Lewis on possible worlds and the grounds of modality

Friends of primitive powers and dispositions often contrast their view with an alternative view, usually attributed to Lewis, on which modal facts about powers, dispositions, laws, counterfactuals etc. are grounded in facts about other possible worlds. But Lewis never held that alternative view – nor did anyone else, as far as I know. The allegedly mainstream alternative is entirely made of straw. The real alternative that should be addressed is the reductionist view that powers and dispositions are reducible to ultimately non-modal elements of the actual world.

Unlike in the case of reference magnetism, the exegetical question is straightforward. Lewis nowhere suggests that natural modality is grounded in other possible worlds.

On the contrary, he declares it an a priori truth that "any contingent truth whatsoever is made true, somehow, by the pattern of instantiation of fundamental properties and relations by particular things" in the actual world ("Humean Supervenience Debugged", p.225). Lewis's hypothesis of Humean Supervenience is a stronger and more speculative version of this assumption, adding that the relevant fundamental properties are all properties of spacetime points and that the only fundamental relations are spatiotemporal relations.

Recall Lewis's most memorable definition of Humean Supervenience:

Humean supervenience is named in honor of the greater denier of necessary connections. It is the doctrine that all there is to the world is a vast mosaic of local matters of particular fact, just one little thing and then another. (But it is no part of the thesis that these local matters are mental.) We have geometry: a system of external relations of spatiotemporal distance between points. Maybe points of spacetime itself, maybe point-sized bits of matter or aether or fields, maybe both. And at those points we have local qualities: perfectly natural intrinsic properties which need nothing bigger than a point at which to be 1instantiated. For short: we have an arrangement of qualities. And that is all. There is no difference without difference in the arrangement of qualities. All else supervenes on that. (Introduction to Philosophical Papers II, pp.ix-x)

No mention here of other possible worlds.

So when it comes to natural modality – powers, dispositions, laws, chance, counterfactuals, and the like – Lewis's position is simply a form of reductionism: he accepts that there are truths of these kinds, but holds that they are ultimately made true by non-modal features of our world. Much of Lewis's work in metaphysics can be seen as filling in the details.

Why do people get this wrong? Where do the rumours come from that Lewis wanted to ground modal truths in truths about other worlds? I don't know. I can think of two explanations.

The first is a deep conviction that modal facts can't possibly be reduced to ordinary non-modal facts, combined with the knowledge that David Lewis (whose work one hasn't actually read) endorsed "modal realism", the view that other possible worlds are just as real and concrete as the actual world. This suggests that Lewis might have proposed the realm of other possible worlds to ground modal facts.

Barbara Vetter nicely expresses something like this in "'Can' without possible worlds" (2013, p.1):

The world (the actual world, which we inhabit), for Lewis and his followers, is modally empty: it contains 'a vast mosaic of local matters of particular fact, just one little thing and then another. ... we have an arrangement of qualities. And that is all.’ (Lewis 1986, ix f.) Modality, for Lewis and Lewisians, has to come from outside that mosaic if it is to be real: it has to be outsourced to other possible worlds.

That modality could be real but reducible – Lewis's actual view – doesn't seem to cross her mind.

A second possible explanation is that people misunderstand the role of possible worlds in Lewis's semantic analyses. In Counterfactuals (1973), for example, Lewis invokes possible worlds to express truth-conditions for counterfactuals: roughly, 'if A then B' is true at a world w iff B is true at all the closest A-worlds to w. One might think this biconditional ('...iff...') specifies the metaphysical grounds for the truth of counterfactuals: what makes it true that I would hurt my head if I were to bang it into the wall are certain basic relations between possible worlds.

This is clearly not how Lewis himself understood the analysis, as he explicitly says (in the introduction to Philosophical Pappers II) that the analysis supports Humean Supervenience. How is that supposed to work?

For a start, note that the "closeness" in Lewis's analysis is an internal relation insofar as the relative closeness between three worlds w1, w2, w3 is a matter of the intrinsic nature of these worlds (unlike closeness between cities). Second, recall that for Lewis what possible worlds there are is not a contingent matter: the space of worlds is fixed once and for all (Plurality, p.80). So whether the actual world is closer to some world w2 than to another world w3 depends only on the intrinsic properties of the actual world. Invoking the other worlds is just a convenient shortcut to isolate the relevant intrinsic properties. In "Ordering semantics and premise semantics" (1981), Lewis actually shows how one could equivalently do without the shortcut.

