Modal Realism and Counterpossibles: A Tension in Lewis

David Lewis held that possible worlds are worlds as concrete as our own (cf. Lewis (1986)). He also held, in his work on counterfactuals (cf. Lewis (1973)), that all counterfactuals with impossible antecedents - 'counterpossibles' - are vacuously true. These two views do not fit together well. Embracing modal realism leads to especially compelling counterexamples - counterexamples given modal realism, that is - to the thesis that counterpossibles are all true. These take the form of conditionals whose antecedents are not intuitively impossible, but which are impossible given modal realism.

These arise because, according to modal realism, reality as a whole – that is, the totality of the posited worlds – is necessarily the way it is. Lewis is very upfront about this. Witness:

There is but one totality of worlds; it is not a world; it could not have been different. (Lewis 1986: 80.)

So, for example:

'If there had been two fewer men in reality as a whole than there actually are, there would have been fewer women.'

There is no reason to think this is true. And yet Lewis's thesis about counterpossibles, together with modal realism, implies that it is vacuously true.

Perhaps worse:

'If there had been fewer men in reality as a whole than there actually are, there would have been just as many men in reality as a whole as there actually are.'

This seems positively false.

Postscript

Thanks to Quentin Ruyant for pointing out that the last counterfactual, given modal realism and the thesis that there are infinitely many worlds with men in them, actually seems to come out true in a funny way: if there had been two fewer men, there still would have been infinitely many. So this was a bad example. Consider instead:

'If there had been no Model-T Fords in reality as a whole, there still would have been some Model-T Fords in reality as a whole'.

References

Lewis, David K. (1973). Counterfactuals. Blackwell Publishers.

Lewis, David K. (1986). On the Plurality of Worlds. Blackwell Publishers.

The Humphrey Objection to Modal Realism

The Humphrey objection to modal realism, due to Kripke, centres on counterpart theory, and alleges that this assigns counterintuitive truth-conditions to modal statements about individuals. It is historically important, as Kripke made the objection in his influential Naming and Necessity lectures, long before Lewis published his full defence of modal realism in 1986.

Kripke put the objection as follows:

Thus if we say "Humphrey might have won the election (if only he had done such-and-such)”, we are not talking about something that might have happened to Humphrey but to someone else, a "counterpart". Probably, however, Humphrey could not care less whether someone else, no matter how much resembling him, would have been victorious in another possible world. Thus, Lewis's view seems to me even more bizarre than the usual notions of transworld identification that it replaces. (Kripke 1980:45 note 13.)

It is by now, I think, pretty widely accepted that Kripke, while he may have been on to something here, did not put the point optimally. To the objection put this way, there is a cogent response: it is not correct to say that, according to counterpart-theoretic modal realism, we 'are not talking about something that might have happened to Humphrey'. What counterpart-theoretic says is that talk about 'what might have happened to Humphrey' is to be analyzed in terms of what does happen to his counterparts in other worlds. So according to the counterpart-theoretic modal realist, when we say 'Humphrey might have won the election', we are indeed talking about what might have happened to Humphrey. Their characteristic claim is to add that this thing we're talking about is to be analyzed in terms of what happens to counterparts. (Lewis drives this point home in On the Plurality of Worlds.)

Similarly, the second part of Kripke's objection – that 'Humphrey could not care less whether someone else, no matter how much resembling him, would have been victorious in another possible world' – can be convincingly argued to miss the mark. The counterpart-theoretic modal realist can agree that Humphrey could not care less about this. For the way they analyze talk about whether 'someone else' (a counterpart) 'would have been victorious in another possible world' is in terms of counterparts of that someone else – counterparts of Humphrey's counterparts. And it is compatible with Humphrey not being interested in what happens to the counterparts of some one of his counterparts, that he be interested in something which – upon analysis – turns out to be a question of what happens to his own counterparts.

This last point may be a bit pedantic, however. What if we simply reform the second part of Kripke's objection by changing the 'would have been' to an 'is'? This yields: 'Humphrey could not care less whether someone else, no matter how much resembling him, is victorious in another possible world?'

This is better, but there is still a strong reply. As Sider says in his unpublished 'Beyond the Humphrey Objection', this is 'just the paradox of analysis':

A reasonable person can care about a property under one description (“possibly winning”) while not caring about the same property under another description (“having a counterpart who wins”), provided it is not obvious that the descriptions pick out the same property. Correct analyses need not be obvious to competent language users. Obviousness may count for something, but theoretical virtues are important as well in determining which analyses we ought to accept (p. 2)

I endorse this as a response to the version of the Humphrey objection just considered. However, I want presently to register a difference with Sider about whether this response also works for another version of the objection.

