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moving finger said:a world is not the same as a geometry.

a Euclidean geometry is a geometry. it is not a "world".

a Euclidean geometry may be a self-consistent geometry, but it does not follow from this that a world based on a Euclidean geometry is a self-consistent world.

MF

Then please, explain to me what you mean by the term "world." You've given one instance of what a world is not, namely a geometry. I'm not sure I agree with this, but that's not relevant. What exactly, then, is this world you refer to? I can't but help think of it as the geometry of the universe. I guess this is just where mathematicians differ from everyone else. For us, so often, the map is the territory. It does not merely describe the thing, it is the thing. At any rate, what is "world?" Sorry about my digression there.