A Rational Cosmology: Infinity and Existence

"Infinity" is one of the most frequently encountered terms in the contemporary culture, and one of the least understood. Too often has its invocation been an attempt to justify mysticism, irrationalism, and contradiction, especially in the natural sciences.

It is the province of philosophy, as a foundational science, to set the very framework without which the natural sciences cannot operate. Unfortunately, numerous contemporary scientists have stepped far outside their field in making generalizations about the nature of existence, and of infinity, deliberations which properly belong in the realm of philosophy and which philosophers must employ to weed absurd and contradictory statements from the natural sciences.

Reality is absolute and every existent has an identity. According to the philosophy of Objectivism, existence and identity are inextricable corollaries. To be is to be something and to be something in particular. To be something in particular means to have a set, deliberate, fathomable nature.

It is no coincidence that the word "to fathom" means both "to measure" and "to understand." In order to be understood by man, a given entity must have attributes that can be measured on some scale, be it a qualitative or a quantitative one. In order to be measurable, an entity must demonstrate a finite quantity of each measurable attribute.

A particular given entity, say, a dog, must have finite mass and length, and its fur must reflect light of a finite measurement. A concept, such as dog, is formed by omitting the particular measurements of every dog and claiming that a dog must have dog-like qualities in some quantity, but could have them in any of a range of quantities.

To claim that any dog has infinite measurements of given qualities is absurd: if something is infinite, and does not have a set, delimited quantity to be measured, how can it be measurable? If it is not measurable in some manner, absolute or relative, how can it serve as a necessary quality in the definition of a concept?

Thus, infinite, that is, limitless measurements of qualities cannot exist if concept formation is to continue to maintain its legitimacy. We shall call the coexistence of infinite and finite measurements or the presence of all infinite measurements within an entity a simultaneous infinity. Simultaneous entities are not to be found in reality; indeed, they are not even consistently conceivable to the human mind.

Using this as a foundation, we can now proceed to investigate prevalent misconceptions and faulty logic in the examination of the notion of infinity and where it is applicable.

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