logic absolutely necessarily presupposes metaphysics, this is an incoherent statement to make unless you are claiming logic itself is not real or doesn't exist. this abstraction you mention itself is a metaphysical claim, if you make claims about the existence of symbols it is a metaphysical claim, if the claim is logic is just a rule of the mind its is making a metaphysical claim of the minds existence. this anti-realist position is nonsensical especially since you admit to believing in God who is the ultimate metaphysical uncreated reality (but have not qualified who this God is in your worldview).
if your understanding of logic is purely formal, why does it correctly predict the behavior of the physical universe and how does it account for God?
I would like to hear your justification that logic does not presuppose metaphysics, or at the very least isn't synergistic with it.
i'm pointing out that godel does not provide ontology which is what my original question is asking, you are pointing at if we assume the axioms of the system it is consistent but my question is a higher order metalogical one. godel's theorem does not explain the ontological status of the laws nor do they justify their authority, which is why your attempted answer to my question is irrelevant. I used your reference to show how it's useless to the question of the possibility of the preconditions of logic itself.
you have still not proven the validity of the initial axioms. I am not saying assume axioms and then show the system is consistent within the set of axioms, I am asking for justification for the axioms themselves.
the issue with kant is he grounds such transcendental categories within the mind itself, so his "general logic" is just an arbitrary set of rules we happen to have in our minds. how do we know this interacts with the many? how do we know knowledge of the universal is possible if it is grounded in the finite? how do we bridge the gap?
This is the problem with not being acquainted with modern theory of models and category theory. I've noticed this a lot with philosophers who think they can talk about topics they don't even know deeply enough. Any reading of graduate level mathematical logic textbook will clear this confusion (you even confused which godel theorem you are referring to since there's a lot of them and they talk about different things). You've said godel's theorem does not explain the ontological status of the laws nor do they justify their authority.
OBVIOUSLY, they are not meant to do that so this is absolutely irrelevant and shows noting but misunderstanding or ignorance of basic first order logic metatheorems. Be honest, have you ever finished a grad level logic textbook covering all the metatheorems such as Lowenheim Skolem, Compactness, Forcing etc.?
Modern logic is developed syntactically (so it doesn't presuppose anything about ontology). I've only mention Godel completeness theorem specifically because it shows
why such a syntactic view of logic is useful. So you're misunderstanding why I've pointed this out. This is a metatheorem in logic that is not even about ontology.
Logic by itself does not claim these symbols exist or doesn't exists in reality. Some logicians (Godel in particular) do believe that mathematical objects including metatheorems are 'out there' in a platonistic sense but you do not add these assumptions in the study of logic itself. I could say that we believe these concepts exists out there and is of course grounded by God i.e. '
ens realissimum' (the most real being) but again, these assumptions are not intrinsic to logic as a study.
// I am asking for justification for the axioms themselves.//
By itself the 'logical axioms' (Hilbert-style presentation) does not give any additional information. A logical system is completely determined by its set of nonlogical axioms so it is moot to ask the justification of these axioms since they are purely syntactical. They are 'what they are'. If you want to say they are metaphysically existent or nonexistent, the onus would be on you.
While I'm not defending Kant, I'm testing your understanding of him. "General logic' for Kant is a determinant for negative metaphysics, a
conditio sine qua non. It is not the same as his transcendental logic but whatever.
This post was edited by Hajun123 on May 12 2026 08:18pm