This other version puts aside what Humphrey cares about, and appeals directly to our intuitions. Sider puts this version of the objection as follows: 'Look, it is just obvious that possibly winning is not the same as having a counterpart who wins' (pp. 1 – 2) And the response quoted above is put forward by Sider as a response to both the previously considered version and this one. (He explicitly prefaces the passage with 'Reply to ii) and iii)' (p. 2).)

Does Sider's response apply here too? On reflection, I think clearly not. The response makes the point that a correct analysis need not be obvious (while granting that obviousness may count for something). But the present version of the objection is alleging, not that it isn't obvious, but that it is obviously not the case. Sider, in putting the passage in question forward as a response to this, is sliding from '(~p) is obvious' to '~(p is obvious)' and thus failing to address the objection.

So we seem to have a version of the Humphrey objection which is stronger than the others so far considered. But we can improve it further by getting away from obviousness altogether, which is a red herring. Saying that possibly winning is obviously not the same as having a winning counterpart risks being too strong. The rhetorically wise thing to do is tone it down, and simply enter a plea that it doesn't intuitively seem that possibly winning is the same as having a winning counterpart. Or putting the point semantically: the truth-condition Lewis assigns to 'Humphrey could have won' is counterintuitive.

So, despite the availability of strong responses to the original and certain subsequent versions of the Humphrey objection, the core point remains that the truth-condition assigned by Lewis is counterintuitive.

(Incidentally, Lewis suggested that forms of ersatzism are no better on this score: in that case, what “gets into the act” is not another person, but 'some abstract whatnot' (Lewis 1986, p. 194.) This isn't a strong reply to the objection, of course, as ersatzism is far from the only other game in town when it comes to the semantics of modal attributions such as 'Humphrey might have won'. Nevertheless and for what it's worth: perhaps an abstract whatnot getting into the act is, from an intuitive point of view, not quite as bad as another person getting into the act. Bringing in another person, it seems to me, feels more like crowding out Humphrey, more like putting something in his place.)

So, there is a version of the Humphrey objection which has some force. However, modal realism with overlap, in contrast to counterpart-theoretic modal realism a la Lewis, is immune to the Humphrey objection. Lewis wasn't swayed by this, since he had reasons to think modal realism with overlap unpalatable. Since then, advocates of overlap have, as might have been predicted, emerged (most notably McDaniel in his (2004), 'Modal Realism with Overlap').

It may be that the considerations against overlap are quite compelling, in which case these together with the Humphrey objection (once it is freed from its initial faulty formulation) have significant force against modal realism in general. However, I do not want to get deep into comparing the relative merits of counterpart-theoretic modal realism and modal realism with overlap, and would prefer to have an objection along similar lines which applies to both. Therefore, I advocate that we take the Humphrey objection, not just as a self-sufficient objection which affects the dominant form of modal realism but not modal realism with overlap, but also as a clue: modal realism – in both flavours – may be counterintuitive on the semantic front, and this may be a good reason to reject it. Since the Humphrey objection itself fails to apply to modal realism with overlap, we should set it aside and go on to try for a more general semantic objection. I hope to develop this in a future post.

References

Kripke, Saul A. (1980). Naming and Necessity. Harvard University Press.

Lewis, David K. (1986). On the Plurality of Worlds. Blackwell Publishers.

McDaniel, Kris (2004). Modal realism with overlap. Australasian Journal of Philosophy 82 (1):137 – 152.

Sider, Theodore. unpublished. Beyond the Humphrey Objection.

Modal Realism

This is just an expository post, but I hope to make some original points in subsequent posts which will consider objections to modal realism.

Central to modal realism are the Leibnizian biconditionals,

(Leib­NEC) A proposition is necessary iff it is true in all possible worlds.
(Leib­POSS) A proposition is possible iff it is true at some possible world.

These tie attributions of necessity and possibility to quantificational statements about possible worlds. Different philosophical accounts which use these sentences accounts differ over what sorts of things possible worlds are taken to be, and over the role given to the Leibnizian biconditionals. (With typical forms of modal fictionalism, the biconditionals are typically augmented with an 'According to F' operator, where 'F' names a fiction.) The distinctive marks of modal realism, setting it apart from other philosophical uses of the Leibnizian biconditionals, are that it takes possible worlds to be of the same kind as the actual, concrete world we live in, that it takes the Leibnizian biconditionals to be true all by themselves (no fiction operator required), and that it takes these to constitute analyses of the modal notions appearing on the left hand sides.

