> it's not at all obvious to me that the set of axioms would be finite or even computable
The reasoning is representable with and by a finite number of elementary physical particles and so must itself be finite. Because it is finite it is computable.
Said another way, you would need an infinitely large brain (or an infinitely deep one) to create infinite reasoning.
The reasoning is representable with and by a finite number of elementary physical particles and so must itself be finite. Because it is finite it is computable.
Said another way, you would need an infinitely large brain (or an infinitely deep one) to create infinite reasoning.