Abstract
This paper is a study of higher-order contingentism – the view, roughly, that it is contingent what properties and propositions there are. We explore the motivations for this view and various ways in which it might be developed, synthesizing and expanding on work by Kit Fine, Robert Stalnaker, and Timothy Williamson. Special attention is paid to the question of whether the view makes sense by its own lights, or whether articulating the view requires drawing distinctions among possibilities that, according to the view itself, do not exist to be drawn. The paper begins with a non-technical exposition of the main ideas and technical results, which can be read on its own. This exposition is followed by a formal investigation of higher-order contingentism, in which the tools of variable-domain intensional model theory are used to articulate various versions of the view, understood as theories formulated in a higher-order modal language. Our overall assessment is mixed: higher-order contingentism can be fleshed out into an elegant systematic theory, but perhaps only at the cost of abandoning some of its original motivations.
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Notes
The present paper is the first of a trio: “Higher-order contingentism, Part 2: Patterns of indistinguishability” and “Higher-order contingentism, Part 3: Expressive limitations” explore further technical issues.
Some prefer to use the word ‘proposition’ for ways reality is represented rather than for ways reality is. This is not our usage; those for whom ‘proposition’ has such connotations may find ‘state of affairs’ or ‘zero-adic relation’ more helpful glosses. As we emphasize below, all such talk is merely gloss on various sorts of non-nominal quantification.
Fritz and Goodman [9] raises an expressive power challenge to higher-order contingentism, drawing on the technical results of Part 3.
This notion differs slightly from the one captured by the predicate fix in Section 5.3, which also incorporates the ‘preservation’ condition to be described presently.
Note that although this gloss on Comp− uses plural quantifiers, the formal language defined in Section 3.1 does not contain such quantifiers.
In a finitary language Comp C fails to entail ∀x□∃F∀y(F y ↔ ◇R x y), which is an instance of Comp−. In an infinitary language, Comp C does entail Comp− relative to the class of models we define in Section 3 (Proposition 9). This result relies on the fact that the language in question allows for formulas with as many free variables as there are entities of a given type in the domain of any world in any model. As such, it is arguably an artifact of the fact that the models in question are set-sized, since allowing for formulas with as many variables as there actually are individuals comes dangerously close to violating Cantor’s theorem; see Fritz and Goodman [9].
A different respect in which the model theory may appear unfaithful to the letter of higher-order contingentism is that, in modeling properties and propositions as intensions, we seem to rule out there being hyperintensional differences among them. In Section 3.4 we suggest a way around this problem by interpreting our higher-order quantifiers as restricted to entities that fail to draw hyperintensional distinctions.
This principle is accepted by Stalnaker but rejected by Fine; it is trivially true according to Williamson’s necessitist view, but he also assumes it in exploring various forms of contingentism.
An example involving possible identical twins is given in Fritz and Goodman [9].
One might think that it is only in the case of individuals that being any way at all requires being identical to something – i.e., perhaps properties can have higher-order properties even in circumstances where they lack being. Someone who accepted such a split decision regarding being constraints at different orders could avoid the above problem by characterizing automorphisms in terms of permutations of possible haecceities rather than of possible individuals; see Section 6.4. One motivation for such a view would be to reconcile propositional contingentism with the existence of a property of propositions intensionally equivalent to negation: i.e., to be able to accept both ¬□∀p□∃q□(p ↔ q) and ∃O□∀p□(O p ↔ ¬p), which given Comp C are inconsistent with the relevant instance of the higher-order being constraint, ∀O□∀p□(O p→∃q□(p ↔ q)).
Fine (p.c.) informs us that he in fact conceived of his project as a way for a higher-order necessitist to make sense of higher-order contingentism. However, there is no mention of this motivation in his paper.
We suspect Stalnaker will want to thread the needle and say that there is a way of appealing to closed models that is not so realist as to be objectionable on the grounds of not validating the object language expression of the underlying ideas Comp F S , but not so instrumentalist as to fail to constitute a helpful metaphysical vision. We are skeptical that there is a needle to be threaded here.
We have recently realized that considerations relating to lambda abstraction provide compelling support for this option, and that on the assumption that necessarily equivalent relations are identical, it solves many of the challenges for higher-order contingentism discussed below. We hope to explore this variant more fully in future work.
