Could you give me a definition for “definition”?
At some point you have to be content that your inability to define every single term in your vocabulary doesn’t hinder your ability to use that term in practice.
All we have in way of creating/communicating knowledge is symbol manipulation. Language.
Turing machines are language recognisers, and I am comfortable using them as practically sufficient (for the purposes of conversation) models of minds.
To be sure you see my point, defining “definition” is recursive and that puts you on the computer science turf.
I am a computer. Mathematics is a language; or more precisely - it is a grammar. Our Mathematical models of the universe are computational, and since Mathematics can only prove things up to isomorphism that is as far as colourless, formal, linguistic reductionism will take us.
As for Kantian transcendentalism. Look no further than Jean-Yves Girard’s work on Linear Logic, Geometry of Interaction and transcendental syntax. Is all computer science intersecting with Quantum Physics.