(2) =Logical or epistemological possibility.=--How can synthetic _a priori_ judgments be _valid_? This question itself involves a twofold problem. How, despite their synthetic character, can they possess truth, _i.e._ how can we pass from their subject terms to their predicates? And secondly, how, in view of their origin in our human reason, can they be objectively valid, _i.e._ legislate for the independently real? How can we pass beyond the subject-predicate relation to real things? This latter is the Critical problem in the form in which it appears in Kant’s letter of 1772 to Herz.[189] The former is the problem of synthesis which was later discovered. (_b_) (1) =Possibility of explanation and= (2) =possibility of existence.=--(1) How can synthetic _a priori_ judgments be _accounted for_? How, despite their seemingly inconsistent and apparently paradoxical aspects, can their validity (their validity as well as their actuality being taken for granted) be rendered _comprehensible_? (2) The validity of such judgments has been called in question by the empiricists, and is likewise inexplicable even from the dogmatic standpoint of the rationalists. How, then, can these judgments _be possible at all_? These two meanings of the term ‘possible’ connect with the ambiguity, above noted, in the term ‘how.’ The former problem can be solved by an analytic method; the latter demands the application of the more radical method of synthetic reconstruction. (_c_) =Real and ideal possibility.=[190]--We have to distinguish between the possible validity of those propositions which the mathematical and physical sciences profess to have established and the possible validity of those principles such as that of causality, which are postulated by the sciences, but which the sciences do not attempt to prove, and which in certain cases they do not even formulate. The former constitute an actually existent body of scientific knowledge, demonstrated in accordance with the demands of scientific method. The latter are employed by the scientist, but are not investigated by him. The science into which they can be fitted has still to be created; and though some of the principles composing it may be known, others remain to be discovered. All of them demand such proof and demonstration as they have never yet received.[191] This new and ideal science is the scientific metaphysics which Kant professes to inaugurate by means of the _Critique_. In reference to the special sciences, possibility means the conditions of the actually given. In reference to the new and ideal metaphysics, possibility signifies the conditions of the realisation of that which is sought. In view of this distinction, the formula--How are synthetic _a priori_ judgments possible?--will thus acquire two very different meanings. (1) How are the existing _a priori_ synthetic judgments to be accounted for? (2) How may all the really fundamental