A Rational Cosmology: Why Space and Time Are Neither Infinite nor Finite

This is Essay LXVIII 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, we identify and refute further common mistakes regarding the concept of "infinity."

Mistake: If infinite quantities cannot exist, then space itself is finite.

All quantities are attributes of existents. Space is not an existent. It is a mere positional relation of existents with respect to each other. There cannot simultaneously exist an infinite number of existents, but space itself cannot be said to be finite or infinite. It cannot be said to be. Something, i.e. an existent, is. Nothing, i.e. space, is not.

This is why all coordinate systems are inherently relative: they must presume an arbitrary origin at some point. But, just as an entity can be conceived to exist at (0,0,0), so can it be conceived to exist at (10⁸⁷, 9*10⁶⁵, 2.79*10⁹⁸⁸⁷⁵⁷), which is just a set of numbers describing its relation to an entity that could exist at (0,0,0).

A spaceship with recyclable fuel could be equipped to distance itself from other existents indefinitely. At any time, it will still be a measurable distance from those existents, and its distance would be finite. No matter how large this distance is, however, it could always become larger. 2.79*10⁹⁸⁸⁷⁵⁷ +1 is a conceivable number, but infinity is not.

Space is neither finite nor infinite, but it can be said to be indefinite.

Mistake: If everything is finite, time must have had an origin.