A Rational Cosmology: Why Matter Cannot Be Infinitely Divisible

This is Essay LXVII of Mr. Stolyarov's series, "A Rational Cosmology," which seeks to present objective, absolute, rationally grounded views of terms such as universe, matter, volume, space, time, motion, sound, light, forces, fields, and even the higher-order concepts of life, consciousness, and volition. See the index of all the essays in "A Rational Cosmology" here.

Here, the insights of rational cosmology will be used to refute the view that matter is infinitely divisible.

I could take a sheet of metal and slice it in two pieces. It could be said then, that the metal is divisible by two. I could, using advanced futuristic technology, dismember it into its constituent atoms. It can then be said to be divisible by about 6.022 * 10²³ (assuming we have a mole of metal to begin with). I may also be able to extract the cores of these atoms and separate them into their constituent nucleons, and, subsequently, split those nucleons into the quarks that comprise them.

Matter can be divisible by a very large factor, and this factor may be far greater than we presently even suspect. Only science can inform us of the precise extent of matter's divisibility. But can matter ever be infinitely divisible?

Can we ever have an infinity of particles originating from some finite object? Just like having infinite mass in a finite volume, this is a simultaneous infinity, and is thus impossible. After all, this would imply that each of these particles would have zero volume, and would thus simply not exist. How one can form an existent piece of metal out of non-existent particles, no matter how many of them there are, is beyond rational comprehension. I will wager my life savings that nobody will ever be able to do this!