I once had someone tell me that the more I learned about math, the less I would believe in God. I’d like to share with you just how wrong that individual was, and why.
Learning math gave me a closer look at logic (in its purest form) than most any field allows. One of the things that learning math led me to see is that our knowledge is founded upon axioms. Axioms are essentially claims that are accepted as true without deduction or proof. (e.g one axiom in Euclidean Geometry—the one you learn in High School— is that parallel lines don’t intersect. This has not proof, it is just accepted as true.) This tells us that all our knowledge is founded upon accepted – not proven— claims. As you may expect, this is a point of contention for many (e.g wanting a justification for claims, but not having a justification for the foundation of all claims). However, through the study of Mathematics I have concluded that it ought not to be a point of contention when viewed in a proper light.
Some, in their attempt to settle the contention, have decided that there is a need to change the definition of “truth”. Since axioms are essentially claims that work and have not been shown to be wrong, some have decided that “truth” should be redefined to “that which works”. There are countless counter examples for this claim that lead us to say, “Well that was true then, but it isn’t true now.” This claim as preposterous as it is silly since it leaves us hopeless of meaningful progress in our search for knowledge.
Another set of people tried to settle the problem of axioms by redefining what it means to “know” something. For years the standard for one to “know” something was that it was a “justified true belief”. This definition combined with the issue of axioms caused many to change the concept of knowledge to something that is only in the negative, claiming that we cannot actually know that which is true, we can only show that something is false. This escapes the problems they found (e.g having a system of knowledge based upon justification that can’t be justified), but only uncovered a contradiction in the system. The contradiction is that once someone proves a claim false, the negation of the claim is simultaneously proven true. Thus, we can prove things true. The answer to this is to accept that we can prove both true and false, since they’re equivalent. (Much of this was done and said regarding science and only being able to prove good theories false. I have no qualms with this.)
These attempts to twist intuitive understandings of knowledge and truth are, in my opinion, unnecessary. In my math studies, I have come to conclude that we can go back to our intuitive understanding of truth and knowledge, we must only do two things extra: not be afraid of belief, and be humble.
Before I defend myself, I’d like to explain what I mean by being afraid of belief. Many people are afraid of saying that they have beliefs. They seem to be afraid to admit that belief plays any role in any valid system of knowledge. This, however, is unfounded beyond their cultural perception of how belief seems to work. In other words, beliefs can have negative ramifications in the pursuit of knowledge, and they have shown that in our culture. For that reason (or perhaps others), they are afraid to admit belief. This however, is not reasonable, for belief is not inherently fallacious. Rather, prideful belief is fallacious.
So when I propose that we stick to a more traditional understanding of truth and knowledge with the addition of humility, what I am proposing is accepting that axioms are beliefs, and we must be humble enough to admit that fact. There is nothing invalid or illogical about stating a belief. What is illogical, is holding to a belief when evidence or proof has shown said belief to be wrong. That is clinging to belief in a prideful way, not being humble enough to admit fault or have an open mind.
This solution to the contention of axioms is the most organic in my opinion. It feels intuitive, it feels familiar, and it really makes sense with no contradictions awaiting. For instance, I could say that I know B because it logically deduces from A. And then to say I know A axiomatically (i.e to say I believe A to be true because I have been given no reason to think otherwise) has no flaw unless I am unwilling to admit that I really just believe A- I don’t know it in any provable sense. Thus, I believe we can create a rational system for obtaining knowledge in an intuitive and open-minded way, if we only accept belief as okay and humility as necessary. To provide an example of the logical deduction from A to B with A just being belief, consider the following situation: My axiom A will be that if two statements contradict, they both cannot be true. My deduction B is that “2 is even” and “2 is not even” are two statements in which both cannot be true. I know B is true because it deduces from A; however, I don’t really have any proof for A. I believe A to be a true law of logic because it works and I’ve been given no reason to think otherwise. Therefore, my knowledge of B being true is completely dependent upon my belief that A is true. This is an easy example of how this rational system works, as it helps us see that even the most basic truths are dependent upon a logical law that is not proven, just accepted because it hasn’t failed us yet. Moreover, this rational system that I developed through the rationale and exposure to logic brought about by Mathematics is precisely what increased my faith.
When I realized that everything I think is true—EVERYTHING— is nothing more than a deduction from belief, I realized that faith is essential for any system of knowledge. Realizing this caused me to not be afraid of saying and admitting that I believed in God or that I believed the Bible. After all, I could honestly do nothing more than say “I believe…” about any given topic! This acceptance of belief as necessary opened the door to two things: a more open-minded search for knowledge and a deeper search for reasons why my belief in God was not unfounded. That is, I began to use other beliefs that most accept as true to deduce or infer that the Bible is indeed reliable and true. This process was a complex one and not at all the focus of this writing, but without Mathematics, the scrutiny and rationale required in that process would have been much more difficult. Furthermore, without Mathematics, I would still be afraid to admit belief. Thus, Mathematics played an essential role in developing not only a new framework for growing in knowledge, but in developing a greater understanding of how knowledge is founded upon faith in some object or statement.
The big so-what I want all to get is that beliefs are not inherently illogical, and Mathematics showed me that. If one will simply allow beliefs and remain humble about the said acceptance of beliefs, one can explore different areas of knowledge and grow in extraordinary ways.