Pluralities

To what does the plural referring expression, 'the cats in my house,' refer? Not to plurality, but to a plurality. A plurality is one item, not many items. It is one item with many members. 'The guitars in my house' refers to a numerically different plurality. It too refers to one item with many members.  It follows that a plurality cannot be identical to its members.  For if it were there would be no 'it.'

I am not saying that a plurality is a mathematical set. I am saying that a plurality is not just its members.  I am rejecting Composition as Identity. If the Londonistas do not agree with the Phoenician on this one, then I fear that there is little point to further discussion. We are at the non-negotiable.  We are at bedrock and "my spade is turned." 

Comments

[David Brightly]

Morning Bill,

Isn't Lewis making a dodgy move here? He says, in effect,

If a cat exists and another cat exists then (a cat and another cat) exists.

He thinks 'exists' distributes through 'and' so that he can factor it out to leave behind a mysterious quotient 'a cat and another cat' that he takes to be some sort of object, or at any rate, something---a 'fusion'---that existence can be attributed to. Also: the 'and' in the antecedent is logical conjunction whereas the 'and' in the fusion 'a cat and another cat' is connective. I would say that Lewis is inventing a language extension, 'fusion-talk', just as Cantor and friends invented 'set-talk'. What is not entirely clear is how fusion-talk interacts with ordinary talk and ordinary expectations. In particular, if we are to begin talking of several things as if they amounted to a new kind of single thing then perhaps we should not be surprised if our intuitions are confounded. Composition as identity may well be the right rule for thinking about these objects of a new kind. It certainly seems so for fusions, sets, and pluralities. However, I suspect that fusion-talk can be rendered into ordinary language by purely surface syntactic transformations. Thus it adds no meaning over ordinary language, and no ontological commitments. It's just a manner of speaking. Hence,

The fusion of a cat and another cat exists

means exactly

A cat and another cat exist.

Something similar, I think, must be happening with 'plurality-talk'. There are no plurality objects as such, just as there are no fusions or mathematical sets. We might say,

The cats in my house are a plurality of which Max is a member,

but this is just to say,

Max is one of the cats in my house.

Perhaps this phenomenon is analogous to making an excursion into the complex numbers in order to prove a result about real numbers.

[BV]

David,

Delete the sentence in which I refer to Lewis, and just tell me directly whether or not you agree that a plurality cannot be identical to its members.

[David Brightly]

Bill, As I understand it, the fusion of x alone is just x yet the set of x alone is not x. If fusions and sets are kinds of plurality then it would seem there is no definite answer to your question. Why is it important?

[oz the ostrich]

Just noticed this.

"It follows that a plurality cannot be identical to its members. For if it were there would be no 'it.'"

Your sole argument for the cats being one thing is the singular 'a'. But the cats are not one thing. They are two, or three or more cats.

You simply have no argument.

[oz the ostrich]

"just tell me directly whether or not you agree that a plurality cannot be identical to its members."

Well clearly the cats cannot be equal to one of the cats. But why does that justify the conclusion that there is another thing (a plurality) in addition to the cats.