Abstract
I argue that deontic modals are hyperintensional, that is, logical equivalent contents cannot be substituted in their scope. I give two arguments, one is deductive and the other abductive. First, I simply prove that the contrary thesis leads to falsity; second, I claim that a hyperintensional theory of deontic modals fares better than its rivals in terms of elegance, theoretical simplicity, and explanatory power (e.g. Ross’s paradox, the Gentle Murderer, The Good Samaritan, Free Choice Permission, and the Miners’ Paradox disappear). I then propose a philosophical analysis of this thesis, and outline some consequences.
If you don’t know where you are going, any road will get you there.
Lewis Carroll
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Such an assumption is the case in most of the logic and linguistic literature. Hansson (2013a), p. 476 maintains that abandoning the rule of substitution of logical equivalents in deontic context ‘would probably be too costly to remove [...] would be a far-reaching weakeninig of deontic logic” . Von Fintel (2012), amply cited in the linguistics literature, is a major effort to amend intensional (in this case Kratzer-style) semantics for deontic modals to deal with several problems, some of which are taken up later in this paper.
- 2.
I will leave aside the question of whether it is truth we are really after, at least when investigating genuine deontic claims. The skeptical reader may mentally substitute truth (veritas) with “designated semantic value(s)” , whatever they are taken to be.
- 3.
For a recent and interesting perspective, see Bacon (2015).
- 4.
Similar definitions appear inWilliamson (2006).
- 5.
The term ‘hyperintensionality’ was proposed by Cresswell some forty years ago (cf. Cresswell 1975), with reference to logical equivalence. Recently there has been a sort of pendulum: hyperintensionality has sometimes been defined in terms of logical equivalence and on other occasions in terms of necessary equivalence (cf.Williamson 2006, 2013; Jago 2014). For an account of how these notions interact see Sects. 4.2.2 and 4.2.3.
- 6.
What does ‘equivalent’ mean here? Since we do not have the formal tools required to deal with it yet (tools which I’ll introduce later on), we could settle for an informal notion of equivalent as being the same obligation (permission, license, belief) for all purposes.
- 7.
Indeed the argument suggests that even first-degree entailment is too strong for deontic contexts.
- 8.
Natural language examples are of course prone to many different factors I am disregarding here. For instance in (81) the pragmatics of disjunction and conjunction is complex and arguably makes them non-boolean; implicit restrictions on the subject of the obligations could be assumed, etc. Indeed, it seems hardly the case that a real speaker would likely consider (80) and (81) equivalent. What matters for the purpose of this argument is that they are nonetheless logically equivalent, even if speakers’ intuitions diverge. Similar considerations apply to the other natural language examples of this paper.
- 9.
Alonso-Ovalle (2005) seems to make a similar point with regard to deontic ‘may’ and ‘must’ with regard to disjunction, favoring a particular conversational implicature analysis. The point I make here is instead fully general, in that it is meant to apply to all logically equivalent sentences, even not involving disjunction and the resulting pragmatic effects. This should also take care of the apparent violation of Hurford’s constraint violation. For some recent semantical consideration on this, see Ciardelli and Roelofsen (2017). The objection that all formulas are equivalent to one in disjunctive normal form is only apparent, for this equivalence is the case only in certain logics (like classical logic), but not in others (like intuitionistic logic).
- 10.
Equivalently, and truth-functionally, just consider using infinitary conjunctions. It is then a schema that for each \( \gamma<\delta , (\wedge _{\epsilon <\delta } A_{\epsilon }) \implies A_{\gamma }\).
- 11.
- 12.
Note that in this context deontic modals are taken to be non-indexed, all-things-considered propositional operators. One plausible way to explain this particular example would be to consider deontic modals as relations between agents and actions (and in this case (148) and (149) would have different truth conditions) or just to index every deontic operator to a specific agent. Both options would allow us to remain in a possible-world semantics setting, but by complicating the framework and with no gain in generality. The debate is alive and well but outside the concerns of this paper.
- 13.
Models come of course with much more than just a set of points, depending on what they are a model for.
- 14.
- 15.
- 16.
For expository reasons, I assume S5, where, in a relational semantics, the accessibility relation is universal.
- 17.
