EXPLAIN SET THEORY TO ME OR I'LL FUCKING KILL YOU! DON'T DUMB IT DOWN INTO SOME VAGUE SHIT! EXPLAIN SET THEORY TO ME RIGHT NOW OR I'LL LITERALLY FUCKING KILL YOU! WHAT THE FUCK IS A SET AND WHY ARE THEY CONSIDERED TO BE LOGICALLY PRIMARY ENTITIES CAPABLE OF SUSTAINING A LOGICAL FOUNDATIONALISM? WHAT THE FUCK ARE VON NEUMANN SETS? DON'T DUMB IT DOWN OR I'LL FUCKING KILL YOU.
EXPLAIN SET THEORY TO ME OR I'LL FUCKING KILL YOU! DON'T DUMB IT DOWN INTO SOME VAGUE SHIT! EXPLAIN SET THEORY TO ME...
Kayden White
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Julian Roberts
Bump
Aiden Hernandez
Watch this.
So there exist objects, presumably. And these objects can be put into collections. These collections are sets. Naively.
Are you still with me? Hold on, things are going to get crazy.
So we also have nothing. Now, a set might be a collection of objects. But it could also contain nothing. It is the set with nothing in it.
{ }.
Nolan Cruz
Sorry, I meant 'union' not intersect. I should also note that 0 ∪ {0} = {0} precisely because the set 0 contains nothing, so its union with anything is just that other thing.
Adrian Cook
Pretty neat desu. I still like literature a lot more but at one point I took logic for fun. Don't see a point anymore though. It's really helped me in my writing, I will say that.
Ian Gonzalez
>when the schroeder-berenstein hits
Isaac Lewis
i am not being pedantic or hostile i swear to god, i genuinely want to understand the epistemology of logicists
>So there exist objects
is this just meant heuristically? it's not a naive realism or platonist realism, right? this is basically shorthand for, "Conventionally, logic needs to refer to 'entities' of some kind." but then: doesn't that convention itself run deeper (i.e., require axiological justification at a level PRIOR to), the axioms of set theory? is "there exist objects" just something taken on faith and understood linguistically & non-logically, here?
>these objects can be put into collections.
similar question here: is this shorthand for, "A convenient way to talk and think about these things, linguistically and conventionally, and therefore pre-logically, is in terms of 'sets'"?
>[the actual derivation of the integers, etc., from the ground-set of nothing]
this is interesting, but unless it's justified post hoc by its (heuristic) utility in allowing for mathematical formalism (this is the case, right?), isn't it arbitrary again? this may be really naive, but: what is the ontological/epistemological status of "nothing" or "the set" or "the set of nothing" in this case? again, are these just linguistic/conventional entities we take on faith as being decently well agreed upon prior to starting the logic proper?
or is there some appeal to self-evidence and intuitive certainty built into the foundations of set theory?
Alexander Reed
You're mostly right.
en.wikipedia.org
"To a non-mathematician it often comes as a surprise that it is impossible to define explicitly all the terms which are used. This is not a superficial problem but lies at the root of all knowledge; it is necessary to begin somewhere, and to make progress one must clearly state those elements and relations which are undefined and those properties which are taken for granted."
Luis Turner
This.
Frege's work explores further consequences logic and theory, though. Cf. "Sense and denotation", for example. Of course this section of his oeuvre has been discarded by mathematicians, but it's still relevant for analytic philosophy of language (thanks, in part, to the developments done by Kripke and others).
Sorry for the shitty English. Great thread and interactions!
Jayden Rogers
are mathematicians and analytic philosophers mostly self-aware about this?
it's always been intuitively difficult for me to grasp how anyone ever thought OTHERWISE than this. to me, wittgensteinian and quinean things about the fundamental undecidability of all definitions/meanings, the irreducible "embeddedness" of all logical arguments in pre-axiomatic, taken-for-granted "grammar" (here "primitive notions"), the fact that all logical "proofs" are universally true only insofar as some individual, contingent, finite mathematician guy goes "Yeah, seems true to me" -- all this seems like it would be the more basic assumption, the starting point. any kind of strong, platonist logicism seems like it would come in much later, not be an intuitive assumption.
not that i'm unsympathetic to the ideal of completely clarified terms in a perfectly leibnizian universal language, locking together in harmony. but it seems to me that anyone interested in such a thing would have to begin pretty self-consciously with a rather strong platonism (actually various esoterics do this - fabre d'olivet tried to do it with hebrew).
so i often can't tell whether math/analytic philosophy people take this shit for granted, or whether they are outstandingly naive/platonic realists without even noticing it. it often seems like the most exaggerated mathematical formalism is underpinned by a more basic assumption of intuitionism or realism.