 Applying these notions to judgments, it follows that a judgment is a posteriori if and only if either its logical form or its propositional content is strictly determined by sensory impressions and/or contingent natural objects or facts; and a judgment is a priori if and only if neither its logical form nor its propositional content is strictly determined by sensory impressions and/or contingent natural objects or facts, and both are instead strictly determined by our innate spontaneous cognitive faculties, whether or not that cognition also contains sensory matter. Kant also holds that a judgment is a priori if and only if it is necessarily true (Axv, B3–4, A76/B101). This strong connection between necessity and apriority expresses (i) Kant’s view that the contingency of a judgment is bound up with the modal dependence of its semantic content on sensory impressions and/or contingent natural objects or facts, i.e., its aposteriority (B3), (ii) his view that necessity is equivalent with strict universality or strenge Allgemeinheit, which he defines in turn as a proposition’s lack of any possible counterexamples or falsity-makers (B4), and (iii) his view that necessity entails truth (A75–76/B100–101). Furthermore Kant explicitly holds that not only do a priori judgments really exist in various sciences, including physics and legitimate (i.e., transcendental idealist) metaphysics, but also that there really are some pure a priori judgments, e.g., in mathematics (B4–5, B14–18).