zerologyMay 11

I'm looking for an intro into set theory for a very non mathematical person. Everything I find uses numbers, sets of sets of sets, and such things.

Did the mathematicians loose their marbles? :-)

I mean, explaining sets using marbles should be an easy way to introduce the concepts. Only if those are understood, it may be sensible to go to Hilberts hotel, Russells paradox, and maybe, just maybe to Cantors diagonal argument.

#math #SetTheory #marbles

Suggestions welcome.

Show threadCardinal ReinhardtMay 11
@zerology Hilbert's hotel and Cantor's diagonal argument can be explained without sets (in the formal sense) at all! The first is a useful thought experiment to explore how infinity behaves differently from finite sizes. The second is a proof that "there is no one to one correspondence between the natural numbers and real numbers", and you can explain why one to one correspondence is a good notion of size without sets. (But you need a good notion of "real number" - is "decimal expansion" enough?
Show threadCardinal ReinhardtMay 11

@zerology so I'd ask what is special about set theory itself that you want to get across. In a first course you'd show how various mathematical objects can be formalised as sets, but this is likely not what you want!

So maybe stick with relatively informal explanations that don't really talk about sets?

Show threadzerology

@cardinal_reinhardt This is right, yes.

I can‘t answer this. I try to suggest an intro into the language of set theory, as background information for a video about philosophy of the infinite in a language that I myself am still learning. So I can’t even watch the video to tell what is needed.

I infer that my help request isn’t well formed yet.

Thank you for the answer nevertheless :)

May 11 at 2:07pmWeb
Show threadCardinal ReinhardtMay 11

@zerology I may just not be best equipped to answer - I'm too deep in the cult already!

An introduction to formal languages might be good if you want to convey the linguistic and formal aspects. That can be accomplished with a small example like group theory or Peano arithmetic.

Show threadzerologyMay 11

@cardinal_reinhardt I’ll try. The person who asked me just started philosophy at university, and has no math background. So I kind of try to point to stuff to read/watch for a start.

I’ll try my best :)

Show threadCardinal ReinhardtMay 11

@zerology if they're starting philosophy then they'll likely take a course in formal logic soon. This tends to be broader than the first order logic used in mathematics, but familiarity with one helps with the other. Both group theory and Peano arithmetic are good ways to explore first order logic imo.

Unfortunately I learnt all of this on a maths degree course so I don't know about videos and such. Maybe it helps still... Hopefully!

Show threadzerologyMay 11

@cardinal_reinhardt Logic, she will need that, yes. But Peano and groups - I have doubts. There are people who are who are very far from a math way of thinking.

I’ll try my best to drag her in :-)

Show threadCardinal ReinhardtMay 11
@zerology you don't need either to understand logic for philosophy, that's certainly true
Show threadzerologyMay 11
@cardinal_reinhardt :-)