In the present paper is analyzed the relationship between Kant's theses concerning unknowability and non-spatiotemporality of things in themselves. First of all, it is argued that even by taking for granted that the Unknowability Thesis does not contradict the Non-Spatiotemporality Thesis, because the former can be thought as a consequence of the latter, this is not enough to avoid another problem, namely, that the Non-Spatiotemporality Thesis is not sufficient to abolish the possibility of thinking consistently of space and time as empirical or material. It is also remembered that this point has already been partially envisaged for the first time by H.A. Pistorius (and later by A. Trendelenburg) and raised as the objection of the "third possibility" or "neglected alternative." Furthermore, it is maintained that although Kant tries to eliminate this possibility in the Metaphysical Expositions of Space and Time (but not in the Antinomies), by attempting to prove that space and time are only formal necessary conditions of sensibility, he cannot do it successfully. Hereafter it is argued that his circumstance is not due to the above objection itself, but to another difficulty that can only be grasped through the analysis of Kant's main argument in the Metaphysical Expositions of Transcendental Aesthetic. Ultimately, in order to show this difficulty, it is argued first that insofar as the Non-spatiotemporality Thesis supposes the validity of the Singularity Thesis, and this supposes the validity of the Apriority Thesis, the whole force of proof reposes on this latter. Secondly, it is shown that, despite his effort, Kant could not justify satisfactorily his claim to the formal apriority of space and time because of his failure to demonstrate necessarily the Apriority Thesis.
Vanishing moments for scaling vectors
