125. A and not-A imply contradiction; but not so that they absolutely cannot be realized. The exclusion is conditional; that is, it exists as long as the contradictory extremes are simultaneous, or referred to an indivisible _now_; but we discover no intrinsic necessity of existence in the idea of A: consequently, although we know that while A is, not-A cannot be, we can very well conceive that A may cease to be, and not-A may begin to be. There is, in, that case, no contradiction, and we can easily reconcile in our mind the two ideas of A and not-A, by referring them to different instants. 126. Hence the perception of time implies the perception of beings that are not necessary,--of beings which, when they exist, may cease to exist, and when they do not exist, may begin to exist. The difference between necessary and contingent being is, that the existence of the former absolutely excludes its non-existence, while the existence of the latter excludes its non-existence only conditionally, or on the supposition of simultaneousness. 127. This is why the principle of contradiction requires the condition of time. The objects which we perceive are changeable; there is nothing either in their nature or in their modifications which involves existence. If they are, they may cease to be; and if this change does not constantly occur in their substance, it does in their accidents. Therefore we cannot affirm the absolute, but only the conditional contradiction of their being and not-being; it exists only on the supposition of simultaneousness. 128. If we conceived only necessary being, we could have no idea of time: its existence absolutely excludes its non-existence, and therefore the contradiction would be always absolute, never conditional. 129. A most important consequence results from this analysis. The perception of time with us implies the perception of the non-necessity of things. When we perceive a being which is not necessary, we perceive a being which may cease to be, in which case we have the idea of succession, of real or possible time. Here another reflection arises which is also important: the idea of time is the idea of contingency: the consciousness of time is the consciousness of our weakness. 130. The idea of time is so deep in our mind, that without it we could not form the idea of the _me_. The consciousness of the identity of the _me_ supposes a link[34] which it is impossible to find without memory. Memory necessarily involves the relation of _past_, and, consequently, the idea of time. [34] See Bk. I., Ch. XXV. CHAPTER XVIII. SUMMING UP. Let us collect together the doctrines of the preceding chapters. 131. Time is a question difficult to explain. Whoever denies this difficulty shows that he has meditated but superficially on the matter. 132. Motion is measured by time; but it is not a sufficient definition of time to call it the measure of motion.