In his “New Work for a Theory of Universals”[1], David Lewis discusses Michael Devitt’s defense of Ostrich Nominalism in his article “‘Ostrich Nominalism’ or ‘Mirage Realism’?”[2], specifically as a response to the One Over Many argument. Devitt had proposed to paraphrase such sentences as
“a and b have the same property, F-ness”
as
“a and b are both F”
which itself can be analyzed as
“a is F”
and
“b is F”.
Lewis thinks that this is not satisfactory. He says:
But Devitt has set himself too easy a problem. If we attend to the modest, untransformed One over Many problem, which is no mirage, we will ask about a different analysandum:
a and b have some common property (are somehow of the same type)
in which it is not said what a and b have in common. This less definite analysandum is not covered by what Devitt has said.[3]
I think there is an obvious paraphrase of Lewis’ example which, though not explicitly covered by what Devitt had said, is in perfect harmony with its spirit. Indeed, I think it’s obvious enough that it's probable someone else has already thought of it, which for a while made me hesitant to make this post. Nevertheless, I’m interested to see if others think the paraphrase works, so I’m posting this anyway, even if I can’t claim originality for it. The paraphrase goes like this (where F, G, H, etc., are all the predicates expressible in the language):
((Fa & Fb) v [(Ga &Gb) v (Ha &Hb)])…
Or, in English:
Either a and b are both F or a and b are both G or a and b are both H…
So my question is: Do you think the paraphrase works? And if not, why not?
4 comments:
A couple of tricks involved in this paraphrase, and I am not sure that Lewis would have liked either of them. The first is that you are cashing out something "existential quantifier"-ish as a disjunction. This is a common way to think about quantifiers, but the obvious difficulty is that any such explicit paraphrase has to be infinite to cover all the cases that would be covered by the quantifier. Second, grant for the sake of argument the resources of an infinitary language, so we can put together infinite disjunctions. In order to get the right paraphrase we need a name for each property, but who is to say that we can name all the properties that exist?
Hi Colin,
Good points. I'm still trying to think of a response. Just so you know, I'm going on vacation and probably won't have computer access until next Thursday, so I can't reply until then. Hopefully by then I'll have thought of something!
Hi, how can I contact you?
I want to start, a list of philosophy BLOGS. A small presentation of the thing, a library or address book. But one question I don't know is, how to contact people through blogs, I'm not familiar with this medium.
If time permits, I want you to make a post here,
http://dissidentphilosophy.lifediscussion.net/conversation-f8/
It will get stickied and start a list of philosophy blogs. You could write a small intro too, like "Here is a index and library of PHILOSOPHY blogs ...."
Already an index of BBS is here,
http://dissidentphilosophy.lifediscussion.net/conversation-f8/the-community-of-ephilosophers-philosophy-bbs-sites-t9.htm
Kind regards,
- Niki
Hi Colin,
Sorry for the delay in responding. I still don't have a *good* reply to your points. Concerning the second, the only thing I can think of is that an Ostrich Nominalist probably would not accept the way you phrased the problem. They could say that we couldn't name all the properties that exist because properties *don't* exist, so there is nothing there to name. Still, this is a bad response. What would happen if, for example, the word "red" were to suddenly disappear from usage? Would every red thing suddenly stop being red? That seems absurd. So I guess Ostrich Nominalism is not as defensible as I thought it was.
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