Well, to relate the vocabularies of two theories you need the appropriate translation manual. The manual I'm considering here would equate a "possible world" in Lewis's terminology to a "universe" in Tegmark's terminology. According to Tegmark, all mathematically possible universes are real in some sense, and according to Lewis all metaphysically possible worlds are real in some sense (and Lewis's conception of metaphysical possibility seems pretty close to mathematical possibility). Lewisian worlds are spatio-temporally isolated from one another, as are Tegmarkian universes. The two theories do seem almost, if not exactly, equivalent.
On the proposed translation schema, the appropriate Lewisian analogue of Tegmark's multiverse would be the entire landscape of all possible worlds. And so, on this translation, modal realism does not entail that there exists a world in which there is no multiverse. That would be equivalent to saying that there exists a world in which modal realism is false (i.e. the landscape of all possible worlds does not exist), which modal realism cannot entail if it is coherent.
Well argued, and fair enough. I guess the question comes down to this:
and Lewis's conception of metaphysical possibility seems pretty close to mathematical possibility
I suppose I'm under the impression that the space of metaphysical possibility is much broader than the space of mathematical possibility. Would the two spaces be identical of a reduction if mathematics to complete and consistent logic had worked out? Does Tegmark take himself to be making an empirical claim, in asserting a multiverse?
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