This section can be skipped if it is assumed that necessarily equivalent relations are identical. On this assumption, ‘hereditarily intensionally equivalent’ can be read as ‘identical’, and ‘hereditarily intensional’ as ‘self-identical’.
References
Blackburn, P., de Rijke, M., & Venema, Y. (2001). Modal logic. Cambridge: Cambridge University Press.
Dickmann, M.A. (1985). Larger infinitary languages. In J. Barwise, & S. Feferman (Eds.), Model-theoretic logics (pp. 317–363). New York: Springer-Verlag.
Dixon, J.D., & Mortimer, B. (1996). Permutation groups. New York: Springer-Verlag.
Fine, K. (1977). Postscript to Worlds, Times and Selves (with A. N. Prior). London: Duckworth.
Fine, K. (1977). Properties, propositions and sets. Journal of Philosophical Logic, 6, 135–191.
Fine, K. (forthcoming). Williamson on Fine on Prior on the reduction of possibilist discourse. In J. Yli-Vakkuri, & M. McCullagh (Eds.), Williamson on Modality, special issue of the Canadian Journal of Philosophy.
Fritz, P. (forthcoming). Propositional contingentism. The Review of Symbolic Logic.
Fritz, P., & Goodman, J. (unpublished). Counterfactuals and propositional contingentism.
Fritz, P., & Goodman, J. (unpublished). Counting incompossibles.
Gallin, D. (1975). Intensional and higher-order modal logic. Amsterdam: North-Holland.
Kaplan, D. (1970). S5 with quantifiable propositional variables. Journal of Symbolic Logic, 35, 355.
Karp, C. R. (1964). Languages with expressions of infinite length. Amsterdam: North-Holland.
Kripke, S. A. (1959). A completeness theorem in modal logic. Journal of Symbolic Logic, 24, 1–14.
Kripke, S. A. (1963). Semantical considerations on modal logic. Acta Philosophica Fennica, 16, 83–94.
Prior, A.N. (1971). Platonism and quantification. In Objects of thought (pp. 31–47). Oxford: Oxford University Press.
Rotman, J.J. (1995). An introduction to the theory of groups, 4th edition. New York: Springer-Verlag.
Stalnaker, R. (2003). The interaction of modality with quantification and identity. In Ways a world might be: metaphysical and anti-metaphysical essays. First published in an earlier form in W. Sinnott-Armstrong, D. Raffman & N. Asher (Eds.), Modality, Morality and belief: essays in honor of Ruth Barcan Marcus (pp. 12–28). Cambridge: Cambridge University Press, 1994 (pp. 144–161). Oxford: Oxford University Press.
Stalnaker, R. (2012). Mere possibilities. Princeton: Princeton University Press.
Williamson, T. (2013). Modal logic as metaphysics. Oxford: Oxford University Press.
Acknowledgments
Many friends and colleagues provided feedback on the present material, and we thank them all for their questions and comments, including audiences at the Ockham Society at the University of Oxford, the 6th Cambridge Graduate Conference on the Philosophy of Logic and Mathematics (where Tim Button gave comments), Logica 2013 at the Hejnice Monastery in the Czech Republic, the eidos Fine Conference in Varano Borghi in Italy, a workshop on Logical and Modal Space at New York University, and a workshop on the Logic and Metaphysics of Predication at the University of Oslo. We are especially grateful to Cian Dorr, Kit Fine and Timothy Williamson for detailed comments on drafts of the paper, Robert Stalnaker for correspondence, and an anonymous referee for this journal for an exceptionally thorough and perceptive review; they have all led to numerous substantial improvements. Peter Fritz gratefully acknowledges the support of an AHRC/Scatcherd European Scholarship and the German Academic Exchange Service; Jeremy Goodman gratefully acknowledges the support of the Marshall Commission and the Clarendon Fund.
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Sections 1 and 2 were written by Jeremy Goodman; Sections 3–7 were written by Peter Fritz; with the exception of formal definitions and proofs, we contributed equally to the ideas throughout the paper. Sections 1, 2 and 7 can be read as a self-contained informal introduction to the formal work done in Sections 3–6.
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Fritz, P., Goodman, J. Higher-Order Contingentism, Part 1: Closure and Generation. J Philos Logic 45, 645–695 (2016). https://doi.org/10.1007/s10992-015-9388-0
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DOI: https://doi.org/10.1007/s10992-015-9388-0