3 ms·
He is obviously a well trained mathematician so reading his pieces (of which there are many) is akin to watching a tsunami come to shore---you cannot look away
by zzless 8y ago
He is obviously a well trained mathematician so reading his pieces (of which there are many) is akin to watching a tsunami come to shore---you cannot look away yet you know that this is a tragedy unfolding.
This said, his complaints about set theory would have been (probably) more convincing if he stated the axioms correctly. The Infinite Set axiom does not simply say that some nebulous infinite set exists it states the existence of a set with some very specific properties. His complaints about the undefined nature of a 'property' are also not above criticism: GB theory (equivalent to ZF) eliminates it completely.
- gchpaco 8y agoIn general his complaints regarding logic are incoherent. A function is not a messy weird object in mathematics; it's a possibly infinite set of ordered pairs where there are no duplicates of the first element of the ordered pair. That's it all it is, formally. Or "class" is a concept that has highly specific meaning in NBG theory—in ZFC it's not a formal distinction and so there's a transformation that must be obeyed where "x \in Class" means "{ x | x satisfies class definition}"; which due to Foundation must be the subset of some other, preexisting, class (and thus is Russell's paradox defeated). Almost all of these things exist and are present and are extremely well defined in the theory, he just doesn't like them for some reason.