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STRONGLY MILLIAN SECOND-ORDER MODAL LOGICS

Published online by Cambridge University Press:  19 June 2017

BRUNO JACINTO*
Affiliation:
Centre of Philosophy of the University of Lisbon
*
*CENTRE OF PHILOSOPHY FACULTY OF LETTERS OF THE UNIVERSITY OF LISBON ALAMEDA DA UNIVERSIDADE, 1600-214 LISBON, PORTUGAL E-mail: jacinto.bruno@gmail.com

Abstract

The most common first- and second-order modal logics either have as theorems every instance of the Barcan and Converse Barcan formulae and of their second-order analogues, or else fail to capture the actual truth of every theorem of classical first- and second-order logic. In this paper we characterise and motivate sound and complete first- and second-order modal logics that successfully capture the actual truth of every theorem of classical first- and second-order logic and yet do not possess controversial instances of the Barcan and Converse Barcan formulae as theorems, nor of their second-order analogues. What makes possible these results is an understanding of the individual constants and predicates of the target languages as strongly Millian expressions, where a strongly Millian expression is one that has an actually existing entity as its semantic value. For this reason these logics are called ‘strongly Millian’. It is shown that the strength of the strongly Millian second-order modal logics here characterised afford the means to resist an argument by Timothy Williamson for the truth of the claim that necessarily, every property necessarily exists.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2017 

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References

Adams, R. M. (1981). Actualism and thisness. Synthese, 49(1), 341.Google Scholar
Barcan, R. (1946). A functional calculus of first order based on strict implication. Journal of Symbolic Logic, 11, 116.CrossRefGoogle Scholar
Correia, F. (2007). Modality, quantification and many vlach-operators. Journal of Philosophical Logic, 36, 473–88.CrossRefGoogle Scholar
Crossley, J. N. & Humberstone, L. (1977). The logic of “actually”. Reports on Mathematical Logic, 8, 1129.Google Scholar
Davies, M. & Humberstone, L. (1980). Two notions of necessity. Philosophical Studies, 38(1), 130.CrossRefGoogle Scholar
Deutsch, H. (1990). Contingency and modal logic. Philosophical Studies, 60(1/2), 89102.CrossRefGoogle Scholar
Deutsch, H. (1994). Logic for contingent beings. Journal of Philosophical Research, XIX, 273329.CrossRefGoogle Scholar
Fine, K. (1980). First-order modal theories. Studia Logica: An International Journal for Symbolic Logic, 39(2), 159202.CrossRefGoogle Scholar
Fine, K. (1985). Plantinga on the reduction of possibilist discourse. In Tomberlin, J. E. and van Inwagen, P., editors. Alvin Plantinga. Dordrecht: D. Reidel, pp. 145186.CrossRefGoogle Scholar
Fine, K. (2016). Williamson on Fine on Prior on the reduction of possibilist discourse. Canadian Journal of Philosophy, 46(4/5), 548570.CrossRefGoogle Scholar
Gallin, D. (1975). Intensional and Higher-Order Modal Logic. Amsterdam: North Holland.Google Scholar
Hodes, H. T. (1984a). Axioms for actuality. Journal of Philosophical Logic, 13(1), 2734.CrossRefGoogle Scholar
Hodes, H. T. (1984b). On modal logics which enrich first-order S5. Journal of Philosophical Logic, 13(4), 423454.CrossRefGoogle Scholar
Hughes, G. E. & Cresswell, M. J. (1996). A New Introduction to Modal Logic. Abingdon: Routledge.CrossRefGoogle Scholar
Kaplan, D. (1989). Afterthoughts. In Almog, J., Perry, J., and Wettstein, H., editors. Themes from Kaplan. Oxford: Oxford University Press, pp. 565612.Google Scholar
Kripke, S. (1963). Semantical considerations on modal logic. Acta Philosophica Fennica, 16, 8394.Google Scholar
Kripke, S. (1980). Naming and Necessity. Cambridge, MA: Harvard University Press.Google Scholar
Linsky, B. & Zalta, E. N. (1994). In defense of the simplest quantified modal logic. Philosophical Perspectives, 8, 431458.CrossRefGoogle Scholar
Menzel, C. (1991). The true modal logic. Journal of Philosophical Logic, 20(4), 331374.CrossRefGoogle Scholar
Prior, A. (1957). Time and Modality. Oxford: Oxford University Press.Google Scholar
Russell, B. (1919). The philosophy of logical atomism. The Monist, 29(2), 190222.CrossRefGoogle Scholar
Salmon, N. (1987). Existence. Philosophical Perspectives 1, Metaphysics, 49108.CrossRefGoogle Scholar
Salmon, N. (1989). The logic of what might have been. Philosophical Review, 98, 334.CrossRefGoogle Scholar
Shapiro, S. (1998). Logical consequence: Models and modality. In Schirn, M., editor. The Philosophy of Mathematics Today. Oxford: Clarendon Press, pp. 131156.Google Scholar
Stalnaker, R. (1976). Possible worlds. Noûs, 10, 6575.CrossRefGoogle Scholar
Stalnaker, R. (1994). The interaction of modality with quantification and identity. In Sinnott-Armstrong, W., Raffman, D., and Asher, N., editors. Modality, Morality and Belief: Essays in Honor of Ruth Barcan Marcus. Cambridge: Cambridge University Press, pp. 1228.Google Scholar
Stalnaker, R. (2006). Responses. In Thompson, J. and Byrne, A., editors. Content and Modality: Themes from the Philosophy of Robert Stalnaker. Oxford: Oxford University Press, pp. 251295.Google Scholar
Stalnaker, R. (2012). Mere Possibilities: Metaphysical Foundations of Modal Semantics. Princeton: Princeton University Press.Google Scholar
Stalnaker, R. (2016). Models and reality. Canadian Journal of Philosophy, 46(4/5), 709726.CrossRefGoogle Scholar
Stephanou, Y. (2005). First-order modal logic with an ‘actually’ operator. Notre Dame Journal of Formal Logic, 46(4), 381405.CrossRefGoogle Scholar
Vlach, F. (1973). “Now” and “Then”: A Formal Study in the Logic of Tense Anaphora. Ph.D. Thesis, UCLA.
Williamson, T. (1996). The necessity and determinacy of distinctness. In Lovibond, S. and Williams, S., editors. Essays for David Wiggins: Identity, Truth and Value. Oxford: Blackwell.Google Scholar
Williamson, T. (1998). Bare possibilia. Erkenntnis, 48, 257273.CrossRefGoogle Scholar
Williamson, T. (2013). Modal Logic as Metaphysics. Oxford: Oxford University Press.CrossRefGoogle Scholar
Williamson, T. (2016). Modal science. Canadian Journal of Philosophy, 46, 453492.CrossRefGoogle Scholar
Williamson, T. (forthcoming). Semantic paradoxes and abductive methodology. In Armour-Garb, B., editor. The Relevance of the Liar. Oxford: Oxford University Press.
Zalta, E. N. (1988). Logical and analytical truths that are not necessary. Journal of Philosophy, 85, 5774.CrossRefGoogle Scholar
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