Thus even if “The pope shakes hands with Shakira” and “Shakira shakes hands with the pope” are mutually co-entailing, as “It ought to be the case that the pope shakes hands with Shakira” and “It ought to be the case that Shakira shakes hands with the pope” are, “The pope ought to shake hands with Shakira” and “Shakira ought to shake hands with the pope” are not.
- 18.
But of course cf. Horty (2001) for an ought-cum-stit operator.
- 19.
- 20.
For such a theory, cf. for instance Bader, Bader (2016) . Similar considerations apply to the stit case, as generally stit operators are closed under the substitution of logical equivalents.
- 21.
Perhaps one could even argue that a hyperintensional theory of deontic modality of the kind put forward here is also “simpler”, to the extent that has fewer rules and axioms (besides avoiding unwanted derivations. Obviously simplicity (like generality) is only one criterion among many, a criterion that has to be balanced against other desiderata.
- 22.
A minimal version of hyperintensional deontic logic is developed in Anglberger et al. (2016).
- 23.
More compact formalizations are of course equivalent and possible. I use the following because it is really easy to see the building block from the minimal classical deontic logic ED to SDL (i.e., KD): MD (monotonic deontic logic) has Inheritance, which is equivalent to SLE \(+\) M; RD (regular deontic logic) has RR (if (\(A_{1} \wedge \dots \wedge A_{n}) \rightarrow B\) then \((\mathcal {O}A_{1} \wedge \dots \wedge \mathcal {O}A_{n}) \rightarrow \mathcal {O}B\), with \(n \ge 1\)), which is equivalent to Inheritance + C, SDL has RK (if (\(A_{1} \wedge \dots \wedge A_{n}) \rightarrow B\) then \((\mathcal {O}A_{1} \wedge \dots \wedge \mathcal {O}A_{n}) \rightarrow \mathcal {O}B\), with \(n \ge 0\)), which is equivalent to RR + \(\mathcal {O}\top \) (or, equivalently, to N + K). All add the deontic schema D and are closed under modus ponens.
- 24.
Rejecting inheritance has been proposed, among others, by Jackson (1985), Goble (1990) , Hansson (2000) , and more recently at least by Cariani (2013) and Lassiter (2011) . Castañeda (1981) , for one, argued that Inheritance is not the real culprit at least in the Good Samaritan paradox. More recently von Fintel (2012) mounted a defense of Inheritance, although from a semanticist’s perspective. Interestingly enough, in the 14th century Roger Rosetus (Commentarius de sententibus, [q. 1]) gave some arguments to reject Inheritance.
- 25.
Goble (2013), pp. 315–18 proposes a logic with limited replacement exactly on these grounds, but without any independent philosophical motivation, nor with a semantic explanation of his “analytical equivalents”. Hansson (1991) discusses a paradox generated by SLE alone (the Revenger’s Paradox), but no alternative system without SLE is presented. SLE is endorsed explicitly at least in Wright (1981), p. 27. A non-normal modal logic (for instance the minimal deontic logic of Chellas (1975) and [Chellas 1980, Sects. 6.5, 10.2] as long as it can be equipped with neighborhood semantics would not work, because it is straightforward to show that SLE is valid in all neighborhood frames. Similarly for Schotch, Peter and Jennings (1981).
- 26.
For an introduction and defense of the notion of hyperintensional equivalence see Chap. 3.
- 27.
A verifier is exact when it is completely and wholly relevant to the claim it verifies, without “extra” irrelevant material. For instance, that Italy is boot-shaped is an exact verifier of ‘Italy is boot-shaped’; but that Italy is boot-shaped and generally sunny is not an exact verifier of ‘Italy is boot-shaped’.
- 28.
- 29.
To have a principled (syntactic) solution to these paradoxes does not mean we also have a (semantic) explanation. For instance, while (syntactic) hyperintensionality makes free-choice inference acceptable, it does not explain the free-choice effect itself. Thus, while these solutions may be accepted by those sympathetic to the (syntactic) hyperintensionality analysis, they would need to be supplemented by choosing a suitable semantics with a certain philosophical adequacy, rather than as a mere technical tool. More than one semantics story is possible, but without one a story of why these solutions work isn’t fully complete. Good Samaritan, Free Choice permission and Ross’s paradox served as a motivation in Anglberger et al. (2016), Ross’s and Good Samaritan, among others, in e.g. Glavaničová and Daniela (2015).
