From Gödel to God

You may be having a tough time connecting the proof with more readily observable reality. This is the page for you! While the proof shows that the inexhaustibility of mathematics, which pervades all material and efficient causes (think of physics, chemistry and biology) of virtually everything in our universe (past, present and future), needs an infinite source (i.e. God), on this page, I'll focus on the past, specifically, the cosmological beginning of our universe. This may help the reader appreciate the incredible force of the proof through to the present (indeed, at this very moment).

How does the proof relate back to the objective reality of the creation of our Universe?

​​Imagine (read: “graciously grant”) a pre-Universe of infinite density and high temperature (this is our current cosmological model of the Universe; "infinite" only in the sense that at the point of the big bang, physics breaks down into a "singularity"). Now, let’s simplify things and grant only the necessity of one natural law, the existence of the law of gravity and let it begin working on these initial conditions after, again graciously granting an unknown trigger of the Big Bang. The law of gravity must pre-exist the basic building blocks (bbb) of the Universe because it is responsible for the creation of the bbb​ ​(granted all the other things, of course). Without its pre-existence, the bbb could not exist, and so it cannot simply be a description of the observed interaction of the bbb (see the video below for a good explanation of the relationship between the laws of nature and our Universe). This law of gravity, by being a mathematically-precise operator, is itself obedient to some axiomatic mathematical truths. Now, notice this implication from Gödel’s Incompleteness Theorem: the law of gravity, as a mathematical reality, exists within an axiomatic system that can be infinitely extended to include ever growing true axioms. The alternative is accepting that the law of gravity (and all scientific laws) operates within a system plagued with inconsistency (see FAQ - Skepticism over Gödel) but never having observed the inconsistency of mathematics, nor would the very existence of our universe be remotely likely if mathematics was inconsistent, smart money is on incompleteness[1]. In fact, a surprising and fascinating thing about our Universe is the reliable applicability of its laws no matter where in the entire cosmos you look. It’s hard to get around the finger pointing to an infinitely great ingredient in the creation of our Universe. Gödel’s Theorem flew against the anti-nonfinitary bias of his day[2] (a philosophy unadmittedly - more likely, unwittingly - still held onto by today’s hardline atheists) and Gödel himself saw it as validation of platonism - a proof of numbers (and all the laws of nature by extension) as real, infinite, timeless, objective entities[3].

[1] "Meta-mathematical arguments establishing the consistency of formal systems...have, in fact, been devised, notably by Gerhard Gentzen, a member of the Hilbert school, in 1936, and by others since then." - Nagel, E. and Douglas R. Hofstadter. 2001. “Gödel’s proof, Rev. ed.” New York: New York University Press

[2] Franzen, T. 2005. “Gödel's Theorem: An Incomplete Guide to Its Use and Abuse” (p. 6). A K Peters, Ltd.

[3] Berto, F. 2009. “There's Something About Gödel: The Complete Guide to the Incompleteness Theorem” (p. 152). Wiley.

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