Thus the statement 'two and two are four' deals exclusively with universals, and therefore may be known by anybody who is acquainted with the universals concerned and can perceive the relation between them which the statement asserts. It must be taken as a fact, discovered by reflecting upon our knowledge, that we have the power of sometimes perceiving such relations between universals, and therefore of sometimes knowing general _a priori_ propositions such as those of arithmetic and logic. The thing that seemed mysterious, when we formerly considered such knowledge, was that it seemed to anticipate and control experience. This, however, we can now see to have been an error. _No_ fact concerning anything capable of being experienced can be known independently of experience. We know _a priori_ that two things and two other things together make four things, but we do _not_ know _a priori_ that if Brown and Jones are two, and Robinson and Smith are two, then Brown and Jones and Robinson and Smith are four. The reason is that this proposition cannot be understood at all unless we know that there are such people as Brown and Jones and Robinson and Smith, and this we can only know by experience. Hence, although our general proposition is _a priori_, all its applications to actual particulars involve experience and therefore contain an empirical element. In this way what seemed mysterious in our _a priori_ knowledge is seen to have been based upon an error. 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 connexion 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 for ever, that gives a connexion 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