- 30.
For solutions to this puzzle different from mine, either involving two different notions of permission, or pragmatic considerations, cf. at least Hansson (2013b).
- 31.
Proof From \(\vDash p \rightarrow (p \vee q)\), apply deontic necessitation: if \(\vDash p \rightarrow (p \vee q)\) then \(\vDash \mathcal {O}p \rightarrow \mathcal {O}(p \vee q)\).
- 32.
Recent bimodal approaches to Ross’s paradox, i.e. using a (normal) metaphysical or alethic modality beside ought in order to restrict some deontic rule or other just to compossible situations (see for instance Danielsson 2007, 2005) have been convincingly defused, in the case that ought remains congruential (i.e. non-hyperintensional) by Humberstone (2016), pp. 324–330.
- 33.
Proof This is straightforward; even weak necessitation cannot be applied. In HDL, \(\alpha \rightarrow (\alpha \vee \beta )\) is not a theorem.
- 34.
Cf. McNamara (2014) . While it is plausible that the Good Samaritan paradox may well depend specifically on its formalization, these logical derivations in SDL seem problematic, also in light of the other cases discussed in the literature, such as Professor Procrastinate, and Nurse.
- 35.
Proof \(\vDash h \wedge r \rightarrow r\) by propositional classical logic. Apply necessitation.
- 36.
For \(\alpha \rightsquigarrow _{H} \beta =_{def} \alpha \approx _{H} \alpha \wedge \beta \).
- 37.
Although a detailed discussion of Kolodny and John MacFarlane (2010) solution and the subsequent literature is not possible, I think that the solution afforded by HDL is superior for many reasons. I will only highlight one: even supposing that there are independent reasons to reject modus ponens, the Miners’ paradox can be recast in terms of disjunction. To deflect this objection, as to confirm that the disjunction solution is more powerful, Kolodny and John MacFarlane (2010), n. 19 are forced to change the understanding of ‘\(\vee \)’, which is exactly what a hyperintensional logic does from the start. Solutions like Willer (2012) and Bledin (2015) keep modus ponens without being hyperintensional, an objection might go. However, my solution rests on a general, rather than an ad hoc, strategy: if we go hyperintensional, this solution to the Miners’ puzzle is just one of the consequence of (an independently established) claim, and it helps explain not only this, but a number of other problems.
- 38.
That agglomeration can be kept even with explicit contradictions is shown by the previous reasoning with Contrary-do-duty: starting from \(\mathcal {O}(\alpha ) \wedge \mathcal {O}(\lnot \alpha )\), even if we get \(\mathcal {O}(\alpha \wedge \lnot \alpha )\), \(\mathcal {O}\beta \) cannot be derived in HDL as \(\alpha \wedge \lnot \alpha \) and \(\beta \) are not hyperintensionally equivalent.
- 39.
- 40.
What about the usual counterexamples to the symmetry of conjunction, i.e. marry and have a child versus have a child and marry? Such questions are usually taken to be in the realm of pragmatics, but, be as it may, one could add a structure of time intervals in the semantics and take into account this and other issues.
- 41.
One could also single out another subset of S, R, to stand for real states, and introduce a formula as necessary when verified by all states of R. What conditions impose on R is of course dependent on one’s conception of reality, if complete, consistent, and so on.
- 42.
Of course implicit versions of obligation and permission can be recovered by adding the duals.
References
Alonso-Ovalle, Luis. 2005. Distributing the disjuncts over the modal space. In Proceedings of the 35th North East Linguistics Society Conference, ed. Leah Bateman, and Cherlon Ussery. University of Massachusetts. GLSA: Amherst.
Angell, Richard B. 1977. Three Systems of FirstDegree Entailment. Journal of Symbolic Logic 47: 147.
Angell, Richard B. 1989. Deducibility, Entailment and Analytic Containment. In Directions in Relevant Logic, ed. J. Norman and Richard Sylvan. Dordrecht: Kluwer.
Anglberger, Albert, Federico L. G. Faroldi, and Johannes Korbmacher. 2016. An Exact Truthmaker Semantics for Obligation and Permission. In Roy et al. [2016], 16–31.
Bacon, Andrew. 2015. Paradoxes of Logical Equivalence and Identity. Topoi 34 (1): 89–98.
