TO the subject of the present and next Book all that has preceded is subordinate and preparatory. In former works we have treated of the History of Scientific Discoveries and of the History of Scientific Ideas. We have now to attempt to describe the manner in which discoveries are made, and in which Ideas give rise to knowledge. It has already been stated that Knowledge requires us to possess both Facts and Ideas;--that every step in our knowledge consists in applying the Ideas and Conceptions furnished by our minds to the Facts which observation and experiment offer to us. When our Conceptions are clear and distinct, when our Facts are certain and sufficiently numerous, and when the Conceptions, being suited to the nature of the {28} Facts, are applied to them so as to produce an exact and universal accordance, we attain knowledge of a precise and comprehensive kind, which we may term _Science_. And we apply this term to our knowledge still more decidedly when, Facts being thus included in exact and general Propositions, such Propositions are, in the same manner, included with equal rigour in Propositions of a higher degree of Generality; and these again in others of a still wider nature, so as to form a large and systematic whole. But after thus stating, in a general way, the nature of science, and the elements of which it consists, we have been examining with a more close and extensive scrutiny, some of those elements; and we must now return to our main subject, and apply to it the results of our long investigation. We have been exploring the realm of Ideas; we have been passing in review the difficulties in which the workings of our own minds involve us when we would make our conceptions consistent with themselves: and we have endeavoured to get a sight of the true solutions of these difficulties. We have now to inquire how the results of these long and laborious efforts of thought find their due place in the formation of our Knowledge. What do we gain by these attempts to make our notions distinct and consistent; and in what manner is the gain of which we thus become possessed, carried to the general treasure-house of our permanent and indestructible knowledge? After all this battling in the world of ideas, all this struggling with the shadowy and changing forms of intellectual perplexity, how do we secure to ourselves the fruits of our warfare, and assure ourselves that we have really pushed forwards the frontier of the empire of Science? It is by such an appropriation, that the task which we have had in our hands during the two previous works, (the _History of the Inductive Sciences_ and the _History of Scientific Ideas_,) must acquire its real value and true place in our design.