JMC : Logic and Mental Philosophy / by Charles Coppens, S.J.

Chapter V. The Chief Perfections of Being.

I. Simplicity is that perfection which makes a being identical with everything that constitutes it; it is a positive perfection, but it is conceived by us in a negative way, viz.: by the exclusion of all composition. A being is absolutely simple if it excludes all manner of composition.

The Potential Infinite is the finite conceived as capable of constant increase; it is, therefore, not truly infinite but indefinite, though in mathematics it is usually called infinite. The infinite cannot be measured or counted; because measure and number express a limit, and the infinite has no limit. It is also to be observed that no amount of finite additions can ever make the finite become infinite.

Proof. Since the essence of quantity implies divisibility, any existing quantity may be divided, at least mentally. Let us, then, cut off a small portion from the quantity which was supposed to be infinite; what remains will be finite; and that finite remainder increased by the small portion cut off will be infinite. But this is absurd, viz., that a finite quantity should differ from the infinite by a small portion. Besides, suppose we add to the finite remainder a portion greater than that cut off; we should then have a quantity greater than infinite, which is impossible. An infinite body would measure an infinite number of yards, and more than an infinite number of feet.

2. The acts of creatures will go on increasing in multitude for ever. Answer. The number of past acts will always be actually finite, though capable of constant increase -- i.e., the multitude of future acts is indefinite.

3. It cannot be indefinite; for God knows all future acts of His creatures distinctly, and therefore definitely. Answer. God's knowledge is conformable to the reality -- i.e., to the object of that knowledge; now, that object is a series of acts, all distinct from one another, ever continuing, but never being an existing infinite series. Besides, distinctness of knowledge is opposed to vagueness of knowledge, and need not imply limitation of the things known.

4. Any extended body contains an infinite multitude of parts. Answer. The number of ultimate particles into which a body can physically be divided is finite; but the extension of the body can be mathematically divided without end -- i.e., it is potentially, not really, infinite in its divisibility.