(2) He can point out that there is a serious _lacuna_ in the logician’s plea for his notion of ‘proof’. The logician has assumed that the only alternative to his belief in absolutely certain premisses is complete scepticism, arguing that it must be possible to start from certainty, because otherwise no knowledge would be possible at all. He then urged ‘but there clearly _is_ knowledge--the sciences attest it’, and consistently inferred that absolutely certain premisses must be obtainable. The more or less obvious failure of his attempts to explain their genesis by ‘self-evidence’, ‘intuition’, ‘necessities of thought’, &c. (§ 15), could not deter him from clinging to his belief, because the principles themselves seemed to him to be inevitable and to admit of no alternative. In fact, however, there _is_ a _via media_ between scepticism and absolutism, and science safely pursues it, though logic has overlooked it. It is _not_ necessary to start with absolutely certain premisses, because it is possible to adopt premisses hypothetically, to take them as true for the argument’s sake and for the purposes of the inquiry, to experiment with them, and to revise them in the light of the results of such experiments. Thus _their_ value may be judged and established, _after_ their adoption, by the experimental results, and they may come to depend logically upon these, and not upon the processes (analogies, suggestions, guesses, fancies, &c.) which led to their adoption. If they show themselves capable of advancing the science and solving its problems, confidence in their ‘truth’ increases progressively, and their initial assumption is justified. They _cease_ to be ‘hypotheses’ and become ‘facts’, and even ‘principles’ beyond dispute. If they fail to ‘work’, they may be discarded in favour of others which are tried in their turn and similarly tested. Hence it is not true that what is uncertain to begin with must always remain so, nor is it hard to understand that hypothesis, willingness to believe, and belief may be the psychological forerunners of logical proof, which, nevertheless, rests not upon them, but upon the solid value of the results subsequently reached by their means. The certainty of scientific premisses then admits of indefinite growth, which at some point or other will overpower even the most obstinately sceptical temper. This point naturally lies at a greater distance from the starting-point for some minds than for others, but when it is reached, and when the last doubts and scruples have been overcome, the triumphant truth will _feel_ absolutely certain, and to all intents and purposes will function as such. But the ‘practical certainty’ thus achieved will still be distinguishable in thought from the absolute certainty which logical theory mistakenly demanded. And logicians, from Plato downwards,[399] will be convicted of having failed to allow for the possibility that the certainty of premisses and principles may