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Politics : Politics for Pros- moderated -- Ignore unavailable to you. Want to Upgrade?

To: LindyBill who wrote (123700)	7/7/2005 12:41:00 AM
From: neolib	Read Replies (1) \| Respond to of 794032

They must be attackable in science. I’m saying this cautiously, but IMHO that is entirely incorrect. Consider Euclidean geometry, surely the widest known axiomatic system. The five starting axioms are simply guessed. What is built from them will be different depending on what those axioms are. So if one says two parallel lines never intersect, we get Euclidean geometry. Change that axiom to allow parallel lines to intersect and one gets Riemannian (sp??) geometry. You might argue the one is intuitive while the other is not, but that is beside the point. If any axiom can be logically built from other axioms, it can be eliminated, reducing the required number of axioms. That, BTW was also a long running mathematical debate wrt to the 5 axioms of Euclidean geometry, over many years (hundreds or even 1K+??) some thought that four axioms are all that was needed. IIRC somebody solved that (when I forget) So if you are appealing to science to validate an axiom, just eliminate the axiom and substitute the line of scientific argument you claim validates the axiom. Keep doing this until you have a minimal set of axioms. Those are then outside the source of logical knowledge. A guy named Godel (sp?) had quite a bit to say on this subject IIRC.