The same remarks are partially true of differences and inequalities, which are also reciprocal to the extent that one thing cannot differ from a second without the second differing from the first. Mars differs in colour from Venus, and Venus must differ from Mars. The Earth differs from Jupiter in density; therefore Jupiter must differ from the Earth. Speaking generally, if A ~ B we shall also have B ~ A, and these two forms may be considered expressions of the same difference. But the relation of differing things is not wholly reciprocal. The density of Jupiter does not differ from that of the Earth in the same way that that of the Earth differs from that of Jupiter. The change of sensation which we experience in passing from Venus to Mars is not the same as what we experience in passing back to Venus, but just the opposite in nature. The colour of the sky is lighter than that of the ocean; therefore that of the ocean cannot be lighter than that of the sky, but darker. In these and all similar cases we gain a notion of *direction* or character of change, and results of immense importance may be shown to rest on this notion. For the present we shall be concerned with the mere fact of identity existing or not existing. *Twofold Interpretation of Propositions.* Terms, as we have seen (p. 25), may have a meaning either in extension or intension; and according as one or the other meaning is attributed to the terms of a proposition, so may a different interpretation be assigned to the proposition itself. When the terms are abstract we must read them in intension, and a proposition connecting such terms must denote the identity or non-identity of the qualities respectively denoted by the terms. Thus if we say Equality = Identity of magnitude, the assertion means that the circumstance of being equal exactly corresponds with the circumstance of being identical in magnitude. Similarly in Opacity = Incapability of transmitting light, the quality of being incapable of transmitting light is declared to be the same as the intended meaning of the word opacity. When general names form the terms of a proposition we may apply a double interpretation. Thus Exogens = Dicotyledons