Friday, June 06, 2008

The meanings of definite descriptions

Nathan Salmon has recently written a paper on that very confusing passage from Russell's 'On Denoting'. Salmon's paper appears in a special issue of Mind. I have not read his paper but I have talked to Rock* about it. In this post, I am going to present an argument that is inspired by my discussions with Rock* about Salmon's paper. I do not claim that that my formulation of the argument below is a decent formulation of the argument presented in Salmon's paper (I am not even sure if it is a formulation of Salmon's argument at all). But, I think it is interesting anyway.

Let's consider the definite description "The center of mass of Earth". The unit meaning of "The center of mass of Earth" is the meaning of that whole phrase which built out of the meanings of words in that phrase, if there is such a meaning. I am inclined to think that there is a unit meaning of "The center of mass of Earth". But, the argument that I present below is supposed to show that there is not such a unit meaning.

Let's also introduce a principle of naive compositionality. I am never sure about how to formulate compositionality principles. Roughly, we want to say that the meaning of a sentence is determined by the meanings of the words that make up that sentence and their order. Here is an attempt to make something like that principle more precise.

Naive Compositionality Principle: If S1 and S2 are made up of some phrases that can be put in a one-one correspondence that preserves their individual meanings and their order in the sentence, then S1 and S2 express the same proposition.

Here is an example of how this principle should work. Consider the following two sentences:

S1. All bachelors are unmarried.

S1. All unmarried adult males are unmarried.

Sentence (S1) can be broken up into the following parts:

P1.1 All Bachelors
P1.2 are unmarried

Whereas sentence (S2) can be broken up into the following parts:

P2.1 All unmarried adult males
P2.2 are unmarried

Clearly, there is a one-one correspondence that preserves word order. We just associate P1.1 with P2.1 and P1.2 with P2.2. Moreover, P1.2 and P2.2 definitely have the same meaning. So, if P1.1 and P2.1 have the same meaning, then according to our principle (S1) and (S2) express the same proposition. A plausible case can be made for the claim that P1.1 and P2.1 have the same meaning. But, I won't get into that right now. I just wanted to give an example which helps to show how the Naive Compositionality Principle works.

Now, here is how the argument goes. First, let's introduce "Fred" as a name for the unit meaning of 'The center of mass of Earth". Now, consider the following sentences:

S3. The center of mass of Earth is a point.

S4. Fred is a point.

Clearly (S3) expresses a truth. However, it seems that (S4) does not. (S4) is about the thing named by "Fred", a meaning, and meanings are not points. So, (S4) expresses a falsehood. But, according to Naive Compositionality and Millianism and under the assumption that "The center of mass of Earth" has a unit meaning, (S3) and (S4) express the same proposition. This is puzzling. We can formulate an argument as follows:

1. If "the center of mass of Earth" has a unit meaning, then (S3) and (S4) express the same proposition.
2. (S3) expresses a truth whereas (S4) does not.
3. If (2), then (S3) and (S4) do not express the same proposition.
4. So, "The center of mass of Earth" does not have a unit meaning.

(1) is justified by appealing to Millianism and the Naive Compositionality Principle. (2) seems pretty plausible. The fact that (S3) expresses a truth is an empirical discovery and I argued for the claim that (S4) expresses a falsehood above. Finally, (3) is justified by Leibniz's Law. So, our argument is valid and has strong support. Moreover, the argument can be generalized in a particular way to show that no definite description has a unit meanings. (Moreover, as Rock* pointed out to me, the same thing can be done with other quantificational sentences such as "All cats are furry" and "some dogs are happy".)

I disagree with the conclusion of the argument and I think the best premise to deny is (1). I think that Naive Compositionality is false. It seems to me that the fact that the subject of (S3) is grammatically a definite description whereas the subject of (S4) is not makes it so that (S3) and (S4) express different propositions. However, these propositions are made up of the same meanings in the same order. We have to replace Naive Compositionality with a principle that allows for grammatically different sentences with the same meanings in the same order to express different propositions.

I know this post is not exceedingly clear, But I hope it is clear enough to convey the puzzle and my solution. I'd like to know what others think of this puzzle.

2 Comments:

Blogger Andrew Cullison said...

Hey Joshua,

I'm interested in this last passage of yours.

>>>>>>
We have to replace Naive Compositionality with a principle that allows for grammatically different sentences with the same meanings in the same order to express different propositions.
>>>>>>>>>>

One of the nice things about propositions is that they are supposed to be the meanings of sentences. I take it on this view we are now going to have two things involved with a sentence - the meaning and the proposition it expresses.

If that's correct, then what are meanings on this view?

Suppose I am a Russellian about propositions and take them to be some sort of ordered set-like entities of particulars and properties (or something like that)

Are meanings going to be another one of those set-like entities? Are they a different kind of thing? If so, how are they different?

12:09 PM  
Blogger Joshua said...

Hi Andrew,

Your comment made me realize my original claim in this passage is misleading:

"We have to replace Naive Compositionality with a principle that allows for grammatically different sentences with the same meanings in the same order to express different propositions."(me)


One way to take this passage is as implying the following: S3 and S4 have the same meaning but they express the different proposition. But, that's not what I intended. After all, I think that propositions just are meanings of sentences.

Another interpretation implies the following: S3 and S4 are made up of the same proper constituent meanings, but their overall meaning is different. This is how I intended the passage.

My idea is that the proposition or meaning of S3 is made up of the following proper consituent meanings (Let * ... * take us from the phrase ... to the meaning of ...):

M3.1: *the center of mass of Earth*
M3.2: *is a point*

Moreover, the meaning of or proposition expressed by S4 is made up of the following proper constituent meanings:

M4.1: *Fred*
M4.2: *is a point*

Since M3.1 = M4.1 (by millianism) and M3.2 = M4.2, the propositions expressed by the two sentences are made up of the same proper constituent meanings but have a different overall meaning (or express different propositions). The difference in overall meaning is a result of grammatical structure. This is what I'd like a new version of Compositionality to account for.

7:02 AM  

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