The chief proponent and developer of modal realism, David Lewis, intends it to be a reductive account of modality – so his theory of possible worlds must be spelled out non­modally. Accordingly, the 'possible' in 'possible world(s)' on the right hand sides of the biconditionals is not supposed to be taken as anything more than part of a conventional, historically familiar way of referring to the worlds which do the work in his account. 

Such is the theory of modal realism in broad outline. Its characteristic commitments may be summed up in one sentence as 'There are other worlds, and every way our world might have been is a way some world is' (cf. Lewis 1986, p. 2).

In future posts I want to consider some objections to modal realism, but first let us consider in a preliminary way three finer points about the theory.

One finer point concerns the individuation of worlds. As Lewis phrases the question, 'What makes  two things worldmates? How are the worlds demarcated one from another? Why don't all the possibilia comprise one big world? Or, at the other extreme, why isn't each possible neutrino a little world of its own?' (Lewis 1986, p.70). Lewis's answer to this is: spatiotemporal relatedness. '[W]henever two possible individuals are spatiotemporally related, they are worldmates. If there is any distance between them – be it great or small, spatial or temporal – they are parts of one single world.' (This gives rise to an objection – the island universes objection – based on the idea that we should not in our analysis of modality rule out the possibility of a world with multiple spatiotemporally unrelated “universes”. I will not consider this objection at length, but cf. Lewis 1986, p. 71, Bricker 2001 and Vacek 2013.)

The second finer point concerns the treatment of propositions about particular individuals, and how they are to be evaluated with respect to worlds other than our own (or more generally, worlds other than the one from which the propositions in question are being evaluated). To begin with, note that general statements pose no corresponding difficulty. Going along with the modal realist's doctrine that there are other worlds, a question like 'Is “All swans are white” true at all worlds?' seems to have a straightforward meaning (at least given the familiar point that we want to hold fixed the meaning of the sentence in question when evaluating the proposition with respect to other worlds). But if we ask 'Is “John is white” true at all worlds?', where John is some actual swan, the question arises: does John himself exist at any of the other worlds?

The two different answers we might give to this question correspond to different forms of modal realism. If we answer in the affirmative, we get what is called modal realism with overlap. If we answer in the negative, get what is called modal realism without overlap. The canonical form of modal realism, David Lewis's as developed in his (1986), is of the latter sort. In order to enable us to evaluate propositions about particular individuals with respect to other worlds in the framework of modal realism without overlap, Lewis developed a theory of counterparts. To evaluate 'John is white' at some world W, we as it were look at that world and select the closest counterpart to our this-­worldly swan John, and then consider whether that swan is white. If so, we say that 'John is white' is true at W. This approach has been felt to be damagingly counterintuitive, giving rise to an objection originated by Saul Kripke called the Humphrey objection, which we will consider in a futute post.

The third and final finer point I want to note concerns the issue of what, if anything, modal realism has to say about the extent or range of the worlds – what worlds are there, and what are they like? As Lewis saw the matter, it was incumbent on him to provide principles which so to speak “generate” sufficient worlds, so that there is one for every possibility. To this end he proposed a principle of recombination, but he admitted that this was inadequate (Lewis 1986, p. 92). More recently, it has been questioned whether any such principles are needed for the theory qua analysis of modality (cf. Cameron 2012).

Note that modal realism is obviously free of the chief defects of pre-Kripkean analyticity approaches – the modal realist analysis does not push us toward the conclusions, implausible ever since Kripke, that necessary truths are true in virtue of meaning, or that they are all a priori. This is one of the things which, together with the boldness and clearness (at least in a certain sense) of the theory, makes it such a serious contender given the present state of play.

In future posts I will consider objections to modal realism, some of which we have just alluded to. My ultimate conclusion will be that the most serious objections are very serious indeed, and devastating when taken together. (General methodological qualms about certainty in philosophy aside, I believe that the theory is certainly incorrect. But it is profoundly incorrect and cannot be discussed too carefully. This series of posts will necessarily fall short of plumbing the full depths of the matter.)

References

Bricker, Phillip (2001). Island Universes and the Analysis of Modality. In G. Preyer & F. Siebelt (eds.), Reality and Humean Supervenience: Essays on the Philosophy of David Lewis. Rowman and Littlefield.

Cameron, Ross P. (2012). Why Lewis's analysis of modality succeeds in its reductive ambitions. Philosophers' Imprint 12 (8).

Lewis, David K. (1986). On the Plurality of Worlds. Blackwell Publishers.

Vacek, M. (2013). Modal Realism and Philosophical Analysis: The Case of Island Universes FILOZOFIA 68, No 10, p. 868-876.