¹ In fact, if it is later discovered that the argument in question is actually a pseudo-problem, then all conceptions that take a stance in the debate must be considered false. The only position that can be considered true in this instance is one that refuses the very grounds for the problem's existence.

² It is significant that in areas where such difficulties in establishing a rational position do not exist, even the problems most laden with value judgments are easily soluble: for instance, the non-philosophical questions of the humanities, and the historical and social sciences. Of course, even in those cases, every researcher attempts to uncover facts and connections which fit his ideology. Nevertheless, he is eventually forced to accept – grudgingly or not – the facts and connections proven by his colleagues of different persuasions.

³ Even the debates of the last few decades around set-theory were more of a philosophical quality than of a true mathematical nature. (And the majority of mathematicians showed surprisingly little interest in them.)

⁴ Mathematics seeks to uncover the formal relations between things: in some instances, it must analyse rather complicated networks of relationships. The complex structure of mathematical inferences only mirrors the complexity of their mathematical objects. Philosophy, on the other hand, concerns itself with the content of reality, so it can make do with simpler forms of reasoning.

⁵ We cannot accept the viewpoint of the Descartes–Leibniz-type rationalism in this question, according to which principles are analytic judgments (and thus their truth can be recognized a priori), because first of all, a number of principles are not analytic (for instance the principle of causation) – modern research agrees with Kant in this question – and even those which appear analytic contain a synthetic statement: namely that the subject and the predicate are concepts with real value, that they are concepts of actually existing things or at least of potentially existing things. (All the sciences are namely forced to suppose that the concepts contained in their principles exist, in the manner appropriate to the science's subject. For instance, mathematics supposes that the basic concepts present in their axioms are endowed with an ideal mathematical existence, i.e., are free of contradiction; philosophy supposes that the basic concepts in its principles refer to really existing, or potentially existing objects) All such existence-claims, however, are synthetic judgments, whether they express true existence, its mere possibility or simply a lack of contradiction.

But here we must break away from Kant: we have every reason to view these synthetic principles as ontological laws, independent of our knowledge, and not to regard them as subjective illusions of our intellect, as synthetic judgments a priori in the Kantian meaning of the phrase.

Thus there is no other alternative than to derive these synthetic judgments from experience.