105. Let us apply these considerations to the sensible world. Motion is a modification to which bodies are subject. This modification is essentially successive. A motion, the parts of which co-exist, is absurd. The co-existence of different states, which result from different motions, is also absurd: things that are contradictory cannot exist at the same time, and many of these situations are contradictory, because one of them necessarily involves the negation of others. If a line falling on another line revolve around a point, it will successively describe different angles. When it forms an angle of 45 degrees, it will not form an angle of 30 degrees, nor of 40, nor 70, nor 80; these angles mutually exclude one another. A portion of matter will form different figures, according to the arrangement which is given to the parts of which it is composed. When these parts form a globe, they will not form a cube; these two solids cannot exist at the same time, formed of the same portion of matter. 106. This variety of motion and form can be numbered. At every step we measure motion, applying to it the idea of number; at every instant we count the forms of a portion of matter, as for example, a piece of wax, to which different forms have been given successively: whatever be the number of the beings which we suppose to exist, every one of them will be susceptible of transformations which may be counted. Therefore, in the very nature of things, there is an intrinsic impossibility of the existence of an actual infinite number. 107. I believe that these arguments fully demonstrate the impossibility of an actual infinite number; and if I do not dare to say that I am sure of having given a complete demonstration, it is because the nature of the question presents so many and so great difficulties, it so bewilders and confounds the weak understanding of man, that there is always reason to fear that even those arguments, which seem the clearest and most conclusive, may conceal some fault which vitiates their force, and makes an illusion appear an incontestible truth. Still I cannot but observe that to combat this demonstration, it seems, to me that it would be necessary to deny our primary ideas, the exclusion of being and not-being, and the necessity of succession, of time, to the realization of contradictory things. 108. Perhaps it may be objected to me that contradictory modifications are not a part of the infinite number, which only relates to the possible: but this does not destroy my demonstration; it rather confirms it. For as the absolute infinite number implies the absolute negation of all limit, when, in treating of the realization of this conception, I meet with things that are contradictory, I say that the realization of the conception is contradictory, because the general and indeterminate conception is more extended than all possible number.