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Is modal realism innate?

It seems to be: I've never heard of anyone being converted to modal realism, or giving it up. In particular, Lewis himself endorses it in his earliest papers, e.g. in the conclusion of 'Convention'. According to this article from the Daily Princetonian, he "worked on" the topic already at the age of 16. Strange.

Is the empty set false?

In "Two Concepts of Modality", Alvin Plantinga argues that propositions aren't sets of worlds, because "you can't believe a set, and a set can't be either true or false" [208]. I think this argument is better than it might appear in the rather Ungerian context of Plantinga's paper, where he uses several arguments of the same kind to support completely crazy views, like that Lewis is an antirealist about possible worlds.

The traditional job description for propositions says that they are a) the ultimate bearers of truth-values, b) the content/object of propositional attitudes, and c) the meanings of declarative sentences. Plantinga is right that sets aren't the most intuitive candidates for this job: Is the empty set an 'ultimate bearer' of the truth-value false? Is it the content of Frege's belief in Axiom 5? Is it what you have to know in order to understand Axiom 5? Well, intuitively not, but I don't think intuition is to judge questions like these. More importantly, there are reasons against the identification of sets with propositions.

Counterfactual confusion

I'm currently writing a chapter on modal realism. I don't like this topic because it always confuses me. Here is one such confusion.

In some world w, pretty much resembling our world, there are two individuals A and B. Let 'A-in-w' be an extremely rich descriptions of A that implies every qualitative truth about w, similarly for 'B-in-w' and B. Now the following two sentences might both be true:

1) If I were A-in-w, I would do X.

2) If I were B-in-w, I wouldn't do X.

Diffbot

I often visited blogs and other websites just to see that nothing has changed there. No more. To save these wasted minutes I've wasted some hours on writing a little script that keeps track of the latest updates of all those websites and displays them using diff.

Lewis on worms and stages

It is easy to overlook that David Lewis has revised his worm view of ordinary things in 'Tensing the Copula', Mind 111 (2002). Here is the passage (p.5):

In talking about what is true at a certain time, we can, and we very often do, restrict our domain of discourse so as to ignore everything located elsewhere in time. Restricted the domain in this way, your temporal part at t_1 is deemed to be the whole of you. So there is a good sense in which you do, after all, have *bent simpliciter*.

In other words: Terms for ordinary things are indeterminate. They don't always pick out worms. Sometimes they pick out segments, and sometimes just stages, depending on the contextually determined domain of discourse.

I think this is an improvement over the worm theory. Is it general enough? Lewis says that our terms pick out the sum of all those temporal parts of the relevant worm that are inside the domain of discourse. But don't we also attribute bent-simpliciter to the whole of me in "I'm bent now, but I wasn't bent yesterday"? Yet here the domain contains yesterday's parts as well.

Describing the world

Brian Weatherson now says that 'the world exists' is exactly as natural as 'there is a G', where G applies to worlds that are exactly like this one. I agree. But this only makes things worse, because the class G denotes seems very natural: It contains our world and all its exact intrinsic duplicates. Is this a gruesome gerrymander? We still need a further restriction on best theories apart from naturalness.

How gruesome is the world?

Intuitively, some objects are more natural than others. For example, cats are more natural than mereological fusions of cats and elephants. I think that ultimately, naturalness of things should be definable in terms of naturalness of the properties the things instantiate. I'm not quite sure how exactly this is to be done, so for now I'll stick with the intuitive notion of naturalness. Intuitively natural things are spatiotemporally connected, constitute a causal unity, contrast with their surroundings, etc. The world, that is, the mereological fusion of everything that exists at any spacetime distance from us, does fairly well here: As far as I know, it is perfectly connected, causally united (indeed, causally closed) and contrasts clearly with everything outside of it (such as numbers or other worlds, if such there be). Why then does Brian Weatherson think that the world is gruesome?

I see two ways to exclude 'the world exists' as the best theory of everything. The first is the one I already mentioned: to state that a good theory must imply interesting truths a priori. The second is to stipulate that a theory must not contain individual constants. I have some sympathy with such a stipulation, though it may stipulate away haecceitism.

Things and Fusions

It is sometimes (e.g. in David Sanford, 'Fusion Confusion', Analysis 63, 2003) said that some things are not fusions of all their parts: cats and fusions of cat-parts for instance seem to differ in tensed and modal properties. It may be noteworthy that on the standard definition of 'fusion', this position is outright inconsistent: X is the fusion of Y1,Y2,... iff all of Y1,Y2,... are parts of X and no part of X is distinct from all of Y1,Y2,.... Hence if X is not the fusion of Y1,Y2,... then either one of Y1,Y2,... is not a part of X or some part of X does not overlap Y1,Y2,.... So nothing can possibly fail to be the fusion of all its parts.

L.A. Paul's logical parts

In her paper 'Logical Parts', forthcoming in the december issue of Nous, L.A. Paul presents a nice theory of objects according to which things are mereologically composed of their properties. Here are a couple of potential problems.

First, the theory seems to conflict with Unrestricted Composition and incompatible properties. For suppose that P and Q are incompatible properties, like being square and being round. By Unrestricted Composition, there is a fusion of P and Q (or, if you prefer, of P and Q and Paul's red cup). This fusion has both P and Q as parts, hence, on Paul's theory, it is both P and Q. But if P and Q are incompatible, nothing can be both P and Q.

Worlds qua truthmakers

I have the vague impression that Lewis' paper 'Things qua truthmakers', and in particular the appendix by Lewis and Rosen, proves something important. But I'm not sure what it is. Maybe it's that the request for truthmakers was thoroughly misguided in the first place.

The problem is that the truthmaker principle is saisfied so eaily: Let 'w' be a name for our world that does not apply to any qualitatively different world, nor to anything inside any world. (That is, 'w' denotes our world under a rather strict counterpart relation.) Let T be any qualitative truth. Necessarily, if w exists, then T, since otherwise 'w' would be applicable to a world in which not-T, even though T holds at our world, contrary to the rule just stated. Hence w is a truthmaker for T, that is, for any truth whatsoever.

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