Many-One Identity Relations

Some people (ahem) want to discuss the notion of a many-one identity relation. I'm a bit puzzled by such talk, since I think it's constitutive of our concept of identity that it's one-one. We don't balk at cases like "Benjamin Franklin is the inventor of bifocals", "Hesperus is Phosphorous", and "Cat Stevens is Yusuf Islam". We might even have many-many cases of identity, like "The candidates who raise the most money are the candidates who get the most votes", though there might be a good way to analyze this in first-order predicate logic with the usual representation of identity. I'm not exactly sure what to make of many-many claims, but set them aside for now.

One has plenty of examples of identity in language from which we try to build our notion, and or familiar identity sign is doing a pretty good job of this. If many-one identity were part of our ordinary concept of identity, we should expect to see all sorts of ordinary uses of it. So, what are the cases that force us to consider a many-one notion? If many-one identity is supposed to be so intuitive, how come we don't see examples of it? How come all uses of it seem ungrammatical and weird?

The only (ordinary) examples I can think of are examples that involve the Trinity. The Father, Son, and Holy Ghost are (is?) one thing, which is God. Is your claim that many-one identity makes exactly as much sense as the Catholic Trinity?

[Note, by the way, that I don't think that claims about intuitions and linguistics are deeply informative about the nature of reality. I'm also not claiming that there's no room for some kind of generalized notion of identity to explain what we mean by "nothing over and above" kinds of claims. I just think it's a mistake to identify this notion with our ordinary uses of identity.]

Many-One Identity

I believe it makes perfect sense to say that some things xx are identical to one thing y. The table is identical to the four legs and table-top; my two legs, two arms, head, and torso are identical to me; etc. I wonder what your immediate gut reactions are to such claims.

-Einar

PS: I also wonder about your reactions to my last entry. Come on, let's bring this blog back to life!

Perfectly Natural Irreducibly Plural Properties

Consider the property of being scattered. It has the logical form: S(xx), where 'xx' takes any plurality as value (including a plurality consisting of only one thing, if one thing can be scattered). The property of being scattered has a fixed adicity (one-place), and it is an intrinsic property (or so it seems).

My question is: Can there be any perfectly natural (fundamental) properties of the logical form F(xx)?

-Einar

In the interests of getting this bog going again, and as an intuition check:

What do you make of the following statement:

(1) If it were to rain and not rain, then it would rain.

Does this strike you as trivially true, non-trivially true, or false?