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?

There are no distributable properties?

Prima facie, there are distributional properties, distributable properties, and they are distinct. It is one thing, Josh Parsons (2004) suggests, to have a redness distribution (say, to be red in such-and-such places but not in others) and another to be just plain red. What I’m interesting in is the claim that there are no distributable properties; there are just distributional properties. Is this a coherent proposal?

One might object as follows. Suppose that D is a distributional property. Intuitively, the instantiation of D involves a distribution of instances of some distributable property D*. On the current proposal, there simply is no property like D*, so the instantiation of D cannot literally involve a distribution of D*-instances. But then how are we to understand what it is for D to be instantiated in the first place? Just as distributors need material to distribute, distributional properties need distributable properties distribute.

I think the thing to say in response to this concern is that it mistakenly, though understandably, assumes that the sense in which distributional properties are ‘distributional’ lines up closely with the everyday sense of the term. Instead, we should think of ‘distributional property’ more as a technical term.

I do not mean to suggest, however, that the notion of distributional property we are working with here is obscure. Suppose that Frank, pointing to Gary who is grimacing and then to Albert who is smiling, says, “There is pain to the left and pleasure to the right.” One might claim in this case that a proper part of the world consisting of Frank, Gary, and Albert involves a distribution of distributable properties including being in pain and having pleasure. Let us call this way of understanding distributional properties the ordinary conception of distributional properties.

One might claim instead that the proper part of the world mentioned above instantiates the distributional property being in pain-to-the-left-and-pleasure-to-the-right. Here the idea is that the truth-maker for Frank’s claim is that the Frank-Gary-Albert fusion instantiates the single aforementioned property. In this case the fusion does not instantiate being in pain and having pleasure qua distributable properties because there are no such properties. To contrast this conception of distributional properties with the ordinary one, call it the minimalist conception (given its commitment to distributional properties but not distributable properties).

Both the ordinary conception and the minimalist conception, as far as I can tell, are coherent, so it seems to me that so far we have not been given a good reason to think that the claim that there are distributional properties but no distributable properties is incoherent. What do you all think?

-Kelly

An Argument Against Unrestricted Composition

What's wrong with this argument?

www.logicoontologicalissues.blogspot.com

-Einar

Believing in Contradictions, why you should

Here’s a quick (and probably pretty bad) argument that it is rational to believe contradictions (or at least why it's not irrational to believe contradictions) inspired by conversation with Dan.

1) One ought not believe contradictions (assume for reductio)
2) Ought implies can (ask Pete about this)
3) Possibly, one does not believe contradictions (from 1 and 2)
4) Necessarily, one believe contradictions.

A few things to note at the outset: First, by ‘believe contradictions’, I don’t necessarily mean believe that p and not-p. Believing that p and believing that not-p (in "separate compartments" if you’d like) would do fine. The ‘cans’ and ‘possibles’ of this argument should be read along the lines of nomic possibility. Also, this is a proof by reductio in favor of believing in contradictions – you might think the argument is self-defeating for this reason. You might also think that ought implies can is a bad principle (or at least shouldn’t be applied to this kind of case). I think premise 4 stands in the most need of justification.

I'm not entirely sure how to justify (4). Maybe we could say that, for some complex propositions P, we might fail to believe that P, fail to believe that not-P, but believe that P or not-P; this might not be a contradiction itself, but maybe we could draw one out. Or maybe we could say that believing the premises of an argument but not its conclusion commits us to contradiction (maybe by way of a possible-worlds analysis of content -- in all belief-worlds where I accept the premise, I accept the conclusion, but by hypothesis, I don't accept the conclusion)... I'm not entirely sure where to go, but I still think there's an argument in the neighborhood. Thoughts?

[Note: I've taken back my original justification for (4).]