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Notes on Kant

A key issue in the discussion of the thing-in-itself as compared
to perception is the notion of isomorphism and other correspondences.
The modern mathematical view would be inclined to regard worlds
isomorphic in the structures of sensation they produces as equivalent
and even to abolish the differences by supposing that the set of
possible worlds is the set of equivalence classes.  Actually the
matter is more complicated than that, because two worlds can be
isomorphic up to now for me, but I may be able to distinguish them
later or someone else may have distinguished them.  It is especially
amusing if he has distinguished them but no one person may know
both his distinctions and mine.

We may suppose that the species is a bit more of a %2tabula rasa%1
than an individual, i.e. the species has evolved innate ideas about
space.

We should compare the efficacy of many specific innate modes of
perception, e.g. spatial and temporal, with the general mode that
says that the world is a causal system mathematically describable,
e.g. by sentences of Zermelo-Fraenkel set theory.  The latter
presumably has a certain universality.  Any specific mode of
perception, e.g. the tendency to interpret sensations as arising
from persistent objects located in three-dimensional space, can
be formulated as a hypothesis in set theory.

categories named by Kant - Being, Quality, Quantity, Relation, etc.