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Topic:
o:^>___? Dan Christensen wins 2017 Nobel prize in logic for elucidation of what is distinct and not distinct
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Last Post:
Oct 4, 2017 4:01 AM



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Re: o:^>___? Dan Christensen wins 2017 Nobel prize in logic for elucidation of what is distinct and not distinct
Posted:
Oct 4, 2017 4:01 AM


On Wednesday, October 4, 2017 at 8:33:48 AM UTC+2, Archimedes Plutonium wrote:
"The axioms that are in need of fixing is the axiom that between any two points lies a third new point." (AP)
"... should be 'between and any two DISTINCT points'." (Dan)
Yes, though this might be considered a question of convention. (Moreover the context may be of importance here too.)
"And yet Mr Plutonium is right." (Parcival)
No, he isn't. Or at least only with certain "provisions".
> Two points are distinct (else they would be one) ...
Yes, if I actually consider *two* points, they are necessarilly distinct.
For example, when dealing with a set M = {p1, p2} with card(M) = 2.
But "For any two points ..." is a mathematical idiom, not necessarly implying that the "points" are distinct. Sometimes we can even find the following: "For any two (not necessarilly distinct) points ..."
Hence if we want to make things clear it's reather "helpful" (if not mandatory) TO POINT OUT that we actually consider two DISTINCT points.
It's a matter of clearity and prescision (if not of necessity).



