There are, we have seen, five facts, one of which every proposition must assert, viz. Existence, Order in Place, Order in Time, Causation, and Resemblance. Causation is not fundamentally different from Coexistence and Sequence, which are the two modes of Order in Time. They have been already discussed. Of the rest, Existence, if of things in themselves, is a topic for Metaphysics, Logic regarding the existence of _phenomena_ only; and as this, when it is not perceived directly, is proved by proving that the unknown phenomenon is connected by _succession or coexistence_ with some known phenomenon, the fact of Existence is not amenable to any _peculiar_ inductive principles. There remain Resemblance and Order in Place. As for Resemblance, Locke indeed, and, in a more unqualified way, his school, asserted that all reasoning is simply a comparison of two ideas by means of a third, and that knowledge is only the perception of the agreement or disagreement, that is, the resemblance or dissimilarity, of two ideas: they did not perceive, besides erring in supposing ideas, and not the phenomena themselves, to be the subjects of reasoning, that it is only sometimes (as, particularly, in the sciences of Quantity and Extension) that the agreement or disagreement of two things is the one thing to be established. Reasonings, however, about _Resemblances_, whenever the two things cannot be directly compared by the virtually simultaneous application of our faculties to each, do agree with Locke's account of reasoning; being, in fact, simply such a comparison of two things through the medium of a third. There are laws or formulæ for guiding the comparison; but the only ones which do not come under the principles of Induction already discussed, are the mathematical axioms of Equality, Inequality, and Proportionality, and the theorems based on them. For these, which are true of all phenomena, or, at least, without distinction of origin, have no connection with laws of Causation, whereas all other theorems asserting resemblance have, being true only of special phenomena originating in a certain way, and the resemblances between which phenomena must be derived from, or be identical with, the laws of their causes. In respect to Order in Place, as well as in respect to Resemblance, some mathematical truths are the only general propositions which, as being independent of Causation, require separate consideration. Such are certain geometrical laws, through which, from the position of certain points, lines, or spaces, we infer the position of others, without any reference to their physical causes, or to their special nature, except as regards position or magnitude. There is no other peculiarity as respects Order in Place. For, the Order in Place of effects is of course a mere consequence of the laws of their causes; and, as for primæval causes, in _their_ Order in Place, called their _collocation_, no uniformities are traceable.