A Rational Cosmology: Why Matter Cannot Be Infinitely Divisible

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!

Thus, matter cannot be infinitely divisible. We do not know the extent of matter's divisibility, and we may be able to continue dividing it for vast periods of time, and still find new division to be possible. But we will only know matter to be divisible as far as we will have divided it. Since simultaneous infinities cannot exist, we will never reach a state where infinite divisibility can be empirically verified. Thus, it is not a legitimate proposition, scientifically or philosophically.

Another mistake related to the proposition that matter is infinitely divisible is often expressed thus: "Division by zero gives infinity. Therefore, infinite quantities must exist."

There is no such operation in the real world called "division by zero." I can split a pie into three pieces, or five thousand pieces (if I have a microscopic cutting tool). I cannot split it into zero pieces. Matter does not originate ex nihilo, nor can it be annihilated. The fundamental constituent quality of that which exists (i.e. matter) cannot all of a sudden stop existing for no apparent reason. The scientific principle of matter conservation is in fact a philosophical proposition which must be true in order to exclude magic from the realm of science.

Division by zero is in fact not even a valid mathematical operation, but rather the description of a trend: the magnitude of the quotient is inversely proportional to the magnitude of the number by which the dividend is divided. Similarly, all other uses of infinity in mathematics are mere convenient shorthand notation to the identification of trends. For example, a quantity "approaching infinity" is the same as a quantity increasing without bound. At any particular time, it will still be a finite quantity.

Read other parts of "A Rational Cosmology" by clicking here.