THIS IS AN INCOMPLETE DRAFT
“Either mathematics is too big for the human mind or the human mind is more than a machine.”
— Kurt Godël
What is the Incompleteness Theorem?
In any logical system as complex as or more complex than the arithmetic of the integers there can always be found either a statement which can be shown to be both true and false or a statement whose truth or falsity cannot be deduced from other statements in the system.
– Godel’s theorem from Merriam-Webster
Just as you cannot define a word without using other terms, you cannot define a logical system without using an outside truth. This outside truth is called an axiom.
To be able to count from 1 to 9, you must first assert that the digits 1 through 9 exist. You cannot prove the existence of those numbers, instead you must assume they exist before you can count.
What is religion?
Every religion is built upon principles, or axioms, that need not be proven outside of its system of belief. Often referred to as faith, it takes the form of rules that govern and justify the followers’ existence.
For the Abrahamic religions, in reductive terms, one follows a set of rules established by scripture; subject to interpretation, scripture dictates what one should eat, how one should act in public, how the universe was created, what a soul is, and many more aspects of life that often require a higher power to explain.
The controversy that surrounds religion is rooted in uncertainty, and that uncertainty is founded on asserted axioms. The belief relies on those claimed axioms, and those axioms then rely on the belief to reaffirm.
In other words:
God proves the existence of Himself because He exists.
For the mathematical thinkers:
The number one proves the existence of itself because it exists.
Is math a religion?
Yes, math is a religion and, by extension, science is, too.
The following is a thought experiment involving particle theory.
Going even deeper, what are the subatomic particles made of?
Subatomic particles are composed of quarks.
Then what are quarks made of?
Quarks are composed of…
Continuing this line of questioning, eventually you should resolve the meaning of the universe. Unfortunately, the reality is that physicists still rely on fundamental axioms, or principles, for which they build the rest of their study upon. In this case, the existence of elementary particles. That isn’t to say there isn’t proof, however, there is faith involved; faith that their currently asserted axioms are true.
One could argue that science isn’t based on faith, instead it’s based on the scientific method. After all, the scientific method follows a series of rules to obtain an objective explanation. Ironically, the scientific method is itself based on an axiom, the idea that objectivity can be determined in an uncertain universe.
The goal isn’t to say science should be rejected, rather, to bring into discussion that every belief is prone to the Incompleteness Thereom.
From a psychologist’s perspective, the human mind operates as a machine. The brain operates using logic that it builds through observation. This logic is built upon several principles depending on what is learned, and from that logic a reality is simulated within the brain. This simulated reality could be seen as a religious interpretation of what the person perceives the universe to be.
If a Christian won the lottery, they might thank the will of God, while a mathematician the grace of probability, and an astrologist the alignment of the stars.
All justify how they won, and their logic within their simulated reality is secure. However, you might expect a sour response when you ask one winner what they think of the other two’s justifications.