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.
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