Philosophy of Mathematics

Whilst the greatest effort has been made to ensure the quality of this text, due to the historical nature of this content, in some rare cases there may be minor issues with legibility. To form a just idea of the object of mathematical sci ence, we may start from the indefinite and meaningless definition of it usually given, in calling it The science of magnitudes, or, which is more definite, The sci ence which has for its object the measurement of mag nitudes. Let us see how we can rise from this rough sketch (which is singularly deficient in precision and depth, though, at bottom, just) to a veritable definition, worthy of the importance, the extent, and the difficulty of the science.