We show that the first order theory of the lattice $\mathscr{L}^{ (S) of finite dimensional closed subsets of any nontrivial infinite dimensional Steinitz Exhange System S has logical complexity at least that of first order number theory and that the first order theory of the lattice L(S ∞ ) of computably enumerable closed subsets of any nontrivial infinite dimensional computable Steinitz Exchange System S ∞ has logical complexity exactly that of first order number theory. Thus, for example, the lattice of (...) finite dimensional subspaces of a standard copy of $\bigoplus_\omega$ Q interprets first order arithmetic and is therefore as complicated as possible. In particular, our results show that the first order theories of the lattice L(V ∞ ) of c.e. subspaces of a fully effective ℵ 0 -dimensional vector space V∞ and the lattice of c.e. algebraically closed subfields of a fully effective algebraically closed field F ∞ of countably infinite transcendence degree each have logical complexity that of first order number theory. (shrink)

In this article, the author proposes to reconstruct Kant's "transcendental deduction" without in any way making use of the results of the so-called "metaphysical" one. His suggestion is that what Kant baptizes "pure concepts" or "categories" are in fact not "concepts" at all, strictly speaking, but rather the very forms of judgment from which these "concepts" were supposed to have been derived in the "metaphysical deduction". The task of the "transcendental" deduction is, then, to show that such forms of judgment (...) can legitimately be applied to empirical contents: to demonstrate, in other words, the possibility of empirical knowledge. (shrink)