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On modal Meinongianism

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Abstract

Modal Meinongianism is a form of Meinongianism whose main supporters are Graham Priest and Francesco Berto. The main idea of modal Meinongianism is to restrict the logical deviance of Meinongian non-existent objects to impossible worlds and thus prevent it from “contaminating” the actual world: the round square is round and not round, but not in the actual world, only in an impossible world. In the actual world, supposedly, no contradiction is true. I will show that Priest’s semantics, as originally formulated in Towards Non-being, tell us something different. According to certain models (especially models that are interesting from a Meinongian point of view), there are true contradictions in the actual world. Berto and Priest have noticed this unexpected consequence and have suggested a solution (I would like to thank an anonymous reviewer for pointing out to me the relevant footnotes in Priest and Berto’s work), but I will show that their solution is highly questionable. In the last section of this paper, I will introduce a new and simpler version of modal Meinongianism that avoids the problem.

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Notes

  1. See Priest (2005, pp. 20–21). Though Priest is sympathetic to a dialetheist view, he makes clear in this passage that according to the standard version of his theory there are no truth-value gaps nor gluts in the actual world.

  2. My technique differs slightly from Priest’s but it does the same work.

  3. Those are the rules as they are given (mutatis mutandis) by Priest (2005) and by Berto (2013); but a footnote in Berto (2013) will bring a significant modification to be discussed later.

  4. It would be a mistake to think that Pa is not false for the reason that it is true and false; being true and false is not a special semantic value; it is nothing but being true and being false. Therefore, Pa is indeed false in w (which does not exclude that it is also true).

  5. I thank an anonymous reviewer for pointing that out.

  6. By “certain” I mean a random number: it might be every couple \(\langle w,\,\upvarphi \rangle ,\) only some of them but not all, or even none of them.

  7. We need this second clause for the following reason: if \({\updelta }(w,\,{\vert }Pa{\vert }) = 1,\) then Pa is \(\mathrm{true}_{Mws}\) and we expect \({\exists } x(Px)\) also to be \(\mathrm{true}_{Mws}.\) But the first clause will not do the work: Pa is not \(\mathrm{true}_{Mws}\) because of a denoting something that x might also denote; Pa is \(\mathrm{true}_{Mws}\) only because it is assigned to be \(\mathrm{true}_{Mws}.\) Thus, if \({\exists } xPx\) is \(\mathrm{true}_{Mws}\) it will only be because of a formula of form Pt being \(\mathrm{true}_{Mws}.\)

  8. It corresponds to Dunn and Bellnap’s interpretation of negation in their four-valued logic (see Dunn 1976; Bellnap 1977). It seems indeed to be the most natural way to understand negation in a four-valued semantics.

  9. There is no sub-rule \((\mathrm{i}_{\lnot })\) for atomic formula because if \(\upvarphi \) is an atomic formula and \({\updelta }(w,\, {\vert }\upvarphi {\vert })\) is not defined, then \({\lnot }{\upvarphi }\) is always not true. (To say it in other terms: a negation of an atomic formula \(\upvarphi \) is true in a non-actual world w only if \({\updelta }(w,\,{\vert }\upvarphi {\vert }) = 0.\))

References

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  1. Institut Jean Nicod, Paris, France

    Thibaut Giraud

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Giraud, T. On modal Meinongianism. Synthese 193, 3329–3346 (2016). https://doi.org/10.1007/s11229-015-0933-8

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