The Commens Dictionary
Quote from ‘Minute Logic: Chapter II. Prelogical Notions. Section I. Classification of the Sciences (Logic II)’
Among the theoretical sciences, I distinguish three classes, all resting upon observation, but being observational in very different senses.
The first is mathematics, which does not undertake to ascertain any matter of fact whatever, but merely posits hypotheses, and traces out their consequences. It is observational, in so far as it makes constructions in the imagination according to abstract precepts, and then observes these imaginary objects, finding in them relations of parts not specified in the precept of construction. This is truly observation, yet certainly in a very peculiar sense; and no other kind of observation would at all answer the purpose of mathematics.