A rather wonderful Introduction to the concept of Axioms. Well worth a read. And all credit to Robert G. Brown, of Duke University Physics Department, who wrote it.

Humankind has, from the earliest glimmerings of sentience on, endeavored to answer certain questions. What time is dinner? What’s for dinner? Who caught dinner?

Once these questions were being answered satisfactorily and moderately regularly for at least a fraction of the proto-human population, we can only imagine that in that warm lull that follows a full belly around a fire beneath the stars, questioning thoughts turned to less important, but nevertheless intriguing, issues. I wonder what those little bitty lights are up there? I wonder how the fire comes out of chunks of cold rock or rubbing sticks? I wonder if I’ll get dinner tomorrow, or turn out to be dinner for something else?

Eventually, humankind developed rudimentary societies, and for the first time at least the ruling class of those societies experienced the luxury of not having enough to do. Others in those societies didn’t have that luxury but wanted to. Together they conspired to extend these questions still further, so that they could spend their overabundance of leisure time working hard trying to answer questions that had little to do, at first glance, with dinner.

[…]

We feel like all questions should have answers, but when we look at them closely we find that certain questions, of certain kinds, don’t. Here is one:

– Why should all questions (including this one) have answers?

This is the kind of obnoxious question that parents eventually learn to answer (like all the rest of the related questions and question chains) with the simple word “Because.” – which is, as any small child rapidly learns, code for “this question cannot be answered”.

“Because.” as an answer to a “big” question often means that it isn’t a question at all. At least, not one that we can answer in the same way that we can give somebody the time upon request.

Such a “question” calls into question – sorry – the foundation of what we know, what it means to ask questions at all, and how we should cognitively interpret the answers (such as they are, if they exist).

All of which leads us, by a roundabout way, to consider the issue of axioms.