Why Axioms?

I spelled out a little why I chose the word belief in the title of this blog, but I didn't explain why I chose the word axioms. An axiom in mathematics is a proposition that is assumed to be true and need not be proven. They are needed in any formal system of mathematics because without some solid foundation of accepted truth, it wouldn't be possible to prove anything.

At first glance there is something a little troubling with the need for axioms. What if a mathematical system chooses an axiom that isn't really true? In practice, this isn't a problem, because mathematics requires that for any given mathematical theory the set of axioms be consistent. If a set of axioms leads to contradictions, then the set of axioms is rejected as useless, and a simpler and consistent set of axioms is used instead.

I like the concept of axioms of belief. Beliefs we hold due to faith are in some ways axioms of belief. It's ok, even necessary, to have axioms of belief, i.e to have faith in certain fundamental ideas. But I believe that problems develop when faiths are not axiomatic. For an axiom to be useful, it must be simple and consistent with the other axioms we hold true. So, for example, one core belief of biblical fundamentalists is that the entire Bible is literally true. This belief is in some sense very simple, but it implies that every simple statement made by the Bible must be treated as an axiomatic truth. This would be fine if each of the statements of the Bible were simple, and if no statement of the Bible contradicted any other statement of the Bible, but this clearly isn't the case. For this reason, the statement the entire Bible is literally true is not an axiom.

Now, the Bible makes various claims that could be axioms of belief, but to my knowledge believers in the Bible never make an attempt to sort out the claims of the Bible into any kind of system resembling an axiomatic one. Religious believers often demand respect for their beliefs. I can't respect the belief that the entire Bible is literally true because it is really a set of beliefs that are not self-consistent, and because many of the beliefs are not consistent with objective reality. But there are some people who hold beliefs based on the Bible who are willing to acknowledge that the Bible is not literally true, but is instead allegorical. This admission is enough to make it possible (in theory) for me to respect their beliefs, or at least much of their beliefs. I think it would be really cool if some liberal Christians would attempt to define a consistent set of axioms of their beliefs. I have a sense that there might be a core set of beliefs that I could respect. But ironically, I think any such set of axiomatic Christian beliefs would be rejected by most Christians.