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For David Lewis's Modal Realism, do the worlds and individuals that inhabit them exist necessarily? In a sense, the answer is "no". For an individual to exist necessarily would be for it to have a counterpart at every world, but Lewis is pretty explicit that this isn't required for counterpart theory or for modal realism.

But, this is where the question gets tricky, in order for the analysis of modality in terms of possibilia to go through it would seem that possibilia would need to exist necessarily. This is because it is generally thought that a successful analysis of a concept should hold necessarily, and if there were no possible worlds or individuals the analysis would break down.

Hence, my question, does the modal realist need "there are possible worlds and individuals that inhabit them" to be a necessary truth, even if he doesn't require any particular possible individuals to necessarily exist?

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  • Perhaps this answers your question. Have a look at p. 127, second paragraph, of this little book. (Click on the link and then perhaps on "127". It depends on location and browser, I guess.) I could easily copy-paste the whole thing into an answer, but I'm not so sure about copyright. Also, I might have completely misunderstood your question and this is unrelated. :) – user3164 Mar 25 '13 at 15:19
  • @Gugg yea I'm not sure that it is directly relevant, since the complaint Stalnaker et. al. seem to be making is about the appropriateness of a modal realist analysis of properties whereas I'm questioning its adequacy (more precisely, I'm asking whether the adequacy of the analysis depends on the necessity of a given presupposition). I do, however, thank you for pointing this section out because it did give me an idea of how to support something I'm arguing for in a paper I'm currently writing (the paper which has inspired most of my recent questions). So, many thanks there! – Dennis Mar 25 '13 at 17:32
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Okay, second try. As far as I can see, the answer to your question is "no."

does the modal realist need "there are possible worlds and individuals that inhabit them" to be a necessary truth

Taking this nice manuscript by Kevin Klement as a basis, let us check whether

(1) ☐∃x∃y(Wx & Iyx)

follows from the axioms of counterpart theory. Using the translation procedure from first-order modal logic to FOL with counterpart axioms, I obtain:

(2) ∀w'[Ww' → ∃x∃y(Ixw' & Iyw' & Wx & Iyx)]

If I'm not mistaken, (2) does not follow from the axioms of CT and is not valid in FOL+CT. In fact, the counterpart theory axioms only assert that there is something actual. Interestingly, there is also no axiom stating that every world inhabits itself.

Since I'm not a Lewis expert, I welcome others to check this answer and perhaps improve it. (It's always better to check for yourself instead of relying on others in such matters, right?)

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    Kevin Klement is one of my advisors, coincidentally. His class handouts (what you found) are generally pretty awesome. The problem I am asking about, though, is not one that will be resolved within the system. It is a sort of second-order modality. Lewis uses worlds to reduce modality, and counterpart theory plays a crucial role in the reduction. I think I've come to my own answer since I first posed the question. Counterpart theory presupposes that the set of worlds is non-empty. -> cont. – Dennis Mar 26 '13 at 15:55
  • If the reduction is to count as an analysis (as Lewis intends) then counterpart theory will, itself, have to be necessarily true. Since a requirement for the truth of the principles of counterpart theory is the existence of at least one world, I think that "possible worlds exist" would have to be necessarily true (at least one possible world must exist for the set to be non-empty). This isn't so problematic, though, because no particular world needs to exist necessarily and assuming we are doing our theorizing in a world (the actual world) it seems this presupposition is fairly benign. – Dennis Mar 26 '13 at 15:58
  • Many thanks for the revisiting this question, though. I'm not sure I would have thought as much about the issue if I didn't have to clarify my question in response to your answers (undoubtedly there is quite a bit of imprecision in the way my question is stated). – Dennis Mar 26 '13 at 16:01

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