Monday, November 17, 2008

A Thought Out Loud

It seems to me that propositions are made up out of objects, properties and relations. Let us take (P) and (NP).

(P) Mary Swims

(NP) Mary doesn't Swim

It seems that the propositions differ. In the one case, we get Mary* and Swims* as constituents; and in the second it is Mary* and Doesn't* and Swims* we get.

The syntax are also different. We get instantiation in the one case, ~instantiation in the other.

Likewise for (1) and (2). I'll not do the LF stuff since it is too much...

(1) First order logic is undecidable

(2) It is not the case that first order logic is decidable

The proposition in (1) is made up of first order logic, the being relation, and undecidability. In (2) it is negation, first order logic, the being relation, and decidability.

Seems like quite different propositions.

I think my thinking is fine here.


Dan said...

I guess this is a continuation of your previous post.
Again, it's admitted that if you have something like King's view then (P) and (NP) express different propositions. The question is whether or not they should express different propositions. This is a question independant of any view of propositions. Recall that one of the main arguments against Stalnaker was that '2+2=4' and 'arithmetic is incomplete' should express different propositions but on his view they don't. Saying that propositions are sets of truth-supporting circumstances, and thus they should express the same thing is not an adequate defense.
You seem to be hitting on something more substantial than that, but still theoretically loaded. To really evaluate whether or not (P) and (NP) should express different propositions or not we should take a pre-theoretic stance.
From a pre-theoretic standpoint your defense of King seems to be something like this:
(1) If propositions have parts, any two propositions that have different parts are distinct.
(2) (P) and (NP) if they express structured propositions express propositions with different parts
(3) Kings view is a-ok
I would deny premise (2). I think the motivation for (2) comes from some trick in the syntax.
Instead of attacking (2), I'll give an example of two syntacticly different sentences that even more plausibly express the same proposition. Consider a fictional language Wenglish that has the following properties:
(1) All rules of Wenglish are exactly like English when speaking to a male.
(2) All rules of Wenglish are exactly like Nenglish when speaking to a female.

Now suppose you have a community of Wenglish speakers. Consider three people: John (a male), Wendy (a female) and Smith (another male). Consider the following dialogue:
John(to Wendy): Wendy's not hot!
John(to Smith): I asserted to Wendy that Wendy's hot.
Assuming Wendy is hot, both assertions made by John seem true.
On King's view that-clauses are singular terms that refer to propositions. So, in his assertion to Smith, John referred to the proposition < Wendy, Hotness>. But he asserted to Wendy < Wendy, Not, Hotness>.
At this point I suggest that King's view is false, and that the propositions reffered to in the that-clause in his statement to Smith is the very proposition expressed in his statement to Wendy. If this is not the case, In this language John would be unable to express to Smith anything he expresses to Wendy and vice versa. Furthermore, the truth conditions and the aboutness facts are the same. Furthermore there's nothing he can express to Wendy that he can't express to John and vice versa. These are all pre-theoretic intuitions.

Wes McPherson said...

I think I understand what's going on now.

I don't think King's view is false. I happen to think that the example is consistent with what I think and what King thinks.

If Wenglish involves different rules, I think that is enough to make them different languages. I think the linguistic differences here are enough to assure the propositions are distinct, even if the same fact, like Wendy's being hot, are captured in two different propositions.

Thus I can say: "Adam says Wes is a bachelor" even if Adam said that I am an unmarried man. These propositions, it seems to me, are different even if they are about the same thing, i.e. my unmarried-maleness.

Wes McPherson said...

I think I hold that distinct sentences = distinct propositions, pretheoretically.

Dan said...

I don't think different rules relative to context makes for different languages. Language is relative to context in all sorts of ways, it differentiates uses of "he" vs. "she" for instance. Many languages are sensitive to gendered nouns in ways that English isn't. I see no reason to think that the variation I gave makes Wenglish into two languages, one only spoken to males and one only spoken to females.
I also think it's more plausible that "Wess is an unmarried man" and "Wess is a bachelor" expressed different propositions than (P) and (NP).
So, do you reject the translation principle in general between languages?

Wes McPherson said...

I think translation works with pragmatic quotes. Thus, we can get stimulus-synonymy. I think that the propositions expressed by

1) Es Regnet
2) Il pleut
3) It rains

are the same, since we get the same semantic contents, plus the *it*, *il* and *es* are •∃x•s, and *regnet*, *pleut* and *rains* are all •rains•s. They are all one place predicates.

Are they predicates? They aren't individuals, are they? Uh, I'm an idiot. I hope you can tell me what I mean to say.

I'm not sure what the translation principle is that you have in mind, but I probably do reject it. I think Sellars method can handle

4) Und
5) And

meaning the same thing without appeal to semantic contents. Maybe (4) and (5) have semantic contents? Well then, cases like:

6) A wooden pawn shaped like a bear
7) A stone pawn shaped like a pizza

It seems it's the pawn function that makes the pawn. But the cases of (P) and (NP) and the Wenglish seem to be saying that pawns in chess are just like checkers in checkers. I think the rules, which play a part in the meaning of the things the rules are about, have to be taken into account.

I'm probably not clear. Sorry.