Thursday, November 8, 2007

(x)(Px⊃Sx)



It occurred to me today that we should have a formal proof that shows that everyone is indeed a Sith.

Notes:
The premises are that 1. All people deal in absolutes and 2. only a Sith deals in absolutes (if x deals in absolutes, then x is a Sith). After that is a little busy work, then the assumption of a person. Given that there is a person, that person must deal in absolutes, and must therefore be a Sith.

Premise 1 isn't exactly elegant, and I'm open to suggestions for better ones.

118 comments:

Kylebrown said...

All people make absolute statements at least once in their lives?

... as I just did....

MA17 said...

I just wonder if there's a way to actually prove that, or if we just have to hope that nobody denies it.

Also, I guess I could have used Hypothetical Syllogism in one step instead of two steps using Modus Ponens. Fuck HS, however.

Mike Lewis said...

since i am a proud respient of a D- in logic class in college i might not be the best person to talk about this...
but

i seem to remember something about valid v. sound?

like the proof is valid, but it is not sound.

or something.

MA17 said...

I think you're right, and probably the thing that'll make it sound is a clear indication that all people deal in absolutes.

Plus, I've been reading up on this topic (god help me) and came across a bit written by Orson Scott Card.

"The new movie itself asserts a kind of equivalence. When the evil Palpatine says, "Good is a point of view--the Sith and the Jedi are almost the same," we can dismiss this moral relativism as part of the deception of the dark side.

But in a pivotal scene, Obi-Wan says what amounts to the same thing: "Only a Sith deals in absolutes."

Isn't that odd? The only thing both sides agree on is that people who believe in absolute good and evil are bad!

I suspect that Lucas realized, after writing "Good is a point of view," that all his friends actually believed that. So he had to make it clear that moral relativism was the right way after all-so he had Obi-Wan say that absolutism was a Sith thing, even though in the actual story, the best of the Jedis show an unbending commitment to absolute Good.

It's a terrible thing, I suppose, for a writer to invent a religion and then discover that he and all his friends are on the wrong side of it."


Doesn't really help what we're trying to prove, but I think he's got the right idea about where the hell that line even came from.

MA17 said...

This thread on theforce.net is a pretty good and pretty awful read.

_J_ said...

AH!

I, like Mikey, took Rogic with with a god-damned Chinese woman who taught the class in Engish. Unlike Mikey, however, I then took another actual logic class.

You're making all of those words come back into my head.

MA17 said...

And for a definition of "deal": the OED puts the current definition somewhere around the word we'd use for handing out cards; the verb itself relating to dividing something, which works, I think, in the Sith / Absolutes context.

The definition I think works best, though is, "14. To have to do with (a thing) in any way; to busy or occupy oneself, to concern oneself with." This sense seems a bit more inclusive, since it can apply to people who have anything to do with absolutes.

_J_ said...

If you read the first two entries on the blog, ever, you can see Mikey and I tackling these topics with apathy and derision.

_J_ said...

The problem is that it may be the case that (makes absolutes statements) ≠ (deals in absolutes)

"It's a trap" is an absolute statement. But to "deal" in absolutes may be something entirely different.

I don't think this is the case, though.

To proclaim that something is a trap is to invoke the notion of many absolutes. Saying "some thing is a trap" requries that there be "trap", "some thing" and "is" in the form of "being".

In other words, to identify an object as a "trap" one must have an absolute notion of trapness and identify the trap as exhibiting that aspect of trapness.

If that whole thing is rogical then I think we're fine and the blog name can stay as it is.

Mike Lewis said...

for the record, i didnt take another logic class because i didnt need to / want to / have to.

also this is the nerdiest ever have ever gotten on EoiaA

_J_ said...

I just wonder if there's a way to actually prove that, or if we just have to hope that nobody denies it.

I think to do this we must use The Square Of OPPOSITION!

And then we have to talk about existential import.

And now I remember why I hate this bullshit as opposed to other types of bullshit on which I thrive. Existential mother-fucking Import.

MA17 said...

To Jay's 10:17 comment:

But doesn't that just prove that Admiral Ackbar is a Sith, and not that everyone is a Sith?

