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

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.

Time, too, is not an entity. While space is a relationship in three dimensions, time is a quality that enables the establishment of relationships in the fourth dimension. It can be measured by any uniform standard we deem fit, and something can be chronologically remote to something else in either direction to any finite quantity. Though this quantity must be finite, there is no limit to how large this quantity can be. Like space, time is neither finite nor infinite, but rather indefinite in two directions (earlier and later).

Here, it is fitting to note that each dimension (and there are only four) describes a particular relationship, and is indefinite in two directions: time (earlier and later), height (up and down), length (front and back), and width (left and right). This is a philosophical insight that the natural sciences cannot nullify by any amount of theorizing or observation.

Mathematics, being a sister foundational science to philosophy, calls this truth in the three spatial dimensions Euclidean space. Perhaps it would be fitting to refer to it in all four dimensions as Euclidean space/time, which is based on arbitrarily designated uniform units. Euclidean space/time is to the natural sciences a metaphysical given that mathematics must accept if it is to function in this world.

Neither the natural sciences nor mathematics can legitimately claim the existence of more than three spatial dimensions and one chronological dimension. Thus, dimensions with numbers like 6, 2.34, or e+3/4 must be immediately rejected as unreal and logically absurd.

Consistent and rational application of philosophy can indeed tell us many things about the nature of existence: indefinite Euclidean space-time, the impossibility of simultaneous infinities, the possibility of indefinite, but not infinite, measurements of all qualities, including the four dimensions of Euclidean space-time, and the nonexistence of infinite divisibility.

Philosophy can also help alleviate senseless scares about the "inevitable end of everything," which threaten, by no legitimate logical basis, to render the long-term purpose of existence itself meaningless.

Whenever one uses the term "infinity," one treads a thin line (though not an infinitely thin one!). I make no apologies for the term's existence, however; like "universe," it can be a convenient intellectual shortcut to lengthier expressions of mathematical and natural trends. It can also be used to point out logical impossibilities.

It is convenient, for example to inform an opponent in debate, "You claim the existence of a simultaneous infinity. This means you have committed a logical fallacy." But, in the vast majority of cases, the term "indefiniteness" is far more suitable to describing an entity or phenomenon than "infinity." The latter term suffers from improper cultural use, and has far exceeded its boundaries, ironically enough. It is time to constrain the term, "infinity," to its proper limits.

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