I’m reading a chapter from David Lewis’s counterfactuals. He says something which I’m confused about, wondering if any of you guys can explain what he's saying...

“ We might take…. ‘Possibly P’ [to mean] that P is a consistent sentence… If a consistent sentence is one that comes out true under some assignment of extensions to the nonlogical vocabulary, then the theory is incorrect: some assignments of extensions are impossible, for instance one that assigns overlapping extensions to the English terms ‘pig’ and ‘sheep’.”

I’ve taken logic so I know what he means by assigning extensions to nonlogical terms but I’m failing to see how some assignments of extensions are impossible. Some extensions are impossible (e.g. the round square), but I'm failing to see how some assignments of extensions to nonlogical terms (given that the extensions exist) is impossible.

Thanks for any answers :))

  • You don't understand how it is impossible for a thing to be both a pig and a sheep? Commented Jun 14, 2023 at 15:49
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    @DavidGudeman Of course I understand so. As I said, some extensions are impossible but I’m not sure how some assignment of extensions to non-logical terms are also impossible. The extension existing or not is a different question from whether said assignment is possible.
    – zzz
    Commented Jun 14, 2023 at 15:59
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    This is part of Lewis's criticism of ersatzism. Ersatzism interprets possible worlds as maximally consistent sets of sentences, and Lewis's point is that our notion of possible cannot be captured by such interpretation. Some assignments are still what we consider impossible (invisible pink unicorns), despite being consistent (no contradiction). So consistency does not capture the intended meaning of possibility, and we have to appeal to "possible" to correctly describe what is possible, which is circular.
    – Conifold
    Commented Jun 14, 2023 at 19:20

1 Answer 1


The extension of a class word (if it has one) is a set. So if you assign overlapping extensions the English words "pig" and "sheep", what he is implying is that the set of all pigs overlaps with the set of all sheep. In other words, there are some objects that are both pigs and sheep. This is a situation that is impossible.

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