A comparison may help. Lewis analysed belief in terms of (centred) possible worlds: you believe a proposition just in case the proposition is true at all your doxastically accessible worlds (e.g. Plurality, pp.27-36). But he did not hold that in order to have a belief one must stand in a mysterious, substantive relation to other possible worlds; the possible-worlds analysis was not meant to provide the metaphysical grounds for beliefs. Instead, Lewis held that to have a given system of beliefs and desires is to be in a state with a characteristic causal role (e.g. Plurality, pp.36-40). The possible worlds are just a convenient way of picking out the relevant roles.

In any case, the idea that counterfactuals have uniform metaphysical grounds is absurd. Any truth p is logically equivalent to if p then actually p.

So these are the two explanations I can think of for the widespread assumption that Lewis held modal facts to be grounded in facts about possible worlds. Am I missing something?

Of course, there's another relevant consideration: the supposedly Lewisian idea is really unappealing. (There's a reason why practically nobody ever endorsed it!) Presenting it as the main rival to anti-Humean primitivism therefore makes primitivism look sensible and attractive.

But it's not the main rival. The real rivals are Humean reductionism and Humean projectivism. Forget about the possible worlds.


# on 09 July 2017, 03:50

I have been dimly aware of what you're pointing out here for a while, but always confused by it. I'm still confused. (Full disclosure: I am not a Lewisian, and while I love his work on counterfactuals and have spent long hours wrestling - mainly as an antagonistic outsider - with On the Plurality of Worlds, I am not really steeped in his work.)

One thing that puzzles me about what you're saying is: if possible world talk, for Lewis, is just a kind of convenience or shortcut, how could he think there was such a strong case for believing in a plurality of concrete worlds? Reading On the Plurality of Worlds, I do not get the impression that the 'philosophers' paradise' he attempts to conjure up is a paradise because we get to take some convenient shortcuts in our expression of things.

I find myself suspicious that Lewis might have different views and tendencies here which are in tension with one another, and that you might just be privileging certain parts of his philosophy at the expense of others.

Also, what role is your singling out of *natural* modality playing here? Are there, in addition to the natural modal facts, other modal facts which perhaps are best thought of, on Lewis's philosophy, as grounded by possible worlds?

I hope you won't judge this comment too harshly.

# on 10 July 2017, 11:28

Interesting stuff, though I think you're being a little uncharitable to Vetter. I read her as talking primarily about non-contingent modal truths, e.g. truths about what is unrestrictedly necessary and possible. While all contingent truths are indeed meant to supervene on the actual, non-contingent modal truths (including all unrestricted de dicto necessity and possibility claims, for Lewis?) fall outside the scope of Humean Supervenience. Presumably Lewis would have rejected any claims about grounding that go beyond supervenience claims for the reasons he gives in 'Reduction of Mind', but still it looks natural for grounding fans who are also modal realists to say that, for example, the fact that there could have been a blue swan is grounded in facts about the swan distribution across other possible worlds.

# on 10 July 2017, 14:06

i agree that it would be nice to see clearer evidence of people making the claim in question about lewis on natural modality (as al says, the vetter passage can be naturally read as concerning metaphysical modality). also, while i agree with the spirit of what you say (lewis is basically a reductionist about natural modality), i'm surprised to see you deny that lewis held that "modal facts about ... counterfactuals etc. are grounded in facts about other possible worlds". he gave an analysis of counterfactuals that pretty clearly did so ground them, at least in part. it's just that for lewis, grounding in facts about other possible worlds is not inconsistent with reduction to facts about the actual world -- roughly because lewis took reduction to be more or less equivalent to necessitation/supervenience (at least for domains other than metaphysical modality itself), and the relevant facts about other possible worlds are necessary.

# on 10 July 2017, 15:39

Hi all! Thanks for the feedback.

I think it's clear from the context of the Vetter passage that she doesn't talk (exclusively) about metaphysical modality. The topic of her paper are modal properties such as "abilities, capacities, powers, dispositions". In the context of the quote, she contrasts her view, on which these properties are irreducible, with the supposedly Lewisian view on which they are grounded in facts about possible worlds. In the paragraph right before the quote, she suggests that according to Lewis, she is able to write the paper because (ultimately) one of her counterparts writes it.

Anyway, I've definitely come across the claim on several occasions. I remember a recent talk by Matt Tugby -- can't find it in print though.

I don't think Lewis's analysis of counterfactuals grounds them (in part) in facts about other worlds, for the reasons I gave: what makes a counterfactual true are always intrinsic features of the actual world.

Here's a relevant passage from Plurality (p.22), where he also addresses the challenged mentioned by Tristan:

"A challenge which goes deeper, and which does question the utility of bringing possible worlds into the story, goes as follows. ... It's the character of our world that makes some A-worlds be closer to it than others. So, after all, it's the character of our world that makes the counterfactual true - in which case why bring the other worlds into the story at all? To which I reply that [it] is indeed the character of our world that makes the counterfactual true. But it is only by bringing the other worlds into the story that we can say in any concise way what character it takes to make what counterfactuals true."

So yes, in this case at least, all we get is some convenient shortcuts in our expression of things.

I agree that the issue becomes murkier for non-contingent modal truths, mainly because it's not clear what Lewis thought about the grounds or truthmakers of such truths. As Al mentioned, there's a plausible reading of Lewis on which he held that (absolutely) necessary truths just don't have grounds or truthmakers. On the other hand, a substantial part of Lewis's metaphysics seems to deal with just such truths: truths about absolute modality, for example, or about mathematics. In Plurality, he presents it as a great advantage of Modal Realism that it avoids primitive modality, which certainly suggests that the account somehow allows a reduction of (absolute) modality.

So there might be a tension here. If we can attribute to Lewis a hyperintensional conception of grounding that is applicable to non-contingent truths, then perhaps we could also attribute to him the view that counterfactuals are partially grounded (in this sense) in facts about other worlds. But I wouldn't say it's "pretty clear" that he held such a view.

It's probably relevant that for Lewis there is no interesting intermediary between sets-of-worlds propositions and linguistic sentences. So when we ask whether some truth X is reducible or grounded in such-and-such, we're either asking about the proposition (set of worlds) X or about a sequence of symbols X. Clearly hyperintensional notions of grounding are not applicable to propositions. So when we talk about non-contingent X, we have to talk about a linguistic construction X. This fits the fact that Lewis usually talks about /analysing/ such truths. There is a possible-worlds /analysis/ of counterfactuals and other modal expressions in natural language. But there is no possible-worlds account of what makes the propositions expressed by these sentences true.

# on 10 July 2017, 17:23

Interesting post Wolfgang, thanks! I think it would be a great starting point of discussion for any dispositionalist. I agree with you that some dispositionalist might have put things in this way (modality grounded on powers vs modality grounded on possible worlds). And I agree that this is not the best way to frame the debate. My preferred way is to say that, while neohumeanism take facts about natural modality to be posterior to facts about the pattern of properties’ instantiation (which is either brute, or to be explained in terms of other-world pattern), dispositionalism take modality to be prior to pattern of instantiation (which is determined/explained by the modal nature of properties, or more simply by *modal properties*, aka powers). This, I think, is the core difference between neohumeanism and dispositionalism. I also think dispositionalism, at least presented in this way, shows what is the core requirement that every non-humean theory of modality more generally should satisfy in order to be properly non-humean.

ps: I think you've been a bit uncharitable with Barbara, as she indeed challenges exactly what you presented as a "real alternative" . Also, I'm not aware Matt does so on paper (maybe he offered such a view during a talk, but that I don't know).

# on 11 July 2017, 08:54

@Andrea: Agreed, that sounds like useful way of putting the difference.

I didn't mean to be uncharitable with Barbara. I do think she sets up her position against a strawman, but of course the position she defends is a genuine alternative not only to the strawman but also to genuine Humeanism.

I'm happy to hear that what I took to be a quite common thought (the misinterpretation of Lewis) isn't that common after all. I guess I was exposed to a non-representative sample.

