Why again should it be assumed that the general account thus extracted from a retrospective study of discoveries must at once coincide with the logical ‘ideal of proof’? Why should it even point to this, or be related to it otherwise than by contrast? Surely the possibility should be discussed that there are _two_ procedures for logic to consider, of which the one describes how human knowers, starting from what they believe themselves to know, set about it to fortify and extend their knowledge, while the other moves on a superhuman plane and describes, with Platonic fervour, how ideal demonstration, descending from absolutely certain principles, moulds into a closed and inexpugnable system all the truths which are deducible from these and alone intelligible. The two accounts must be distinct, for they have different starting-points and work upon different material. Nor need they ever have any point of contact. For it may well be that human knowing never attains to an absolute certainty and a completed system, while deductive proof never condescends to notice mundane fact. This was certainly so in the first rapturous vision of _a priori_ ‘proof’ which solaced Plato amid the elusiveness and opacity of the flow of happenings. The deduction of the intelligible order of the ideal ‘Forms’ from their supreme ground and (_sole_!) premiss in the ‘Idea of the Good’ stopped short of facts and events at the _laws_ of minimum generality,[393] and recognized in all the happenings of the sensible world an ineradicable taint of ‘not-being’ which rendered their stability impossible and their prediction vain. Aristotle similarly distinguished between the procedure which started from the _notiora nobis_, the apparent facts of perception, and that which began with the _notiora naturae_, the self-evident principles which could form the ultimate premisses of demonstrations. But that these two methods must somehow coincide was assumed rather than proved, in a way that should have discredited the doctrine. For Aristotle also was not able to explain how ‘science’, being of ‘universals’, could apply to particulars, which nevertheless he would not with Plato stigmatize as ‘unreal’, while the ascent from the sensible fact to the ‘universal’, which was called the ‘induction’ of the ‘principle’, is hardly validated by the naïve allegation of a mental faculty of ‘intuitive reason’ (νου̑ς) endowed with the special function of apprehending principles in their particular exemplifications. It is high time, therefore, that this whole assumption that a necessary congruity exists between the logic of discovery and of proof should be subjected to a thorough examination. III § 18. Such an examination will speedily establish that the mental attitude of the discoverer is, and must be, quite different from that of the prover.