Thus our Ideas of Space and Time are the necessary Forms of our geometrical and arithmetical knowledge; and no sensations or experience are needed as the matter of such knowledge, except in so far as sensation and experience are needed to evoke our Ideas in any degree. And hence these sciences are sometimes called _Formal_ sciences. All other Sciences involve, along with the experience and observation appropriate to each, a development of the ideal conditions of knowledge existing in our minds; and I have given the history, both of this development of ideas and of the matter derived from experience, in two former works, the _History of Scientific Ideas_, and the _History of the Inductive Sciences_. I have there traced this history through the whole body of the physical sciences. But though Ideas and Perceptions are thus separate elements in our philosophy, they cannot in fact be distinguished and separated, but are different aspects of the same thing. And the only way in which we can approach to truth is by gradually and successively, in one instance after another, advancing from the perception to the idea; from the fact to the theory. 2. I would now further observe, that in this progression from fact to theory, we advance (when the theory is complete and completely possessed by the mind) from the apprehension of truths as _actual_ to the apprehension of them as _necessary_; and thus Facts which were originally observed merely as Facts become the consequences of theory, and are thus brought within the domain of Ideas. That which was a part of the objective world becomes also a part of the subjective world; a necessary part of the thoughts of the theorist. And in this way the progress of true theory is the _Idealization of Facts_. Thus the Progress of Science consists in a perpetual reduction of Facts to Ideas. Portions are perpetually transferred from one side to another of the Fundamental Antithesis: namely, from the Objective to the Subjective side. The Centre or Fulcrum of the Antithesis is shifted by every movement which is made in the advance of science, and is shifted so that the ideal side gains something from the real side. 3. I will proceed to illustrate this Proposition a little further. Necessary Truths belong to the Subjective, Observed Facts to the Objective side of our knowledge. Now in the progress of that exact speculative knowledge which we call Science, Facts which were at a previous period merely Observed Facts, come to be known as Necessary Truths; and the attempts at new advances in science generally introduce the representation of known truths of fact, as included in higher and wider truths, and therefore, so far, necessary.