Science and Hypothesis

Abstract

Henri Poincaré's Science and Hypothesis is a foundational work of modern philosophy of science that challenges superficial views of scientific certainty. Poincaré argues that the logic of science is not infallible, and that mathematical truths are not simply derived from self-evident propositions. Instead, he examines the indispensable role of hypothesis, which he insists is as necessary for the experimenter as it is for the mathematician. The book distinguishes between different kinds of hypotheses: some are verifiable and become fertile truths, while others are merely "conventions in disguise". This is especially true in mathematics. Poincaré argues that the axioms of geometry, for example, are not experimental facts or à priori intuitions, but conventions. However, these conventions are not arbitrary; they are guided by experiment to find the "most convenient path". By surveying the sciences — from arithmetic and non-Euclidean geometry to classical mechanics and modern physics —Poincaré redefines the aim of science. He concludes that its goal is not to discover "things themselves", but rather "the relations between things", as "outside those relations there is no reality knowable". The book also explores the true nature of mathematical reasoning, arguing that it is not purely deductive but a fruitful inductive process.

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