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"Average person discovers infinitely many infinities per year" factoid is actually just a statistical error. The average person discovers 0 infinities per year. Cantor Georg, who introduced the diagonal argument and discovered infinitely many infinities in 1891 alone, is an outlier and cannot be counted.
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the idea that philosophy and mathematics are polar opposites of eachother is so wrong if you have studied both. they are so similar that my maths professor and my philosophy professor argue daily which is a subset of the other. it really is beutiful doing both, it feels like you are applying mathmatical thinking to the world.
this is why famous mathmaticians also did philosophy (eg. descartes)
the first rule of fight club is that two fight clubs are equal if they have the same members
would the set of all infinite ordinals less than why did it delete the epsilon εbut anyway it's epsilon-0 be considered the omegavers- NO NO NEVERMIND POST CANCELLED POST CANCELLED NEVER FUCKING MIND
To any set theory wizards following me: What's the least inconvenient way to add a hierarchy of universes to set theory, similar to the way dependent type theory does it? Specifically, I always felt that "resolving" Russels paradox by introducing proper classes and then only allowing quantification over sets was deeply unsatisfying, since on a philosophical level, this just pushes the issue up one step - I think it is intuitively clear that the "collection of all proper classes" should still be a valid object that exists, even if it can't be a proper class itself. I assume what I want is hyperclasses, but I'm having a real hard time finding basically any writing on them, and from what little I do find even these seem to usually just be considered as "collections of classes", and not a full hierarchy where an (n+1)-class is a collection of (n)-classes.... Are Grothendieck Universes (and/or Tarski Universes) already enough to solve this issue, even though they are formally just classified as sets? Also how come this isn't talked about more? I'd be fine switching out ZFC for some version of NBG or MK or even ETCS for this, but I do think that doing all of my future math in MLTT or HOTT because of this seems a bit unreasonable for now ^^
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countability
Mathematical platonists are so funny to me because they will say shit like "mathematics has this beautiful elegant design" meanwhile you get to the foundations and find out you have those "beautiful elegant statements" that are independent of ZF (or even ZFC), are not compatible with each other and each of them implies some insane monstrosity that shouldn't ever be true.
