Tue, Jan. 25th, 2005, 04:19 pm
I've often heard/seen set theory considered the most fundamental branch of mathematics, insofar as most (all?) other mathematical subjects can be described in set-theoretic language.
It doesn't take a very large leap of intuition to see that many academic disciplines other than mathematics could be cast in terms of set theory, given enough time and effort.
Do you believe a functional, philosophical paradigm could be constructed entirely in set-theoretic terms?
Tue, Jan. 25th, 2005 10:45 pm (UTC)
Define "functional", "philosophical", and "paradigm" and I'll let you know.
I'm prone to say that no given paradigm can both be functional and philosophical -- particulalry not the functional ones. :P
Tue, Jan. 25th, 2005 11:21 pm (UTC)
Well, if you want to skew it, Formalists tried to make it into a philosophy, at least of what mathematics is. There are always alot of problems (Incompleteness Thoerem) but it is still mostly functional.
However, due to the inductive nature of most sciences, they can only use set theory/mathematics to try to describe their phenomenom. So many sciences do benefit from sets (Computer Science to a large degree) but I am not to sure they could be cast in terms of set thoery, except that they all use it's logical consequences.
Wed, Jan. 26th, 2005 01:47 am (UTC)
The problem with basing anything about mathematics is that mathematics isn't necessarily about anything outside of itself. This is rather odd given that mathematics is extremely useful in describing much of the world. Thing is, though, that many of the things we want to describe, or at least talk about, don't arise solely from mathematical methods.
Wed, Jan. 26th, 2005 03:31 am (UTC)
I've always considered it a great and impressive miracle that mathematics is useful. There is absolutely *no* purely logical reason for mathematics to apply to reality (or vice versa). I tried to explain this to people over in another community, and they all said, "But it *arose* through real, physical problems!" Well, yes, but it has long since transcended them, and if the 'real, physical problems' all went away, mathematics would still be true.
It's truly incredible.
Wed, Jan. 26th, 2005 06:14 am (UTC)
I would have to say no.
On one hand, in any real-life-based field (almost anything but math), there is almost no such thing as a "true" or "false" statement, the way there is in math. The world isn't based on Zermelo-Fraenkel, it's based on string theory or something like that.
On the other hand, you could make some mathematical definitions that approximate real-world things, and theorems based on them would also approximate real-world things, more or less. Unexpected results would come up, because of the places where the definitions could not match the real world. Academians do just fine with natural language and logic.
Wed, Jan. 26th, 2005 06:15 am (UTC)
I guess those are the same hand.
Thu, Aug. 23rd, 2007 02:56 am (UTC)
yes, the latin alphabet.