a couple thoughts

Just a few thoughts I thought I'd air here.

Is GMR contingently true? So far I've seen nothing that would indicate that if there are a plurality of concrete worlds there are necessarily a plurality of concrete worlds. Consider a Lewisian universe in which all worlds with green rabbits aren't there. That seems just as metaphysically possible as the universe in which all Lewisian worlds are there. If that's true, any given Lewisian world is a contingent entity (the fact that he lacks the vocabulary to describe what that would mean irregardless). In other words, most actualist possible worlds exist in virtue of the world possibly being a certain way (and thus all possibilities are necessarily represented). Lewisian worlds don't have this to fall back on.

utterly contingent.... disgusting!

Also, I had a couple chats with the reductionists of the class about the epistemology of modality. The question had come up, "how can we know about possibilities". This could be directed to either realist theory.
Well, I'll attempt an empiricist approach to this problem. We can observe actual properties and relations and conceptually divide them from their instances. We can also notice scientific trends, or natural laws. If we can conceive of a few properties and relations combined, and notice that nothing in our natural laws prohibits this combination, voila! We've conceived of a possibility. Of course hard determinists will have to be more strict about the laws they employ, and give a story about a causal history. But that's ok, we don't need to be hard determanists (at least no present natural law entails HD).
If we grant Lewis that all possibilities are realized in a concrete world, then voila! We know stuff about other concrete worlds. However, if all these worlds are contingent, we have less cause to grant then to Lewis.

Accidental Intrinsics and Counterpart Theory

In an endnote, Divers presents an argument from Lewis for counterpart-theoretic accounts of de re modality. Since not everyone has the endnote and since the sort of argument Divers mentions from Lewis is oft-discussed in metaphysics, I thought I would reproduce it here:

"Why does a world represent Carnap vicariously, by means of a counterpart of Carnap rather than by means of Carnap himself? This is a complex question that speaks to issues at many levels. The immediate answer is two-fold: (i) in GR worlds represent individuals by having individuals as parts; and (ii) every individual that is part of any world is part of exactly one wold, so when many worlds each represent possibilities of Carnap, it cannot be as a result of Carnap being part of each world. GR cleaves to (i) since tehreby representation can be accounted for directly by one of the conceptual primitives of the theory, viz. parthood (see (4.2)). GR cleaves to (ii) because, given (i), an adequate account of the modal phenomenon of accidental intrinsics forces one's hand. (Lewis 1986a: 198-209). Swiftly, having a certain number of fingers is an intrinsic property of Carnap. But how can the individual Carnap have ten fingers at w and have only nine fingers at v, if Carnap having a certain number of fingers at a world is (a) a matter of one individual (Carnap) being part of a world and (b) the one individual having different numbers of fingers at different worlds? It seems that something has to give, and Lewis holds that it should be tolerance of individuals that are wholly present in more than one world. Consequently, de re representation of individuals is achieved vicariously, by counterparts, rather than directly." - Divers pp. 306 n. 4, Possible Worlds.

A Famous Argument from Lewis for GR

Divers cites two sorts of justification given by Lewis for GR. One he calls "The Argument from Paraphrase". Here is the passage that Divers cites:

"If an argument is wanted, it is this. It is uncontroversially true that things might have been otherwise than they are. I believe and so do you that things could have been different in countless ways. But what does that mean? Ordinary language permits the paraphrase: there are many ways that things could have been, besides the way they actually are. On the face of it, this sentence is an existential quantification. It says that there exist many entities of a certain description, to wit "ways things might have been". I believe things could have been different in countless ways; I believe permissible paraphrases of what I believe; taking the paraphrase at its face value, I therefore believe in the existence of entities that might be called "ways things might have been". I prefer to call them "possible worlds"." - David Lewis, pp. 84, Counterfactuals, Oxford: Blackwell.

"I do not make it as an inviolable principle to take seeming existential quantifications of ordinary language at face value. But I do recognize a presumption in favor of taking sentences at their face value unless (1) taking them at face value is known to lead to trouble and (2) taking them some other way is known not to." - David Lewis, pp. 90, Counterfactuals, Oxford: Blackwell.

Truthmakers

Divers spends a good deal of Chapter 4 evaluating the claim that GR provides truthmakers for modal claims (utterances? sentences? propositions?). I thought it would be helpful to say a bit more about what truthmakers are supposed to be. Here's Armstrong on truthmakers:

"The idea of a truthmaker for a particular truth, then, is just some existent, some portion of reality, in virtue of which that truth is true. The relation, I think, is a cross-categorical one, one term being an entity or entities in the world, the other being a truth. (I hold that truths are true propositions, but will leave this matter aside . . . ) To demand truthmakers for particular truths is to accept a realist theory for these truths. There is something that exists in reality, independent of the proposition in question, which makes the truth true. The 'making' here is, of course, not the causal sense of 'making'. The best formulation of what this making is seems to be given by the phrase 'in virtue of'. It is in virtue of that independent reality that the proposition is true. What makes the proposition a truth is how it stands to this reality."