I totally agree with the assertion that using an absolute statement is enough to justify that person's "dealing in absolutes", given the definition of "deal" in the OED. But the problem as I see it is that we don't have a way to show that, without exception, all people use absolute statements. If we are presented with someone who is unable to communicate, we either have to assume that person uses absolute statements in some internal wordless form, that the person is not actually a person, or we must conclude that person is not a Sith.

Maybe a way around that is to use an implied absolute that we can show everyone to hold. I'd argue that all living creatures believe that "taking on nutrients will allow me to keep living", whether they are aware of it or not. What's critical here is that eating or photosynthesizing or whatever is an implicit admission that performing that action will sustain the individual's life. I don't want to hear that moss absorbs shit off tree bark because it thinks it might work.

Re: Square of Opposition:
In class yesterday a kid was trying to fish for information about what would be on the final and what would not, and asked "is the Square of Opposition important?" to which the prof replied "Of course it is. Most squares don't have names." Which was doubly awesome because this kid takes himself way too seriously.

And I'm not entirely sure I follow where you're going by invoking the square.

_J_ said...

If we invoke the idea of universal a priori concepts, such as math, then we can state that all people deal in absolutes. If we can't...

At the most fundamental level, the notions of "self" and "else" are themselves absolutes. I think we can safely say that even a child has a notion of self, or at least differentiates their self from things in the world with which they interract. OR we can say that at some point a child will differentiate things within the world. If a child puts down one toy and picks up another they've dealt in absolutes; they have identified some objects as being seperate and distinct from other objects.

And that is an absolute.

Square:
Whenever people talk about proving or denying universal statements I think of the Square of Opposition.

_J_ said...

*

That whole seperate and distinct thing assumes that we ignore all that Eastern Daoist bullcrap about things being different yet the same, or co-dependent and part of the same whole.

Because even if one wants to go away from mind/body dualism and argue that the human being is a combination of mind and body the forces of which are intermingled and inseperable we still have "mind" and "body" as two seperate things forever entwined.

Sort of like how "blood" is one thing, but not really, as it is a combination of a bunch of whatnot that a biologist would know. Platelettes and vessels and liquid and whatnot.

Or how if one took a bowel full of cosmopolitan ice cream and let it melt one could still seperate the strawberry, chocolate, and vanilla if they took the time to do so.

Caleb said...

"bowel full of cosmopolitan ice cream"

Is that really what you meant?

_J_ said...

neopolitan - ice cream
cosmopolitan - vodka

Though, I now know what I'm going to make when I get home tonight.

MA17 said...

"What-the-STOP EVERYTHING! I don't remember writing a check for bowling."
"No sir, that's boweling."
"Oh yes, that's very important. Remember that month we forgot? *Shudders*

_J_ said...

God damn you and your references I have to google.

_J_ said...

Also, damn me for making two mistakes in the same sentence and then only correcting the least problematic of them.

cosmopolitan - vodka
neopolitan - ice cream
bowl - container
bowel - ...I guess that's a container, too.

I hate english.

Caleb said...

Engish is definitely the most difficult language I have ever encountered.

_J_ said...

English is Nintendo Hard.

Lady Enide said...

All your base are belong to us!

I laughed so hard over those last eight entries, I can't even tell you.

Caleb: really now? Harder than Latin or Greek?

_J_ said...

Latin makes sense.

Caleb said...

Engish is hard language. I learned it for a long time. Now, I understand it better than native speakers.

Caleb said...

All your bowel is belong to we.

_J_ said...

All your bowel is belong to we.

You say that to all the girls.

Caleb said...

You are stupid like girl, Tommy!

MA17 said...

You know, if he had just said "Only a Sith deals in that kind of absolute", then maybe none of this would have ever happened.

_J_ said...

I would switch propositions 1 and 2.

"Only a Sith deals in Absolutes" is an assumption grounded in fact. It is true.

Proposition 2 is the assumption that all people deal in absolutes and that can be argued against.

So if I were writing the proof I would start with "Only a Sith deals in Absolutes" and make the "everyone deals in absolutes" second.

_J_ said...

You know, if he had just said "Only a Sith deals in that kind of absolute", then maybe none of this would have ever happened.

That's dangerous thinking.

It's akin to when I wonder what would have happened if I hadn't got on that ICQ userboard and met Lauren.

Which is not a topic for discussion.

_J_ said...

The Px > Ax statement could possibly be not an "if / then" statement, but rather an identity statement.

But that may be one of those things logic does not have that I think logic ought to have.

