This section is obviously incomplete, but when it is complete it will talk about how Ockham's Razor - the notion that when presented with a choice of axioms or laws, or explanations, it is wise to choose the one that is the simplest, the one that requires the least fixing up with new axioms to make them consistent. Note very carefully that I said wise, not correct. Ockham's Razor can be wrong, and shave the true away as easily as the false.
Ockham's Razor is at its best when it is perceived of, and applied as, an esthetic principle instead of an axiom. As such, it can be a powerful tool to use in our search for an axiom set we can wisely live with. When presented with two competing alternative axiom sets, knowing that we cannot prove either one right or wrong by definition, we can nevertheless choose to believe the one that is simpler, more consistent, sparser, because it is prettier.
As such, Ockham's Razor is an essential component of both natural science and physics and of latter day scientific pseudophilosophies like Logical Positivism. After all, if you add enough exceptions, if you create a complex enough reality, you can explain anything in a way no Logical Positivist can ever empirically refute.
Those complex realities (the ``it's God's will'' variety of explanation for whatever you like) can only be rejected on esthetic ground. Would God create a Universe that required the breaking of its own laws in order for miracles to occur? Well, maybe (Berkeley would say so as the Church requires miracles outside of natural law) but then again, maybe not - C. S. Lewis seemed to think not as he put God's word's in Aslan's mouth declaring that He would not break the laws that He made.
Somehow Ockham's Razor ends up being as important as the axiom of causality in determining what we believe in Physics, Chemistry, and many empirical sciences. It isn't enough to construct a theory, we need to construct a beautiful theory, one that is simple and yet powerful. Why should this be? Why should nature be simple? We can't even say why nature should be at all and now we're imposing a constraint of simpliticity and esthetic beauty on it?
Yes we are, and no we can't prove why we do it (and note that it can lead us to make mistakes!) but still, we do it anyway and are proud of it. Or we should be proud of it. If you are a human who believes in the Axioms of Religion (for all of their apparent flaws) it is likely because of an esthetic principle - the beauty and simplicity of a Universe under God. And it is beautiful, and simple, to so believe. The problem comes when locking into the rest of the Standard Axioms of religion.
What, precisely, about Hell is esthetic? Or simple? Note that when I even try to pick a fight with religion, it is best framed in these very terms - the concept of Hell isn't wrong because I can prove it wrong, it isn't wrong because it couldn't be right (if we live in a Universe with an all powerful, all sadistic God), it is wrong because I find the notion of an Omnipotent deity casting a living soul into a state of eternal pain and torture ugly! Ugly and inconsistent. To make it consistent, still more properties have be added to to justify this sort of incredible behavior (that we would consider to be outright Evil were we to apply a similar standard to, say, our own children) make it more Ugly still.
Ockham's Razor is a lovely meta-axiom, but as you can see we are already extending it beyond its immediate purvue. Somehow the term esthetics and an associated judgement has crept into the discussion. It seems sensible to go beyond the Razor and craft an up-front meta-axiom associated with esthetics itself.