ABSTRACT
In this book2, which consists in the main of previous articles somewhat re-written, M. Poincaré’s well-known merits appear to the full-his lucid and trenchant brevity, his air of easy mastery, which often makes his thought appear less profound than it is, and his power of co-ordinating the whole domain of mathematics and physics in a single system of ideas. But these merits, great as they are, are accompanied by what cannot but appear as defects to anyone accustomed to philosophy. His fundamental principles, as a rule, are assumed without discussion, presumably on the ground that they are self-evident, yet many of them are at the extreme of one side in time-honoured controversies. Such are: Deduction can never give new truth; mathematics, so far as it is not mere definition, derives its certainty from the fact that its principles concern not nature, but properties of the mind; science teaches us, not about things themselves, but about their relations; ‘experiment is the sole source of truth. It alone can teach us something new; it alone can give us certainty.’ There are also some principles embedded in
the chapter on probability; but these are harder to discover or to state precisely.