Bader, Ralf. 2016. Hyperintensional Equivalence.
Blackburn, Patrick, Johan Van Benthem, and Frank Wolter (eds.). 2007. Handbook of Modal Logic, Studies in Logic and Practical Reasoning, vol. 3. New York: Elsevier.
Bledin, Justin. 2015. Modus Ponens Defended. The Journal of Philosophy 112 (2): 57–83.
Cariani, Fabrizio. 2013. Ought and Resolution Semantics. Noûs 47: 534–558.
Castañeda, Héctor-Neri. 1981. The Paradoxes of Deontic Logic: The Simplest Solution to all of Them in One Fell Swoop. In Hilpinen [1981], 37–85.
Chellas, Brian F. 1975. Conditional Obligation. Logical Theory and Semantic Analysis, 23–33. D. Reidel: Dordrecht.
Chellas, Brian F. 1980. Modal Logic. An Introduction. Cambridge: Cambridge University Press.
Ciardelli, Ivano, and Floris Roelofsen. 2017. HurfordConstraint, the Semantics of Disjunction, and the Nature of Alternatives. Natural Language Semantics 25 (3): 199–222.
Correia, Fabrice. 2004. Semantics for Analytic Containment. Studia Logica 77: 87–104.
Correia, Fabrice. 2016. On the Logic of Factual Equivalence. The Review of Symbolic Logic 9 (1): 103–122.
Cresswell, Max J. 1975. Hyperintensional Logic. Studia Logica 34 (1): 25–38.
Crossley, J.N., and L. Humberstone. 1977. The Logic of ’Actually’. Reports on Mathematical Logic 8: 11–29.
Danielsson, Sven. 2005. Taking Ross’s Paradox Seriously A Note on the Original Problems of Deontic Logic. Theoria 71 (1): 20–28.
Danielsson, Sven. 2007. Ross’s Paradox Again. Theoria 73 (3): 256–258.
Faroldi, Federico L. G. 2019. Deontic modals and hyperintensionality, forthcoming in Logic Journal of IGPL.
Ferguson, Thomas Macaulay. 2014. Faulty Belnap computers and subsystems of FDE. Journal of Logic and Computation 26 (5): 1617–1636.
Ferguson, Thomas Macaulay. 2016. Correia Semantics Revisited. Studia Logica 104 (1): 145–173.
Fine, Kit. forthcoming. Truthmaker Semantics. In Blackwell Handbook of Philosophy of Language London: Blackwell.
Fine, Kit. 2014. Permission and PossibleWorlds. Dialectica 68 (3): 317–336.
Fine, Kit. 2016. Angellic Content. Journal of Philosophical Logic 45 (2): 199–226.
Gabbay, Dov, J. F. Horty, X. Parent, R. van derMeyden, and L. van der Torre (eds). 2013. Handbook of Deontic Logic and Normative Systems, vol. 1. London: College Publications.
Geach, Peter Thomas. 1981. Whatever Happened to Deontic Logic? Philosophia 11: 1–12.
Glavaničová, Daniela. 2015. Kanalýze deontických modalít vTransparentnej intenzionálnej logike. Organon F22(2): 211–228.
Goble, Lou. 1990. A Logic of Good, Should, and Would: Part I. Journal of Philosophical Logic 19 (2): 169–199.
Goble, Lou. 2013. Prima Facie Norms, Normative Conflicts, and Dilemmas, in Gabbay et al. [2013], vol. 1.
Halbach, Volker, and Philip Welch. 2009. Necessities and Necessary Truths: A Prolegomenon to the use of Modal Logic in the Analysis of Intensional Notions. Mind 118: 71–100.
Halbach, Volker, Hannes Leitgeb, and Philip Welch. 2003. Possible-Worlds Semantics for Modal Notions Conceived as Predicates. Journal of Philosophical Logic 32: 179–223.
Hansson, Sven Ove. 1991. The Revenger’s Paradox. Philosophical Studies 61 (3): 301–305.
Hansson, Sven Ove. 2000. Structure of Values and Norms. Cambridge: Cambridge University Press.
Hansson, Sven Ove. 2013a. Alternative Semantics for Deontic Logic. In Gabbay et al. [2013], vol. 1, pp. 445–497.
Hansson, Sven Ove. 2013b. Varieties of Permission. In Gabbay et al. [2013], vol. 1.
