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Roads to Necessitarianism

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  • Published: 16 June 2020
  • volume 50, pages 89–96 (2021)
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Roads to Necessitarianism
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  • Matthew Mandelkern  ORCID: orcid.org/0000-0002-2140-75181 &
  • Daniel Rothschild2 
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Abstract

We show that each of three natural sets of assumptions about the conditional entails necessitarianism: that anything possible is necessary. Since most agree that this conclusion is obviously false, this shows that at least one member of each set of assumptions must be rejected. All of these assumptions are, however, widely accepted and well-motivated. This creates a puzzle which we leave open.

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References

  1. Arló-Costa, H. (2001). Bayesian epistemology and epistemic conditionals: on the status of the export-import laws. The Journal of Philosophy, 98(11), 555–593.

    Google Scholar 

  2. Fine, K. (2012). Counterfactuals without possible worlds. The Journal of Philosophy, 109, 221–246.

    Article  Google Scholar 

  3. Fine, K. (2017). Truthmaker semantics. In Wrigh, B.H.C., & Miller, A. (Eds.) Blackwell companion to the philosophy of language: Blackwell.

  4. Gibbard, A. (1981). Two recent theories of conditionals. In Harper, W.L., Stalnaker, R., & Pearce, G. (Eds.) Ifs: conditionals, beliefs, decision, chance, and time (pp. 211–247). Dordrecht: Reidel.

  5. Gillies, A. (2009). On truth conditions for If (but not quite only If). Philosophical Review, 118(3), 325–349.

    Article  Google Scholar 

  6. Hakli, R., & Negri, S. (2011). Does the deduction theorem fail for modal logic? Synthese, 187(3), 849–867. https://doi.org/10.1007/s11229-011-9905-9.

    Article  Google Scholar 

  7. Khoo, J. (2013). A note on Gibbard’s proof. Philosophical Studies, 166(1), 153–164.

    Article  Google Scholar 

  8. Khoo, J., & Mandelkern, M. (2019). Triviality results and the relationship between logical and natural languages. Mind, 128(510), 485–526. https://doi.org/10.1093/mind/fzy006.

    Article  Google Scholar 

  9. Kratzer, A. (1981). The notional category of modality. In Eikmeyer, H., & Rieser, H. (Eds.) Words, worlds, and contexts: new approaches in word semantics (pp. 38–74): de Gruyter.

  10. Kratzer, A. (1986). Conditionals. Chicago Linguistics Society, 22(2), 1–15.

    Google Scholar 

  11. Lewis, D. (1973). Counterfactuals. Oxford: Blackwell.

    Google Scholar 

  12. Mandelkern, M. (2019). Crises of Identity. In Schlöder, J.J., McHugh, D., & Roelofsen, F. (Eds.) Proceedings of the 22nd Amsterdam Colloquium (pp. 279–288). University of Amsterdam.

  13. Mandelkern, M. (2020). If p, then p! Manuscript, All Souls College, Oxford. https://philpapers.org/rec/MANIPT-2.

  14. Mandelkern, M. (2020). Import-export and ‘and’. Philosophy and Phenomenological Research, 100(1), 118–135. https://doi.org/10.1111/phpr.12513.

    Article  Google Scholar 

  15. McGee, V. (1985). A counterexample to modus ponens. The Journal of Philosophy, 82(9), 462–471.

    Article  Google Scholar 

  16. Ramsey, F.P. (1978/1931). General propositions and causality. In Mellor, D.H. (Ed.) Foundations: essays in philosophy, logic, mathematics and economics (pp. 133–51): Routledge and Kegan Paul.

  17. Stalnaker, R. (1968). A theory of conditionals. In Rescher, N. (Ed.) Studies in logical theory (pp. 98–112). Oxford: Blackwell.

  18. Stalnaker, R.C., & Thomason, R.H. (1970). A semantic analysis of conditional logic. Theoria, 36(1), 23–42. https://doi.org/10.1111/j.1755-2567.1970.tb00408.x.

    Article  Google Scholar 

  19. van Wijnbergen-Huitink, J., Elqayam, S., & Over, D.E. (2014). The probability of iterated conditionals. Cognitive Science, 1–16. https://doi.org/10.1111/cogs.12169.

  20. Yalcin, S. (2007). Epistemic modals. Mind, 116(464), 983–1026. https://doi.org/10.1093/mind/fzm983.

    Article  Google Scholar 

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Acknowledgments

Many thanks to two anonymous referees for this journal and to Angelika Kratzer for helpful feedback on this paper.

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Authors and Affiliations

  1. All Souls College, Oxford, OX1 4AL, UK

    Matthew Mandelkern

  2. UCL, London, UK

    Daniel Rothschild

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  1. Matthew Mandelkern
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Correspondence to Matthew Mandelkern.

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Appendix

Appendix

1.1 A.1 First Proof: Right Monotonicity

For arbitrary p:

  1. i.

    \(\models \Box (\neg (\neg p \wedge p))\supset { ((\neg p \wedge p)>\neg p)}\) Conditional Quodlibet

  2. ii.

    \( \Box \neg (\neg p \wedge p) \models { (\neg p \wedge p)>\neg p}\) Deduction Theorem, (i)

  3. iii.

    ⊧(¬p ∧ p) > ¬p K, (ii)

  4. iv.

    ⊧¬p > (p > ¬p) Import-Export, (iii)

  5. v.

    \(\models \lozenge p \supset \neg (p>\neg p )\) Restricted Aristotle’s Thesis, PC, K

  6. vi.

