I know Modal Realism well enough itself, and have read many of the objections (and subsequent responses) that David Lewis himself took up in relation to the philosophical position.

My question is, do impossible worlds have to be incorporated in some way if one maintains he/she is a modal realist? I've always had an attraction to the Lewis's idea and I think he gives some pretty strong reasons to consider it. That being said, I don't remotely believe there could be a world with a squared circle or where 1 + 1 = 3. Like many philosophers who have worked on these subjects in logic/metaphysics, I would agree that these world's aren't even conceivable. But if incorporating them is an absolute must for one to maintain a consistent version of the theory, I would definitely start questioning whether I could subscribe to it.

Any input from the people here would be greatly appreciated.

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    Can you clarify what you mean by "incorporate"? It seems like any modal realist must "consider" them and take a position on handling them, but what do you mean by "incorporate"? – virmaior May 23 '16 at 15:19
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    (I'm not sufficiently an expert on modal realism to answer this -- I ran into an interesting critique briefly googling it -- users.ox.ac.uk/~shil0124/mystuff/lycan.html -- but I didn't find an explicit acceptance of "impossible worlds" from Lewis) – virmaior May 23 '16 at 15:19
  • @virmaior my fault for not making it more clear. I literally mean something like "one's ontology as a modal realist must include impossible worlds." I hope that helps! – Pete1187 May 23 '16 at 16:11
  • Modal realism is a philosophical position, i.e. there are no musts. You can specify what you mean by "possible", and if that excludes logical and mathematical impossibilities so be it, you are only committed to existence of possible worlds you declared possible. Although this flexibility should give one a pause concerning modal realism altogether. Even Lewis hints that his "realism" is of make believe variety, and makes case for usefulness rather than reality. – Conifold May 23 '16 at 22:04
  • @Conifold He thought it was all make believe? Here's a quote from Lewis: "When I profess realism about possible worlds, I mean to be taken literally. Possible worlds are what they are, and not some other thing. If asked what sort of thing they are, I cannot give the kind of reply my questioner probably expects: that is, a proposal to reduce possible worlds to something else. I can only ask him to admit that he knows what sort of thing our actual world is, and then explain that possible worlds are more things of that sort, differing not in kind but only in what goes on at them." – Pete1187 May 24 '16 at 14:44

A traditional modal realist, which is a possibilist, would assume that all and only possible worlds are real worlds that exist and that an impossible world is an existing world that is not real. By "existing", I mean "being" in the Kantian sense of specifying particulars pertaining to particular domains of discourse (or universes of objects). Therein, modal realism does not preclude Meinong's Jungle, which is a domain of discourse in which impossible things exist, but before getting to that it is important to establish some foundation.

Perhaps not ironically, your question is a modal question. "Do impossible worlds have to be incorporated in some way if one maintains he/she is a modal realist?" means to ask (as a modal realist), "Are impossible worlds possible worlds?" Answering "yes" seems to pose a contradiction, but the question is not specific enough. "Impossible real worlds are possible real worlds" is a contradiction and "impossible real worlds are possible unreal worlds" is not. That is, if "R" stands for "real world" such that ¬R denotes "unreal world" then ¬◇R∧◇R is a contradiction and ¬◇R∧◇¬R is a tautology.

Much of modern ways of thinking about the metaphysics of modality can be traced back to Leibniz, and Leibniz associated impossibility with contradiction. For him, contradictions were impossible combinations such that, for any ontology, the only necessarily false statements were contradictory statements. To be more specific, necessitatem absolutum, in Leibnizian philosophy, entails truth in all possible worlds by virtue of principium contradictionis. “Les vérités nécessaires sont fondées sur le principe de contradiction” (Leibniz 1686). Likewise, impossibility entails falsity in every possible world, which justifies principium exclusi tertii sive medii inter duo contradictori. “In like manner as […] an assertion cannot be both true and false, so […] an assertion must be either true or false” (Mill 1843).

Meinong's Jungle can be regarded as the singular unreal world, the only impossible world, and the sole world wherein there are unreal things like 4-vertice triangles.

Whereas the actualism-possibilism debate is one about whether or not non-actual real things are possible, your question reduces to a question about whether or not impossible things are real.

Note: Necessitatem absolutum ought not to be confused with necessitatem ex hypothesi. “Necessity […] consists either in the constant conjunction of like objects, or in the inference of the understating from one object to another” (Hume 1748). Necessitatem ex hypothesi is the truth/falsity of an apodosis as being contingently necessary for the truth/falsity of any hypothesis to which that apodosis belongs (irrespective of any protasis in particular). On the other hand, necessitatem absolutum may invoke a Parmenideanistic mundus intelligibilis (perhaps evocative of Platonic-Pythagorean εἶδοη). “Indépendamment de la preuve qu'on appelle apodictique [il y a donc] une certitude que nous avons souvent [...] qualifier de philosophique ou de rationelle, parce qu'elle résulte d'un jugement de la raison” (Cournot 1851).

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