Hanson, William H. 2006. Actuality, Necessity, and Logical Truth. Philosophical Studies 130: 437–459.
Hilpinen, Risto (ed.). 1981. New Studies in Deontic Logic. Dordrecht: D. Reidel.
Horty, John F. 2001. Agency and Deontic Logic. Oxford: Oxford University Press.
Humberstone, Lloyd. 2016. Philosophical Applications of Modal Logic. London: College Publications.
Jackson, Frank. 1985. On the Semantics and Logic of Obligation. Mind 94 (374): 177–195.
Jago, Mark. 2014. The Impossible., An Essay on Hyperintensionality. Oxford: Oxford University Press.
Kolodny, Niko, and John MacFarlane. 2010. Ifs and Oughts. Journal of Philosophy 107 (3): 115–143.
Lassiter, Daniel. 2011. Measurement and Modality: The Scalar Basis of Modal Semantics. Ph.D. thesis, New York University.
McNamara, Paul. 2014. Deontic Logic. In The Stanford Encyclopedia of Philosophy, ed. Edward N. Zalta.
Meredith, C., and Arthur Norman Prior. 1965. Modal Logic with Functorial Variables and a Contingent Constant. Notre Dame Journal of Formal Logic 6: 99–109.
Montague, Richard. 1969. On the Nature of Certain Philosophical Entities. The Monist 53 (2): 159–194.
Muskens, Reinhard. 2007a. Higher Order Modal Logic. In Handbook of Modal Logic, ed. by Patrick Blackburn, Johan Van Benthem, and FrankWolter, 621–653. Amsterdam: Elsevier.
Muskens, Reinhard. 2007b. Intensional Models for the Theory of Types. The Bulletin of Symbolic Logic 72 (1): 98–118.
Nauze, Fabrice. 2008. Modality in Typological Perspective. Ph.D. thesis, Universiteit van Amsterdam.
Nelson, Michael, and Edward N. Zalta. 2012. A Defense of Contingent LogicalTruths. Philosophical Studies 151 (1): 153–62.
Partee, Barbara Hall. 2008. Symmetry and Symmetrical Predicates. In Computational Linguistics and Intellectual Technologies: Papers from the International Conference "DIALOGUE" (2008), ed. A.E. Kibrik, 606–611. Moskow: Institut Problem Informatiki.
Prior, Arthur Norman. 1958. Escapism: The Logical Basis of Ethics. In Essays in Moral Philosophy, ed. A.I. Melden, 135–146. Seattle: University of Washington Press.
Rosetus, Roger n.d. Commentarius de sententibus. Oriel College: Oxford. 15 fol 235r-279.
Roy, Olivier, Allard Tamminga, and Malte Willer (eds.). 2016. Deontic Logic and Normative Systems, DEON16. London: College Publications.
Schotch, Peter K., and R.E. Jennings. 1981. Non-Kripkean Deontic Logic. In Hilpinen [1981], 149–164.
Schroeder, Mark. 2011. Ought, Agents, and Actions. The Philosophical Review 120 (1): 1–41.
van Fraassen, Bas C. 1969. Facts and Tautological Entailment. Journal of Philosophy 66 (15): 477–487.
Von Fintel, Kai. 2012. The Best We Can (Expect to) Get? Challenges to the Classic Semantics for Deontic Modals. In Paper Presented in a Session on Deontic Modals at the Central APA, Feb 17.
Wright, Georg Henrik von. 1981 On the Logic of Norms and Actions. In Hilpinen [1981], 3–35.
Willer, Malte. 2012. A Remark on Iffy Oughts. Journal of Philosophy 109 (7): 449–461.
Williamson, Timothy. 2006. Indicative versus Subjunctive Conditionals, Congruential versus Non-Hyperintensional Contexts. Philosophical Issues 16 (1): 310–333.
Williamson, Timothy. 2013. Modal Logic as Metaphysics. Oxford: Oxford University Press.
Yablo, Stephen. 2014. Aboutness. Princeton: Princeton University Press.
Zalta, Edward N. 1988b. Logical and Analytical Truths That Are Not Necessary. The Journal of Philosophy 85: 57–74.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Faroldi, F.L.G. (2019). Deontic Modals are Hyperintensional. In: Hyperintensionality and Normativity. Springer, