The _à priori_, since Kant at any rate, has generally stood for the necessary or apodeictic element in knowledge. But modern logic has shown that necessary propositions are always, in one aspect at least, hypothetical. There may be, and usually is, an implication that the connection, of which necessity is predicated, has some existence, but still, necessity always points beyond itself to a _ground_ of necessity, and asserts this ground rather than the actual connection. As Bradley points out, "arsenic poisons" remains true, even if it is poisoning no one. If, therefore, the _à priori_ in knowledge be primarily the necessary, it must be the necessary on some hypothesis, and the _ground_ of necessity must be included as _à priori_. But the ground of necessity is, so far as the necessary connection in question can show, a mere fact, a merely categorical judgment. Hence necessity alone is an insufficient criterion of apriority. To supplement this criterion, we must supply the hypothesis or ground, on which alone the necessity holds, and this ground will vary from one science to another, and even, with the progress of knowledge, in the same science at different times. For as knowledge becomes more developed and articulate, more and more necessary connections are perceived, and the merely categorical truths, though they remain the foundation of apodeictic judgments, diminish in relative number. Nevertheless, in a fairly advanced science such as Geometry, we can, I think, pretty completely supply the appropriate ground, and establish, within the limits of the isolated science, the distinction between the necessary and the merely assertorical. =7.= There are two grounds, I think, on which necessity may be sought within any science. These may be (very roughly) distinguished as the ground which Kant seeks in the _Prolegomena_, and that which he seeks in the _Pure Reason_. We may start from the existence of our science as a fact, and analyse the reasoning employed with a view to discovering the fundamental postulate on which its logical possibility depends; in this case, the postulate, and all which follows from it alone, will be _à priori_. Or we may accept the existence of the subject-matter of our science as our basis of fact, and deduce dogmatically whatever principles we can from the essential nature of this subject-matter. In this latter case, however, it is not the whole empirical nature of the subject-matter, as revealed by the subsequent researches of our science, which forms our ground; for if it were, the whole science would, of course, be _à priori_. Rather it is that element, in the subject-matter, which makes _possible_ the branch of experience dealt with by the science in question[2]. The importance of this distinction will appear more clearly as we proceed[3].