MA17 said...

If I'm following you correctly, then I'd say that yes, (x)(Px⊃Ax) is a generalized identity statement. It's literally saying something like "in every instance of x, if x is a person, then x deals in absolutes, which is the same as "All people deal in absolutes" or "Every S is a P".

Interestingly, it also implies that anything that is not a person is free to deal or not to deal in absolutes. Also Obi-Wan is saying that anyone who is not a Sith may or may not deal in absolutes. By his statement alone, if Ackbar is not a Sith and can somehow demonstrate it by some other accepted criteria, he can say "it's a trap!" and not be a Sith. Hell, so could Anakin.

And if we didn't already know that everyone is a Sith, I'd suggest we could use Howie Mandell and his newly revitalized "Deal or No Deal" to find closeted Sith.

Caleb said...

Also Obi-Wan is saying that anyone who is not a Sith may or may not deal in absolutes.

huh?

"Only a Sith deals in absolutes"

Doesn't it mean that everything which deals in absolutes is a Sith, and a Sith may or may not deal in absolutes?

MA17 said...

You're right. I had it backwards in my head.

Roscoe said...

Ye gods, I'm fairly certain I hate all of you.


Especially Jay. How in the Name of Tony Sinclair am I going to make a decent Tom Collins gelato without being a rip-off now?

_J_ said...

How in the Name of Tony Sinclair am I going to make a decent Tom Collins gelato without being a rip-off now?

HA! And I've already declared it to be a girly drink.

Double HA!

in every instance of x, if x is a person, then x deals in absolutes

There is no "personhood" requirement.

It ought to be "in every instance of x, if x deals then x deals in absolutes".

There is no way to not deal in absolutes. The act of dealing cannot be done in a non-absolute fashion.

MA17 said...

I'm glad you brought that up.

Personhood is involved because the conclusion is that everyone is a Sith, not that everything is a Sith. And since it was in the conclusion I put it in a premise to make reaching the conclusion possible (or at least easier).

But you're saying that the absolute-dealing premise should be "everything that deals does so in absolutes", which I think might be a good idea, but I'm not sure we can get away from personhood entirely. In order to reach the conclusion, we're going to need to define what deals, and that'll lead us back to people, and our conclusion could then be that every person is a Sith, by the logic that every person deals, and every dealer deals in absolutes, and everything that deals in absolutes is a Sith.

Then again, maybe people is the wrong word. Maybe being is more accurate, since it would allow for aliens to deal and not be people. Not sure if that distinction needs to be made. ?

Caleb said...

Are people things such that we can say: If x is a person, then x is a thing?

If so, then everything which deals with absolutes is a Sith implies that everyone who deals with absolutes is a Sith, correct?

Caleb said...

So, we can have a more general premise.

MA17 said...

I think for that to work, we'd have to introduce a category for Things (Tx), and a premise that says that all things deal. I realize Tx might sound like "things are things", but as I understand it, x means 'thing' only in the sense that x can stand for whatever your imagination cares to allow it to stand for, and not for an explicit category called 'things', so if we start talking about Things, we need to give them a category.

_J_ said...

We could include another proof showing that "dealing" is an aspect of personhood and to "deal" one must be a person or a thing which merits the term "everyone" rather than "everything".

Hmm.

Or we could leave it so that the assumptions only deal with persons.

_J_ said...

It's not the case that everythink is a sith; not all things "deal". But all "ones" deal. So we can say that everyone is a sith.

Caleb said...

So, we're going to say that being a person means one deals and that dealing is only done in absolutes?

_J_ said...

So, we're going to say that being a person means one deals and that dealing is only done in absolutes?

Dealing denotes personhood. Dealing can only ever be done in absolutes.
Only a Sith deals in absolutes.

Therefore, etc.

Caleb said...

Therefore, etc.

&c., indeed.

Lady Enide said...

Caleb caught it, but also. I realized, after sifting through all the incredible noise here, that we've got a severe logical contradiction which everyone (Sith or not) has overlooked.

"ONLY Sith deal in absolutes."
"EVERYONE deals in absolutes."

The use of the word "only" assumes that there is such a thing as not being a Sith; it's a partitive adjective, meaning that the Sith are one group out of a larger collection.

"Every," on the other hand, regardless of what *kind* of every, means the entire collection itself.

