A Natural System is one which attempts to make all the divisions natur — William Whewell

"In Deductive Reasoning, we cannot have any truth in the conclusion which is not virtually contained in the premises."

"We unfold out of the Idea of Space the propositions of geometry, which are plainly truths of the most rigorous necessity and universality. But if the idea of space were merely collected from observation of the external world, it could never enable or entitle us to assert such propositions: it could never authorize us to say that not merely some lines, but all lines, not only have, but must have, those properties which geometry teaches. Geometry in every proposition speaks a language which experience never dares to utter; and indeed of which she but half comprehends the meaning."

"The antithesis of Sense & Ideas is the foundation of the Philosophy of Science. No knowledge can exist without the union, no philosophy without the separation, of these two elements."

"Among the foundations of the Higher Mathematics is also the Idea of a Limit. The Idea of a Limit cannot be superseded by any other definitions or Hypotheses."

"The solution is, that we do not see the image on the retina at all, we only see by means of it."

"We cannot observe external things without some degree of Thought; nor can we reflect upon our Thoughts, without being influenced in the course of our reflection by the Things which we have observed."