/lit/ - Literature

>>11769018
>100% chance god don't real; 0% god do real
>100% * teeny tiny reward = teeny tiny reward
>0% * infinite reward = zero reward
>expected outcome of not believing = teeny tiny reward
>expected outcome of believing = zero reward
pascal btfo

>>11418567
But there's no a priori reason we couldn't just write "Parchment N" on Parchment N. The student just arbitrarily said we can't, when, in fact, we can.

It's a mangled version of "the set of all sets that do not contain themselves," but since sheets of paper aren't abstract objects, the same rules don't apply.

>>11370169
>Would this also be (~S), the negation of set S in theory?

Depending on what kind of notation you use, yeah. If we say that ~S is the set of all things not in S (that is: the set of all things that don't exist), then ~T is in ~S. Sets are constructed by defining them, so you can have ~S be whatever you want, as long as you're consistent throughout the paper/argument/discussion/etc.

It's worth remembering that you can't really negate a set (or a number, or an object, or anything "noun-ish"). We negate truth values (e.g. "not true" is "false") or statements which yield truth values (e.g. "not greater than" is "less than or equal to"), but there's a different term for getting the opposite of something.

In the example we're working with, ~S, we've actually negated the "predicate" of S, or the statement that determines membership in S. We've gone from "Thing X exists" to "Thing X does not exist."

If this is the kind of thing you find interesting, I'd recommend a discrete mathematics textbook. It'll introduce you to several flavors of logic, most of which have immediate practical applications.

>Or does it have a quality that makes it's 'S-ness' exist outside all things?

This depends on who you ask. There's 2 main schools of thought — the mathematical realists, who believe mathematical objects "exist" in some sense, and the anti-realists, who think of math more like a useful story we tell ourselves. I lean more towards the anti-realist position, because people often literally "make new math up," but a realist would counter by saying that they're actually "discovering" that math.

The realist would say that because S exists, the fact that an object is in S is intrinsic to it, in the same way that location in space is.

The anti-realist would say that S is just a way to describe lots of things at once, and a thing is only "in" S because we say so.

I wouldn't worry too much about this question —it's the kind of thing that can't really be solved, or even argued about all that convincingly. What's more interesting to most analytics are questions like the one I responded to, where a bit of simple math lets us demonstrate something controversial in an uncontroversial way.

Another interesting example of the power of simple math (this time in moral philosophy) is illustrated here: https://www.youtube.com/watch?v=vqBl50TREHU..

>>11151203
>start reading book
>"With an introduction by Bertrand Russel"

>>11151339
>not "Phillip K's Dick"
For shame, anon.