On this supposition the most perfect created beings possible would exist, and no more perfect being in the sphere of creatures could be conceived. All that can be imagined would already exist, from nothing to infinite perfection.
100. Still it must be observed that the collection of created beings, whatever be their perfection, are necessarily subject to the condition of dependence on another being; a condition from which the infinite being above is essentially exempt. This condition involves limitation; therefore, all created beings must be finite.
101. Does the character of finite, which is met with in all created beings, involve a determinate limit beyond which they cannot pass? If this limit exists, is not the number of possible species also limited? And if these species are not infinite, is not an infinite number an illusion?
Although the intrinsic possibility of the infinite scale of beings seems beyond a doubt, we must beware of solving too quickly the present question. With respect to indeterminate conceptions, we see no possible limit; but would this still be so, if we had an intuitive knowledge of the species? Are we sure that in the particular qualities of beings, combined with limitation and dependence, which are essential to them, we should not discover a term beyond which they cannot go, by reason of the constitution of their nature? How impotent philosophy is to solve such questions!
102. Whatever may be concluded as to this infinity of species and their respective perfection, I do not believe that an actually infinite number can exist. Among these species must be counted intelligences which exercise their acts in succession. This is evidently so; for in this number are included human minds which think and wish in a successive manner. The acts of these intelligences may be numbered: this we know from consciousness. Therefore there would never be an infinite number, because these acts, being successive, can never be all at the same time.
103. It may be answered that in this case we might suppose that spirits, including our own, have only one act of intelligence and will. To this I reply, that besides contradicting the nature of created beings, which, because they are finite, must be subject to change, it is also open to another objection, inasmuch as it eliminates at once many species of beings, and thus, instead of preserving the infinity, renders it impossible. Who can deny the possibility of that which exists? If, as our experience informs us, there now exist beings of successive activity, why would not these beings be possible on the supposition that the divine omnipotence had exerted all its infinite creative power?
104. This difficulty, which is founded on the nature of finite intelligences, seems to render the existence of an infinite number impossible, and it becomes still stronger if we examine the question under a more general aspect.
The existence of an absolutely infinite number excludes the existence of any other number. That which is numbered is not substance alone, but its modifications also. This has already been demonstrated with regard to intelligences, and is true in general of all finite beings. Every finite being is changeable, and its changes may be counted. The modifications produced by the changes cannot all exist at once, for some of them exclude others. Therefore, an actual infinite number is never possible.
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.