Claim ID: MATH-IS04

Claim: Implausibility of Infinity Past

Summary: Mathematicians have long argued that an actual infinity cannot exist. Infinity is a concept. It serves as a potential limit which is never reached. Essentially, it is merely a figment of human imagination, not reality.

Description: Infinity is perhaps the most misunderstood concept. Many regard infinity as reality.

While infinity is a useful theoretical tool used in the field of Mathematics to understand infinite sets of objects and estimate a convergent series of numbers, it is not observed as a factual reality in the material world comprised of time, space and matter. It is merely a figment of human imagination.

Implications of Infinity Past

What are the implications of an infinity past as it relates to creation?

Infinity has been used to justify a number of cosmological theories, most notably the multiverse (multiple universes) and a self-existent universe. These concepts were first espoused in the mid 1500's by Thomas Diggies and Giordano Bruno [REF-INF01]. They postulated that there were an infinite number of universes and planets, unbounded space, and so on. In the absence of scientific evidence, their concepts were assumed to be plausible.

Infinity has also been used to justify the theory of evolution in the mid 1800's. The implication was that "given enough time", evolving genetic traits would prove viable and freely propagate to future generations. Unfortunately, these suppositions are not evinced by the fossil records nor the findings of modern biological research.

Absurdities

In his book Reasonable Faith [REF-WLC03], William Lane Craig argues,

"A potential infinity can exist, but an actual infinity cannot exist. … For if an actual infinity could exist, this would spawn all sorts of absurdities."

These absurdities result from a tension between a theoretical infinity and the finiteness of creation itself. They also contradict the laws of logic, most notably, the Law of Causality [PHY-IS01] and Law of Contradiction [PHY-IS02].

In order for an actual infinity past to exist, the past must be comprised of an infinite numbers of events. This implies that the universe did not have a beginning, and that the universe has been in a steady state of cause and effect forever. Using simple logic, this premise can be refuted by the following absurdities:

The implausibility of an actual infinity past is best illustrated by the paradox of the Grand Hotel developed by the German mathematician David Hilbert [REF-HIL01]. Imagine that Hilbert's Hotel is full and yet can accommodate an infinite number of new guests. This implies Hilbert's Hotel must have an infinite number of rooms. The marquee on the hotel would read "NO VACANCIES, GUESTS WELCOME". Because of the Law of Non-Contradiction [PHY-IS02], Hilbert’s Hotel can’t be infinitely full and infinitely empty at the same time.

The illustration of Hilbert's Hotel becomes even more absurd if it has a finite number of rooms. It is impossible for Hilbert's Hotel to accommodate an infinite number of guests past, present, and future when it only has a finite number of rooms. Essentially, anything that is finite cannot be simultaneously infinite [PHY-IS02].

Observations

Because the universe has been proven by modern science to be bounded in terms of time, space and matter, infinity past cannot exist.

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