Thursday, September 4, 2008

propositions as 0-place predicates

I don't intend this post to be my comment paper, but I thought one (in particular) distinction brought up in class was interesting. Consider the sentences:
(H) Harry likes horses.
(C) Harry likes chickens.
(&) (H)&(C)

Suppose margaret asserts all of (H), (C) and (&). Margaret asserts that Harry likes horses. Therefore there is some thing that is asserted by Margaret using the sentence (H). That is the thing asserted by (H). Fine.
By asserting (&), Margaret asserts the same thing about horses and chickens: that Harry likes them. Therefore there is some thing asserted of horses, and some thing asserted of chickens, and those two are one and the same thing.
From these two little facts we drew the distinction between the 'thing asserted' and the 'predication'. If this is a genuine distinction, then 'asserted' is ambiguous (or the other thing) about these two uses. I don't think this is in fact a genuine distinction. I believe the 'thing asserted' is just a special case of predication.
Consider (H) again. There is another thing asserted. It's asserted that the non-symetrical liking relation holds between Harry and horses. There's a third thing asserted, that liking horses applies to Harry. The liking relation is asserted of two things, Harry and horses (in that order). However the inclination to draw a distinction between asserting of (two things) and asserting of (one thing) isn't so pressing. I'd like to say that simple assertion is just a case of asserting of (0 things). It's not unheard of in logic to treat propositions as 0-place predicates. The idea seems exactly right to me.
One could say that there's a genuine distinction, since simple assertions are truth evaluable, while predicates aren't. I'd simply respond that the addicity of the predicate (whether it's firts, second place etc.) is simply the number of things that the predicate must be applied to in order to evaluate truth. Treatment of propositions as 0-place predicates falls neatly in line. If this is all right then we have a collapse of assertion-of and assertion, and we have a hint as to what propositions might be.
If anyone wants a formal argument, I guess it would go like this:
(1) There's no ambiguity in the word 'assert' between uses where it's used to speak of assertion of an individual or assertion of multiple individuals.
(2) (1) -> (3)
(3) Addicity of predication doesn't cause ambiguity in the word 'assert'
(4) 0-place predication makes sense.
(5) (3)&(4)
(6) (5)->(7)
(7) There's no ambiguity in the word 'assert' when asserting things of individual(s) or asserting things of no individuals


Chris Tillman said...

Nice post, Dan. One quibble: predicates are linguistic expressions: the token or type 'is hairy' is rightly called 'predicate'. But if our argument that what is asserted is not a sentence type (or token) is sound, then it should carry over straightforwardly to the claim that propositions are 0-place predicates. So perhaps it would be better to suggest that we may think of propositions as 0-place properties, where 'property' is just intended as a place-holder for the semantic content of a predicate in a context.

Chris Tillman said...

Here's another consideration: many (including King) hold that propositions are representational entities, but properties are not. So perhaps the identification is not harmless. For a reply see Deutsch's review of King's book in the online Notre Dame Philosophical Review.

Dan said...

What's a representational entity?

Chris Tillman said...

A representational entity is just something that represents things as being a certain way. Truth-apt entities, like sentences and propositions, are true if they represent the way things are and false if they do not.

Wes McPherson said...

Just curious: are all propositions representational entities?

I presume that not all sentences are representational, since some sentenced have justification-conditions and not truth-conditions.

How about with propositions?

In his Tractatus, Wittgenstein though that there are 'significant' propositions, propositions with senses, but also 'senseless' propositions. For him, the propositions of mathematics or logic are not representational.

Does King hold that the propositions of mathematics and logic are representational? Are analytic or necessary truths going to be representational?

Chris Tillman said...

Any truth-apt proposition is representational. If things are the way the proposition "says" they are, it's true. And of not, not.

What's an example of a sentence with justification-conditions but no truth-conditions?

I honestly don't get the Wittgensteinian view. The reasoning seems to be that if something holds of everything, or applies to everything, then it holds of or applies to nothing. That is clearly fallacious. So maybe the idea's something else. Perhaps LW wanted to distinguish propositions knowable only a posteriori from others. But then 'if gold exists then gold has atomic #97' is a sentence that expresses a necessary, a posteriori truth.

King and others do hold that logical tautologies and mathematical sentences encode propositions, even when the propositions they encode are necessary, a priori truths.

Wes McPherson said...

Professor Tillman,

I think a sentence like "Hello" seems to have no truth-conditions, does it? But it seems to have certain appropriate contexts of utterance. The utterance may be justified, say, when I see you for the first time in the morning.

I think Kripke gives as good as an account as anyone with LW on sense and senseless propositions. LW claimed Tractatus era that the only statements with a sense are those which represent a state of affairs. But this last sentence itself, it seems to not represent a state of affairs but gives a rule. It isn't meaningless, but lacks a sense. So it get stuck with a third status.

The Tractatus is a strange book because it sets out rules that it clearly violates, and that in the end is supposed to be the point. So perhaps I should stop appealing to arguments it contains...

Chris Tillman said...

Thanks, Wes. Certainly there are sentences with no truth conditions: interrogatives, imperatives, etc. And it's true that for these sentences, as well as any others, there are some circumstances under which it's more or less appropriate to utter those sentences. If that's what's meant by 'justification conditions', then I think I get the idea.

To have a sense in Frege's sense is just for an expression to have a semantic content with respect to a context. I think the colloquial sense of 'sense' is something like this, though of course it's neutral on whether Frege's account of senses (in the ordinary sense) is right. Note that on this characterization, interrogative and imperative sentences may encode propositional contents with respect to contexts, but these propositional contents would not have truth values.

Dan said...

Hi Wes,
Do you mean 'justification conditions' in the epistemic sense? If so, it's hard to see how something can be apt for justification but not truth-apt. What are you justified in, if not belief, i.e. holding that it's true.
Do you mean 'justification conditions' as the conditions under which it's appropriate to utter a sentence? If so, I don't think it can be a substitute for truth, even with mathematical and logical truths. For instance, a serious logician who holds by a false logical theory is often in an appropriate situation to utter something necessarily false. If this is a senseless propositions (i.e. not truth apt), then something about it is left unexplained.

Wes McPherson said...

Some people do hold a 'pragmatic theory of truth' whereby we only ever had conditions of utterance which obtain or fail to obtain. I used to find this appealing because it equates a sentence like "Hello" with a sentence like "It is raining". The appeal here: simplicity!

It seems on this view, 'favorable conditions' replace 'truth conditions'. One is disposed to utter, or believes they are warranted to utter, etc.

But if we understand a distinction between statements and sentences, this seems to help us. I can utter sentences which don't state anything. I was just wondering about this notion of 'stating anything'.

The view which you two seem to hold seems good enough for me, as I do think that a cat's meow and my uttering "Hello" are wanting in the 'stating' department, lacking content, but think that it is reasonable to hold that the propositions of logic or statements of science have content.