It will serve to make the point clearer if we contrast our genuine a priori judgement with an empirical generalization, such as “all men are mortals.” Here as before, we can “understand” what the proposition means as soon as we understand the universals involved, namely “man” and “mortal.” It is obviously unnecessary to have an individual acquaintance with the whole human race in order to understand what our proposition means. Thus the difference between an a priori general proposition and an empirical generalization does not come in the “meaning” of the proposition; it comes in the nature of the “evidence” for it. In the empirical case, the evidence consists in the particular instances. We believe that all men are mortal because we know that there are innumerable instances of men dying, and no instances of their living beyond a certain age. We do not believe it because we see a connection between the universal “man” and the universal “mortal.” It is true that if physiology can prove, assuming the general laws that govern living bodies, that no living organism can last forever, that gives a connection between “man” and “mortality” which would enable us to assert our proposition without appealing to the special evidence of “men” dying. But that only means that our generalization has been subsumed under a wider generalization, for which the evidence is still of the same kind, though more extensive. The progress of science is constantly producing such subsumptions, and therefore giving a constantly wider inductive basis for scientific generalizations. But although this gives a greater degree of certainty, it does not give a different kind : the ultimate ground remains inductive, i.e. derived from instances, and not an a priori connection of universals such as we have in logic and arithmetic.
Two opposite points are to be observed concerning a priori general propositions. The first is that, if many particular instances are known, our general proposition may be arrived at in the first instance by