Wednesday, February 14, 2007

Mass Terms

Suppose that there is a single gold atom lying on a table, T. In such a situation, is the following sentence true?:

(G) Some gold is on T.

I'm curious about this because, in many ways, mass terms seem to behave a lot like plurals. Suppose, for instance, I have some gold and this gold is subsequently scattered. Then the gold I had still exists, although it has been broken up into different portions of gold. Similarly, if I have some coins, those coins still exist even if they become scattered.

A natural proposal, then, is to take (G) to be true in just the same circumstances as:

(A) Some gold atoms are on T.

But if (G) is true in just the same circumstances as (A), then (G) should be true in the circumstances described above, in which there is only one gold atom on T.

I suppose that this train of thought leads to the idea that the mass term "gold" means the same thing as "gold atoms", or something along those lines, along with some sort of explanation of why "is" is appropriate in (G) but "are" is appropriate in (A). And perhaps such an idea could be extended to other mass terms as well.

So, what do you guys think about (G) and (A) and what do you think about mass terms?


Blogger Chris Tillman said...

(G) and (A) are true under the same conditions, but they don't mean the same thing. '(G) iff (A)' is plausibly necessary a posteriori, since it is not a priori that (say) there are gold atoms if there is gold.

3:11 PM  
Blogger Joshua said...

I'm not sure I understand Greg's originaly post. However, here are four statements that are jointly inconsistent. Perhaps Greg's original point had something to do with these three statements:

1. Some Gold is on T iff some gold atoms are on T
2. If there is only one gold atom on T, then it is true that some gold atoms are on T.
3. If there is only one gold atom on T, then it is not true that some Gold is on T.
4. There is only one gold atom on T.

Presumably, we can make (4) true just by putting exactly one gold atom on a particular table, T. So, we must deny one of (1)-(3).

I take it that (A) is supposed to be a statement that invokes a plural quantifier. Given this fact, one might argue for (3) based on the fact that the logic of plurals allows a single thing to satisfy the plural variables. However, this may be a simplifiying assumption that is not matched in ordinary english. Perhaps in ordinary english, when we say that some gold atoms are on the table, we have said somethig that entials that there is more than one gold atom on the table.

I personally am unsure about the correct account of ordinary english plurally quantified expressions. I guess I am inclined to take the standard line and suggest that putative entailments are actually conversational implicatures. But I am really, really only very slighlty inclined to accept this.

I guess the main point that I would like to make in this comment is that we may grant that (A) is true under the circumstances in which there is only one atom on T, deny (1) and still keep with the spirit of the original proposal. Perhaps something like the following is true.

Some gold is on T iff some gold atoms that are more than one in number are on T.

I think this might have a better shot at being a decent proposal. But, I am slightly reluctant to even accept this. I am reluctant because I remember a conversation that Greg and I had in Buffalo about this kind of proposal. I remember that there were a couple of problems that we had for these kinds of proposals. But, I do not, right now, remember what the problems were.

1:24 PM  

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