5 ms·

> I think Cantor’s set theory and everything that flows from it is a bunch of hokum. Why?

• jacobolus 8y ago
  In my opinion it is entirely speculative, built on largely unconvincing foundations (involving a lot of hand waving and circular reasoning when you start poking at them) whose implications are often absurd. But it doesn’t really matter what I think. This is not a fight I care about. It’s like arguing with Buddhists about the nature of suffering or something. YMMV.
  • bordercases 8y ago
    Are you more comfortable with a different set of foundations? Intuitionistic? Finitistic or non-completable infinities?
    • antidesitter 8y ago
      Can a statement like Goodstein's theorem (which is about finite objects) be proven by finitist mathematics? It cannot be proven by Peano arithmetic, which is bi-interpretable with ZFC with the axiom of infinity replaced by its negation [1], or any weaker theory. [1] https://math.stackexchange.com/questions/315399/how-does-zfc-infinitythere-is-no-infinite-set-compare-with-pa https://math.stackexchange.com/questions/315399/how-does-zfc...
  • throwawaymath 8y ago
    Could you expand on this a little? Which reasoning do you find to be circular and which implications to you find to be absurd? If you explain what you an issue with others may be able to help you understand it more clearly.
    • deleted 8y ago
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  • antidesitter 8y ago
    What does "speculative" and "unconvincing" mean, in the context of a mathematical theory? What do you find hand-wavy or circular about it? Can you specify which absurd implications you're referring to? Not trying to argue, just genuinely curious.
    • deleted 8y ago
      [deleted]