i wrote:In maths everything is derived from a set of laws (called axioms) which are just assumed to be true.

I think it would be more accurate to say that axioms (or "postulates") are "statements which seem self-evident but which cannot be proven". They become the starting point for mathematical proofs, but with the clear acknowledgement that should one of them be disproven, all proof using the disproven axiom will become invalid.

An example would be, "For any give point A and point B, where A and B are not the same point, there exists between then another point, C." This, then, can be used to "prove" that between any two points, there exists an infinite number of points.

Not all axioms are universally assume to be true. Euclid's parallel postulate is the most common example of an "axiom" that is not universally assumed to be true. It is a postulate of great consequence. Much of our engineering relies on theorems proved using this postulate.

For instance, everyone "knows" that the sum of all the angles in a triangle is exactly 180. However, no one has ever managed to prove this without Euclid's PP.

Thus, there are two basic types of geometry. "Euclidean" geometry uses Euclid's PP as a postulate. "Non-Euclidean" geometry basically says, "Okay, let's propose alternatives to Euclid's postulates, and see what we get."

In fact, Einstein's "General Relativity" works much better in non-Euclidean systems because when you start talking about "curvature of space", Euclid's systems get thrown all out of whack.

The Wikki articles on

Euclidean geometry and

Non-Euclidean geometry explain it pretty well. And I can only remember so much from my Non-Euclidean geometry class 20 years ago.

Oh ... I have no idea if Lewis may have addressed this concept more specifically than what I read in "Abolition of Man".