Given this, our two premises are directly contradictory. You can't have both "if not Q then not P" (that is, if you're not a Sith, then you don't deal in absolutes--which I believe is the contrapositive of premise #1) and "if not Q then P" (that is, even if you're not a Sith, you deal in absolutes--which is an inference of "everyone deals in absolutes").

I don't think our problem lies in what comes after "every" but in "every" itself. Make sense?

Lady Enide said...

...So in order for our message to make logical sense, it'd have to look like this:

Only Sith deal in absolutes.
Everyone is a Sith.
Therefore, everyone deals in absolutes.

...except now we have our celebrated conclusion as a premise, and it's not even a supportable premise because we need this *new* conclusion as a premise for it. Dang it.

_J_ said...

"The use of the word "only" assumes that there is such a thing as not being a Sith; it's a partitive adjective, meaning that the Sith are one group out of a larger collection."

Things which do not deal in absolutes would not be Sith.

Or, things which do not "deal" as to deal is to deal in an absolute.

_J_ said...

"The use of the word "only" assumes that there is such a thing as not being a Sith; it's a partitive adjective, meaning that the Sith are one group out of a larger collection."

I think that is existential import, and I don't think we get to do that.

That's my second assessment.

Lady Enide said...

I think not, because "only a Sith deals in absolutes" is different from "all Sith deal in absolutes," though we've been treating them as the same statement. That's why we have a problem. I pointed out the distinction, I didn't bring in any new connotations or meanings.

MA17 said...

"ONLY Sith deal in absolutes."
"EVERYONE deals in absolutes."

I don't think those are contradictory, and if we have a problem, I'm not sure this is it. (x)(Ax⊃Sx) is false only when Ax is true and Sx is false (an instance of x deals in absolutes but is not a Sith). All other statements are true using this form, including x does not deal in absolutes and is not a Sith, and x does not deal in absolutes, and x IS a Sith. And I don't see any reason why it should be impossible for something to not be a Sith. When we have Px involved, we're only really talking about people, so anything that is not a person is free to not be a Sith and to deal or not deal in absolutes.

MA17 said...

"I think not, because "only a Sith deals in absolutes" is different from "all Sith deal in absolutes," though we've been treating them as the same statement."

I disagree.
We've been using : (x)(Ax⊃Sx) for "only a Sith deals in absolutes", which I think is correct, because it does not allow for something to deal in absolutes and not be a Sith, from which we can infer that if something deals in absolutes, then that thing is a Sith. A parallel statement might be that only people with lottery tickets can win the lottery. There will not be someone who wins the lottery who does not have a ticket, but having a ticket does not mean you will win the lottery, that would be expressed by the reverse form (x)(Sx⊃Ax) which would work for all Sith deal in absolutes, because there will be no Sith who does not deal in absolutes, and no holder of lottery tickets who does not win the lottery.

I'm pretty sure we've kept those statements separate, and only used the correct one where appropriate.

MA17 said...

"When we have Px involved, we're only really talking about people, so anything that is not a person is free to not be a Sith and to deal or not deal in absolutes."

I mean that x will not deal in absolutes, so x may or may not be a Sith, which is only possible for non-people because all people deal in absolutes and must be Sith.

MA17 said...

That said, we might just say (x)(Ax≡Sx), which would make anything that deals in absolutes a Sith, and anything that's a Sith deal in absolutes, and cut out the question of "what about non-Sith" altogether. The proof would need some more steps, but I don't think it invalidates it.

_J_ said...

I think not, because "only a Sith deals in absolutes" is different from "all Sith deal in absolutes," though we've been treating them as the same statement. That's why we have a problem. I pointed out the distinction, I didn't bring in any new connotations or meanings.

"Only a Sith deals in absolutes" is different from "all sith deal in absolutes" but they are related statements which are consistent with one another.

Only a Sith deals in absolutes states that if one deals in absolutes then one is a sith, for it is not the case that an X dealing in absolutes is not a sith. The statement that all sith deal in absolutes is consistent with this.

To combine them one would say that only a sith deals in absolutes, and all sith deal in absolutes.

That's fine.

We don't have to care about the possibilty of a non-sith, or a being which does not deal in absolutes. We're just talking about what we're talking about, which is the fact that only a sith deals in absolutes.

_J_ said...

I think we need to finalize this proof so it can go into the Header.

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