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> The way to avoid all the contradictions is to weaken the underlying logic Pet peeve: I would argue that constructive logic is stronger, in the sense that it
by erichocean 11y ago
> The way to avoid all the contradictions is to weaken the underlying logic
Pet peeve: I would argue that constructive logic is stronger, in the sense that it allows more reliable (read: usable in the real world) results than classic logic allows. But that's a value judgement, and there's no definitive right answer here.
Totally agree Re: Infinitesimals. Dual numbers[0] are crazy useful in computer science (c.f. Google's Ceres Solver[1]).
[0] https://en.wikipedia.org/wiki/Dual_number https://en.wikipedia.org/wiki/Dual_number
[1] http://ceres-solver.org/ http://ceres-solver.org/
- mathgenius 11y agoI agree with you, there's going to be more shades of grey using intuitionistic logic. I guess I was taking the point of view of the Jesuits! So actually I understand about Dual numbers, but from what I see this is not the same thing as smooth infinitesimal analysis (there's no playing around with the logic.) I feel like if we scratch this a bit more we are going to understand what Grothendieck was on about with topos theory [1]. [1] http://www.oliviacaramello.com/Unification/Unification.htm http://www.oliviacaramello.com/Unification/Unification.htm