be a fruit of continuous experience and experiment, and to perceive that this is the method the sciences have actually employed. In short, necessary (needed) ‘truths’ need _not_ be regarded as ‘_a priori_’, if it is seen how hypotheses are consolidated by experience. (3) The scientist can deny that the ideal case, contemplated with so much satisfaction by the logician, can ever occur in actual knowing. He can point out that if the logical apparatus of demonstration is to work, it must be supplied with premisses that are absolutely true. But whence is the logician to obtain them? The ‘self-evident’ principles and ‘necessary’ axioms, for which so much has been claimed, have been shown (§ 15) to be highly disputable, and are themselves in need of support and verification. The truths which the sciences supply abundantly are all products of the method to which he takes exception. There are no scientific truths which have not to be, and have not been, verified, and if verification is logically vicious, and cannot amount to proof, they are not absolutely true. But if the premisses of a demonstration are not absolutely true, neither can its conclusion be. What then becomes first of the value, and ultimately of the ‘validity’, of an ideal of proof which can never be exemplified by actual reasoning, and serves only to condemn it? (4) The ideal of absolute certainty may be repudiated altogether, even as an ideal, for sound scientific reasons. It may be shown that if it were possible it would be scientifically undesirable. For it would mean the creation of absolute bars to scientific progress. If truths existed which were absolutely certain, this would mean that nothing more could be learnt about them, and nothing could be done to strengthen their position. No experience, no inquiry, no experiment, could any longer affect them, and add to or detract from their value. They could not, therefore, form avenues to further knowledge. They would simply be stops which would arrest scientific inquiry. But how could such things form an ideal of scientific knowledge? How could it be in the spirit, and to the interest, of science to recognize them? They would merely be for science brute facts which it was forbidden to investigate. And must not science on principle hold out for the right to inquire into everything, to test every belief, however true it may seem? How, then, can it be the ideal of science to adopt an ideal which would stop inquiry?