In the Prolegomena to any Future Metaphysic (1783) Kant presented the central themes of the first Critique in a somewhat different manner, starting from instances in which we do appear to have achieved knowledge and asking under what conditions each case becomes possible. So he began by carefully drawing a pair of crucial distinctions among the judgments we do actually make. The first distinction separates a priori from a posteriori judgments by reference to the origin of our knowledge of them. A priori judgments are based upon reason alone, independently of all sensory experience, and therefore apply with strict universality.
A posteriori judgments, on the other hand, must be grounded upon experience and are consequently limited and uncertain in their application to specific cases. Thus, this distinction also marks the difference traditionally noted in logic between necessary and contingent truths.
But Kant also made a less familiar distinction between analytic and synthetic judgments, according to the information conveyed as their content. Analytic judgments are those whose predicates are wholly contained in their subjects; since they add nothing to our concept of the subject, such judgments are purely explicative and can be deduced from the principle of non-contradiction.
Synthetic judgments, on the other hand, are those whose predicates are wholly distinct from their subjects, to which they must be shown to relate because of some real connection external to the concepts themselves. Hence, synthetic judgments are genuinely informative but require justification by reference to some outside principle.
Kant supposed that previous philosophers had failed to differentiate properly between these two distinctions. Both Leibniz and Hume had made just one distinction, between matters of fact based on sensory experience and the uninformative truths of pure reason. In fact, Kant held, the two distinctions are not entirely coextensive; we need at least to consider all four of their logically possible combinations:
- Analytic a posteriori judgments cannot arise, since there is never any need to appeal to experience in support of a purely explicative assertion.
- Synthetic a posteriori judgments are the relatively uncontroversial matters of fact we come to know by means of our sensory experience (though Wolff had tried to derive even these from the principle of contradiction).
- Analytic a priori judgments, everyone agrees, include all merely logical truths and straightforward matters of definition; they are necessarily true.
- Synthetic a priori judgments are the crucial case, since only they could provide new information that is necessarily true. But neither Leibniz nor Hume considered the possibility of any such case.
Isaac Newton<--example.
Unlike his predecessors, Kant maintained that synthetic a priori judgments not only are possible but actually provide the basis for significant portions of human knowledge. In fact, he supposed (pace Hume) that arithmetic and geometry comprise such judgments and that natural science depends on them for its power to explain and predict events. What is more, metaphysics—if it turns out to be possible at all—must rest upon synthetic a priori judgments, since anything else would be either uninformative or unjustifiable. But how are synthetic a priori judgments possible at all? This is the central question Kant sought to answer.
