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IN reference to the controversy between Mr. Spencer and his reviewer about Sir I. Newton's calling his laws of motion â axioms,â it is to be observed that there is a certain ambiguity in the word. â Axiomâ is from à ξcÃ³Ï (I demand), and would thus signify a first principle to be taken for granted. It does not, of course, carry with it the meaning of a necessary judgment which cannot be contradicted. Whatever may be considered the ground of Euclid's â axiomsâ so called, Euclid himself did not apply that name to them ; but the first nine he called â common notions,â and the last three (which are peculiar to geometry) he placed among the postulates (óμλoÎ³Î·Î¼Î±Ï Î±), and heads them with â let it be granted.â Now it is clear, from Newton's own words, that in calling his Leges raotus â axioms,â he does not imply that they are necessary judgments, but that he requires them first of all to be granted (however established) in order to the following reasoning. In other words, they are postulates, like Euclid's last three â axioms.â In our modern use of the words â axiom,â â axiomatic,â there is always implied the ground why a proposition is demanded as granted, viz., because its necessity is self evident; but this wider use is not required by etymology,· or (I think) in interpreting all ancient writings. |
