Fact _and_ Theory _correspond to Sense on the one hand, and to Ideas on the other, so far as we are_ conscious _of our Ideas: but all facts involve ideas_ unconsciously; _and thus the distinction of Facts and Theories is not tenable, as that of Sense and Ideas is._ (I. 2.) VI. _Sensations and Ideas in our knowledge are like Matter and Form in bodies. Matter cannot exist without Form, nor Form without Matter: yet the two are altogether distinct and opposite. There is no possibility either of separating, or of confounding them. The same is the case with Sensations and Ideas._ (I. 2.) VII. _Ideas are not_ trans_formed, but_ in_formed Sensations; for without ideas, sensations have no form._ (I. 2.) VIII. _The Sensations are the_ Objective, _the Ideas the_ Subjective _part of every act of perception or knowledge._ (I. 2.) IX. _General Terms denote_ Ideal Conceptions, _as a_ circle, _an_ orbit, _a_ rose. _These are not_ Images _of real things, as was held by the Realists, but Conceptions: yet they are conceptions, not bound together by mere_ Name, _as the Nominalists held, but by an Idea._ (I. 2.) X. _It has been said by some, that all Conceptions are merely_ states _or_ feelings of the mind, _but this assertion only tends to confound what it is our business to distinguish._ (I. 2.) XI. _Observed Facts are connected so as to produce new truths, by superinducing upon them an Idea: and such truths are obtained_ by Induction. (I. 2.) {7} XII. _Truths once obtained by legitimate Induction are Facts: these Facts may be again connected, so as to produce higher truths: and thus we advance to_ Successive Generalizations. (I. 2.) XIII. _Truths obtained by Induction are made compact and permanent by being expressed in_ Technical Terms. (I. 3.) XIV. _Experience cannot conduct us to universal and necessary truths:--Not to universal, because she has not tried all cases:--Not to necessary, because necessity is not a matter to which experience can testify._ (I. 5.) XV. _Necessary truths derive their necessity from the_ Ideas _which they involve; and the existence of necessary truths proves the existence of Ideas not generated by experience._ (I. 5.) XVI. _In Deductive Reasoning, we cannot have any truth in the conclusion which is not virtually contained in the premises._ (I. 6.) XVII. _In order to acquire any exact and solid knowledge, the student must possess with perfect precision the ideas appropriate to that part of knowledge: and this precision is tested by the student's_ perceiving _the axiomatic evidence of the_ axioms _belonging to each_ Fundamental Idea. (I. 6.) XVIII.