PRESIDENTIAL ADDRESS — SECTION F. I25 



Poincare affirms that all the fundamental principles of 

 science, including- even mathematical axioms and postulates, are 

 hypotheses suggested by experience and therefore not arbitrary, 

 but conventional in the sense of being not the only possible bases 

 for theoretical constructions, and giving certainty only within 

 the limits implied in their acceptance in preference to others. 

 They have an intuitive or experiential along with a conceptual 

 or constructive character, and their fertility proves them to be 

 in keeping with reality, but they have no justifiable claim to 

 finality.* 



Karl Pearson contends, as against the tendency even of first- 

 rank scientists to objectify their definitions and conceptions, that 

 scientific notions express ideal limits to processes which begin 

 from sense-perception, but can never be carried to a limit in 

 actual experience. To take the very simplest case — " The fly- 

 leaf of this book," he says in his "Grammar of Science," "appears 

 at first sight a plane surface bounded by a straight line, but a 

 very slight inspection with a magnifying lens shows that the 

 surface has hollows and elevations in it, which quite defy all 

 geometrical definition and scientific treatment. The straight 

 line which seems to bound its edge becomes, under a powerful 

 glass, so torn and jagged that its ups and downs are more like a 

 saw-edge than a straight line." Similarly, the idea of distance, 

 as the length from one point to another, is a conception reached 

 as a limit to perceptual experience. So it is with all scientific 

 concepts. They are ideal symbols by which we describe, classify, 

 and formulate the characters or elements of immediate or per- 

 ceptual experience, and their validity lies in their power of 

 resuming past and predicting future experience. But what we 

 get in this way is not — at any rate, not directly — anything beyond 

 perception, anything underlying phenomena, such as matter in 

 motion or absolute space and time, nor anything that has actuality 

 in the phenomenal world, but a conceptual representation of ex- 

 perience, a means of describing the order of our sense-perceptions 

 or interpreting the perceptual changes which are the actual facts 

 of experience.'-* 



Along with this criticism of ifundamental conceptions and 

 postulates in the work of the philosophical scientists there goes 

 as its correlate the recognition that the justification of scientific 

 concepts at the bar of philosophic doubt must consist in their 

 derivation from the facts or data of immediate or sense ex- 

 perience. This is the reverse of what has been the customary 

 or traditional attitude, though its truth may have been recognized 

 or even enforced by the greatest scier!.tific thinkers. For example. 

 Newton's general standpoint is not inconsistent with it ; and it 

 seems to have been a recurrent thought of, among others. Clerk 

 Maxwell. But the ordinary attitude is dififerent. It is con- 

 stantly assumed not only that well-established scientific laws and 



^Science and Hypothesis, e.g., pp. xxiii, 70-1, Tio. 

 * Grammar of Science, pp. 197-9, 266-7, 287-8, etc. 