    \(\models \lozenge p \supset (\neg (p>\neg p )\vee p)\) PC, (v)

  7. vii.

    \(\models \lozenge p\supset ((p>\neg p )\supset p)\) PC, (vi)

  8. viii.

    \(\lozenge p\models (p>\neg p )\supset p\) Deduction Theorem, (vii)

  9. ix.

    \(\Box \lozenge p\models \neg p> p\) Right Monotonicity, (iv), (viii)

  10. x.

    \(\Box \lozenge p\models \Box p\) Restricted Aristotle’s Thesis, PC, (ix)

  11. xi.

    \(\lozenge p\models \Box \lozenge p\) 5

  12. xii.

    \(\lozenge p\models \Box p\) PC, (x), (xi)

1.2 A.2 Second Proof: Logical Implication and Logical Ad Falsum

We note first that the following is entailed by our definition of entailment and our classical semantics for ‘∧’:

  • Monotonicity: If p⊧q then (p ∧ r)⊧q

Then, for arbitrary p:

  • i.   \(\models \Box (\neg ((\lozenge p\wedge \neg p )\wedge p))\supset (({(\lozenge p\wedge \neg p) \wedge p)>\neg p)}\)

  •        Conditional Quodlibet

  • ii.   \(\Box \neg ((\lozenge p\wedge \neg p) \wedge p)\models ({(\lozenge p\wedge \neg p) \wedge p)>\neg p}\)

  •        Deduction Theorem, (i)

  • iii.  \( \models ((\lozenge p\wedge \neg p) \wedge p)>\neg p\)    K, (ii)

  • iv.    \(\models {(\lozenge p \wedge \neg p) > (p>\neg p) }\)    Import-Export, (iii)

  • v.     \(\models \lozenge p \supset \neg (p>\neg p )\)     Restricted Aristotle’s Thesis, PC, K

  • vi.     \(\lozenge p \models \neg (p>\neg p ) \)     Deduction Theorem, (v)

  • vii.     \(\lozenge p\wedge \neg p \models \neg (p>\neg p )\)     Monotonicity, (vi)

  • viii.     \(\models (\lozenge p\wedge \neg p)> \neg (p>\neg p )\)    Logical Implication, (vii)

  • ix.     \(\models \neg (\lozenge p\wedge \neg p)\)     Logical Ad Falsum, (iv), (viii)

  • x.     \(\models \lozenge p \supset p\)     PC, (ix)

  • xi.     \(\models \Box \lozenge p \supset \Box p\)     K, (x)

  • xii.     \(\models \lozenge p\supset \Box \lozenge p\)     5

  • xiii.     \(\models \lozenge p \supset \Box p\)     PC, (xi), (xii)

  • xiv.     \(\lozenge p \models \Box p\)     Deduction Theorem, (xiii)

1.3 A.3 Third Proof: Nothing Added

For arbitrary p:

  • i. \(\models \Box (\neg (\neg p \wedge p))\supset {((\neg p \wedge p)>\neg p)}\) Conditional Quodlibet

  • ii. \( \Box \neg (\neg p \wedge p)\models {(\neg p \wedge p)>\neg p}\) Deduction Theorem, (i)

  • iii.. ⊧(¬p ∧ p) > ¬p K, (ii)

  • iv. ⊧¬p > (p > ¬p) Import-Export, (iii)

  • v. \(\models \lozenge p \supset \neg (p>\neg p )\) Restricted Aristotle’s Thesis, PC, K

  • vi \(\models \Box (\lozenge p \supset \neg (p>\neg p ))\) K, (v)

  • vii. \(\models \Box \lozenge p \supset \Box \neg (p>\neg p )\) K, (vi)

  • viii. \(\models \lozenge p\supset \Box \lozenge p\) 5

  • ix. \(\models \lozenge p \supset \Box \neg (p>\neg p )\) PC, (vii), (viii)

  • x. \(\lozenge p \models \Box \neg (p>\neg p )\) Deduction Theorem, (ix)

  • xi. \(\lozenge p \models \Box \neg (p>\neg p ) \supset ((p>\neg p)>(\neg p>p))\)

  • Conditional Quodlibet

  • xii. \(\lozenge p \models {(p>\neg p)>(\neg p>p)}\) PC, (x), (xi)

  • xiii. \(\lozenge p \models {((p>\neg p)\wedge \neg p)>p}\) (xii), Import-Export

  • xiv. \(\lozenge p \models {(\neg p \wedge (p>\neg p))>p}\) (xiii), PC

  • xv. \(\lozenge p \models {\neg p > ((p>\neg p)>p)}\) (xiv), Import-Export

  • xvi. \(\lozenge p \models (\neg p > ((p>\neg p)>p)) \equiv ({\neg p> p})\) (iv), Nothing Added

  • xvii. \(\lozenge p \models {\neg p> p}\) (xv), (xvi), PC

  • xviii. \(\lozenge p \models \Box p\) Restricted Aristotle’s Thesis, (xvii), PC

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Mandelkern, M., Rothschild, D. Roads to Necessitarianism. J Philos Logic 50, 89–96 (2021). https://doi.org/10.1007/s10992-020-09562-9

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  • Received: 12 August 2019

  • Accepted: 13 May 2020

  • Published: 16 June 2020

  • Issue Date: February 2021

  • DOI: https://doi.org/10.1007/s10992-020-09562-9

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Keywords

  • Logic of conditionals
  • Triviality results
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