# on 11 July 2017, 11:48

Hi Wo,

I agree with you that this misunderstanding is widespread. I remember commenting on a paper by a pretty well known philosopher at a conference at least two decades ago who insisted that Lewis reduced natural modality to other possible worlds I think part of the fault is Kripke's who is often quoted as objecting to Lewis by asking "what does the fact that a counterpart to this match ignites in another world have to do with whether this match would ignite if struck' I don't know any source for this in Kripke's writing but the philosopher I mentioned earlier insisted that he heard Kripke say this.


# on 08 April 2018, 18:56

It is really difficult to see how the intrinsic features of the actual world could ground counterfactuals. Here's one obvious reason. We cannot determine from the intrinsic features of the actual world whether there is more than one possible world. We cannot read off the intrinsic features of the actual world that our world is not, for instance, a Spinozistic world. If it is--if there is just one possible world--then counterfactuals are ion general trivially true. So there really do have to be these other possible worlds, if any counterfactuals are non-trivially true.

# on 09 April 2018, 10:31

Hi Mike,

right, I should have mentioned this line of thought as another reason for the misunderstanding. It's still a misunderstanding though.

Lewis's analysis of counterfactuals /presupposes/ that there is a plentitude of possible worlds. If one believes there is only one possible world, the analysis becomes completely implausible. In a context where the plentitude of worlds is in doubt, the analysis itself is therefore in doubt. So on Lewis's view, if (per impossibile) there is only one possible world, we cannot conclude that all counterfactuals are trivially true. Rather, we have to revise our semantics for counterfactuals.

As I mentioned in the post, for Lewis the plurality of worlds is not a contingent or a posteriori fact, and therefore doesn't enter into the truth-makers of anything.

# on 09 April 2018, 13:50

Thanks Wo!. Couple of other questions. If the analysis depends on there being a plurality of worlds, then the truth or falsity of counterfactuals is not simply read off 'the pattern of instantiation of fundamental properties and relations by particular things'. It depends in addition on there existing a plenitude of worlds. Isn't that what you've been denying? The fact that the pluriverse is necessarily existing (I agree it is) doesn't affect the fact that the truth-value of counterfactuals (under Lewis's analysis) depends on there being such a necessarily existing pluriverse. Hard to see how it is not a truthmaker. Suppose we offer an alternative analysis that presupposes there is no pluriverse. Counterfactuals under that presupposition depend on the non-existence of the pluriverse. Either way, something other than 'the pattern of instantiation of fundamental properties and relations by particular things' is relevant to the truth or falsity of counterfactuals.

# on 10 April 2018, 12:17

@Mike: Yes, I'm denying that on Lewis's view the truth or falsity of counterfactuals depends on anything other than the character of the actual world. Lewis himself says as much, so the question is what he meant by that.

The point is relatively straightforward on a merely intensional (as opposed to hyperintensional) conception of dependence or truthmaking. On such a conception, nothing at all depends on things that are necessary and a priori. When Lewis talks about Humean Supervenience, he often expresses his views in merely intensional terms (e.g., in terms of "supervenience"). So that's a simple explanation.

Merely intensional dependence is sufficient to answer your worry about reading off: if it is a priori that there is a plurality of worlds, then one /can/ in principle read off the truth of counterfactuals from the pattern of instantiation of fundamental properties and relations: no further information is required.

You might nonetheless object that there's a more important hyperintensional conception of metaphysical dependence on which things look different. But (a) I'm not sure if there is such a conception or that there is one in Lewis's metaphysics (although the matter is tricky). Moreover, (b) it's not obvious that the hyperintensional conception gives us the supposed dependence on other worlds.

If, as I suggested above, Lewis's analysis of counterfactuals presupposes the plurality of worlds, then it simply doesn't tell us whether a given counterfactual is true or false on the supposition that there are no other worlds.

A comparison: suppose I say that "X is taller than Y" should be analysed as "X's height in meters is greater than Y's height in meters", thereby reducing the taller-than relation between physical objects to the greater-then relation between numbers. Would you say that on my proposal, facts about comparative tallness are made true by the existence of numbers? At best, I'd say that's a very misleading characterisation. My suggestion presupposes the existence and plentitude of numbers. If we're suspending our belief in numbers, of course I would suspend my suggestion.

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