"Two questions immediately arise. First, do truthmakers actually necessitate their truths, or is the relation weaker than that, at least in some cases? Second, do all truths have truthmakers, or are there some areas of truth that are truthmaker-free, modal truths, for instance? My answers to these questions are, first, that the relation is necessitation, absolute necessitation, and, second, that every truth has a truthmaker. I will call these positions respectively 'Truthmaker Necessitarianism' and 'Truthmaker Maximalism'."- D. M. Armstrong, pp. 5, Truth and Truthmakers, 2004, Cambridge University Press.

Paradox of Analysis and Reduction

Lots of interesting issues came up today. One of them concerned what, exactly, we're trying to do when we attempt to give a philosophical analysis. Jeff King has a good discussion of that issue here. Another issue concerned reduction. One idea we discussed was that a reductive account of something gives some sort of account in terms of a more fundamental ontological level. This presupposes that there are distinct ontological levels and some are more fundamental than others in the sense that more fundamental levels are more real than less fundamental levels. Ned Markosian discusses that presupposition here.

Re-characterizing realism

Let’s call any sentence in which a modal word such as “possible”, “necessary”, “impossible”, “can”, “cannot” etc. plays a decisive role in determining the truth of that sentence a “modal sentence”.
A modal realist(MR) would subscribe to the following:
a) There are modal sentences.
b) The truth values of some modal sentences are fixed by the behavior of something(s) that is not both actual and concrete. (call these things m-entities)
c) M-entities exist.

A genuine modal realist (GMR) would add the following:
d) Some m-entities are concrete

An abstract modal realist (AMR) would add the following:
e) No M-entities are concrete.

Note that (d) -> (f)
(f) Some m-entities are non-actual

And that (e) is compatible with (g)
(g) All m-entities are actual

Note that (d)-> ~(e) and (e) -> ~(d), thus GM and AM are exclusive. Note also that ~(d) -> (e) and ~(e) -> (d), thus GM and AM are exhaustive.

A couple things are worth noting here. If we're speaking of possible worlds (for example), the m-entities would be all merely possible worlds. I'm not trying to parse out what different theories think of the actual concrete world (and actual concrete objects), since that is trivial (I hope) and would make the characterization needlessly confusing.
It may seem that (b) makes (c) redundant, but I threw (c) in to exclude noneism.
The versions of abstract realism he mentions in the book still fall under AMR under my characterization. In addition, Soames would count as an AMR under my characterization.
A fault of this characterization is the extremely vague notion of a "modal sentence" I employed. I'm still kind of fuzzy on the whole relationship between everyday english usage and the more strict philosophical talk. If only english had boxes and daimonds!

OPC2

The 2nd Online Philosophy Conference is here. There is only one metaphysics paper in the first week and it's by Delia Graff Fara with comments from Ted Sider and Joseph Melia. The discussion gets technical, but the basic problem she raises for Lewis is not terribly hard to grasp.

Characterizing the Positions

There are several things I don't like about the way things proceed in chapter 2. A major problem I have is that views that seem intuitively relevant to the sort of debate that Divers wants to consider are rendered irrelevant to the debate given the way things are set up in chapter 2. A good example of a position that is defined away by Divers is presented in the first ten pages of Scott Soames's "Actually".

Necessity, Contingency, and Essence

Today I gave a brief consideration that could be turned into an argument against the following thesis from Divers (which Divers was just presenting, not defending):

(1) x is essentially F iff for all metaphysically possible worlds w, if x exists in w then x is F in w.

Here is a case (this is from Kit Fine's "Essence and Modality"): the essential properties of an object, in the Aristotelian sense, stem from the nature or identity of that object. Intuitively, it is no part of the nature of Sparky that he is a member of a set. But if he exists at w, then he is a member of a set at w. So by (1), being a member of a set is an essential feature of Sparky. So (1) is false. (I hope it's obvious how to make this argument valid.)

If this is right, then the right-to-left direction of (1) fails, but (2) may still be plausible:

(2) If x is essentially F, then for all metaphysically possible worlds w, x is F in w.

Carl suggested that Ben rejects (1) because of the "existence restriction" in the right-hand side. I take it that Ben instead endorses (3) (?):

(3) x is essentially F iff for all metaphysically possible worlds w, x is F in w.

(I assume Ben holds that objects can have properties at worlds where they are absent? (Homework: State the assumption I am attributing to Ben in a way that does not imply the truth of that assumption.))

So if one accepted both Fine's argument and Ben's point, the (partial) account would be (4):

(4) If x is essentally F, then for all metaphysically possible worlds w, x is F in w.

Joe Salerno at Knowability argues here that there are contingent essential properties. So his view is that (5) is correct:

(5) x is essentially F iff if nothing were F, then x would not exist.

This account has several interesting features. One of them is that the right-hand-side counterfactual conditional is, on his view, not vacuously true if the antecedent is impossible. Any thoughts on which, if any of these accounts, is correct, or on what, if anything, can be added to (2) or (4) to yield a more complete account?