Impossibilities without impossibilia

Inquiry: An Interdisciplinary Journal of Philosophy (forthcoming)
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Circumstantialists already have a logical semantics for impossibilities. They expand their logical space of possible worlds by adding impossible worlds. These are impossible circumstances serving as indices of evaluation, at which impossibilities are true. A variant of circumstantialism, namely modal Meinongianism (noneism), adds impossible objects as well. These are so-called incomplete objects that are necessarily non-existent. The opposite of circumstantialism, namely structuralism, has some catching-up to do. What might a structuralist logical semantics for impossibilities without impossibilia look like? This paper makes a structuralist counterproposal. We present a semantics based on a procedural interpretation of the typed λ-calculus. The fundamental idea is that talk about impossibilities should be construed in terms of procedures: some yield as their product a condition that could not possibly have a satisfier, while the rest fail to yield a product altogether. Dispensing with a ‘bottom’ of impossibilia requires instead a ‘top’ consisting of structured hyperintensions, intensions, intensions defining other intensions, a typed universe, and dual (de dicto and de re) predication. We explain how the theory works by going through several examples.



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On the Plurality of Worlds.David Lewis - 1986 - Revue Philosophique de la France Et de l'Etranger 178 (3):388-390.
The dispositionalist conception of laws.Alexander Bird - 2005 - Foundations of Science 10 (4):353-70.
Impossible Worlds.Mark Jago - 2013 - Noûs 47 (3):713-728.
Sylvan's Box: A Short Story and Ten Morals.Graham Priest - 1997 - Notre Dame Journal of Formal Logic 38 (4):573-582.

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