PHILOS 146 Lecture Notes - Lecture 25: Real Number, Law Of Excluded Middle, Finitism
Document Summary
Psychological: math is based on an a priori intuition of time. Specifically the splitting of a moment of time (in two). In infinite sets, f may not be decidable. If you go intuitionistic, you lose a lot of math. Intuitionist: in order to state a disjunction, you must be able to prove one of the two disjuncts. Or at least a method: classical math intuition: things are out there independent of us, so an assertion of a fact must hold or not. For intuitionist: things are constructed, the end product of a mathematical activity up to a certain point. If we have a rule that allows us to compute at each step what the sequence will be like. 1/(2^n: weak counterexamples, r = 0 or r =/= 0 a. i. If that result were to hold intuitionistically you be able to decide things that are known to be not known. Possible only after logic is formalized: poincare objection b. i.
