You might be tempted to leave out concise (because completeness is a tempting thing to have!), but then, as Godel proved, you literally need an infinite number of axioms. If you leave out consistent, you can prove that 0 = 1, so that's not very useful. Godel's incompleteness theorem in a nutshell: I don't understand Gödel's Incompleteness Theorem so I've stopped at that. Anyho, I made-up the above dialogue between a layman and a physicist to keep my wife from dozing-off while I waxed on and on about cats and strings. Often, the beauty has proved to be a reliable guide to Reality. String Theory is beautiful (so I hear, unfortunately, the math is beyond me). To me, 'by definition' is equivalent to a big acknowledgment - atleast among peers - that is not based on a proven fact. Consider the question: Are the Strings in String Theory fundamental? By definition Strings are fundamental.
In many ways, it surely is (and personally for me, to acknowledge this is to make peace with myself). So, I re-read Physicist Edward Witten's beautiful article on String Theory yesterday night and kept thinking about what Wittgenstein said: Knowledge is in the end based on acknowledgment. Gödel's Incompleteness Theorem has seen to that. Physicist: He said it before, not anymore. I think he said we would know Everything. I don't think he meant to say we know a lot. Hawking says a Theory of Everything is just around the corner. Layman: I suppose this is your personal view. A Theory of Everything is a grand way of saying we know a lot. We can never be sure if a theory explains everything in the Universe because we don't and can't possibly know all that the Universe is made of. Physicist: Well, a Theory of Everything is a linguistic construct, not a physical one. Everything is provisional? There will never be a Theory of Everything? Layman: Nothing is really fundamental then.
Scientific progress is this continuous illumination of newer vistas, the lighting of hidden parts of an inexhaustibly large picture. The earlier theories are still true but they are now a small part of a bigger picture. New models of reality that change our conception fundamentally are found and we begin again. Sometimes, we have breakthroughs: times such as when Newton published his Principia, when Einstein published his Theory of Gravitation or when Quantum Mechanical Laws were published. Physicist: You see, physics usually advances gradually, building upon our earlier understanding. Layman: Like how sometime back protons were fundamental, and then how quarks were fundamental? Physicist: Well, they are not made of anything. Layman: What are the strings in String Theory made of?
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