third the ontological proof. There are no more of them, and there also cannot be any more.
– Immanuel Kant, Critique of Pure Reason
Of course, you can categorize the proofs that way… as a relatively idle exercise.
But Kant makes the implicit (?) claim here that his refutations are “future-proof”, i. e. his refutation of the ontological argument refutes all ontological arguments you could ever construct.
Yet if we take St. Augustine’s proof, for example, while it would be ontological (??) according to Kant’s classification, it doesn’t reason from the “concept of God” itself, which Kant – it seems – really had in mind. It reasons from the bare fact that there are abstract concepts. I don’t see how Kant’s refutation of the ontological argument (which is basically Anselm’s argument) applies to this proof.
Other proofs include the Neo-Platonic* proof (a cosmological proof, I suppose?) or C. S. Peirce “A Neglected Argument for the Reality of God” – a physico-theological proof (???). Both are very far removed from the “textbook” cosmological or physico-theological proof refuted by Kant.
Kant makes a very strong claim: That he refuted all proofs for the existence of God which pure reason could ever construct.
What are well-known critiques of Kant’s classification or at least this claim?
* admittedly, I don’t know if there really is such a thing as a Neo-Platonic proof (by Plotinus or others). A proof with this name is presented in Edward Feser’s “Five Proofs for the Existence of God”.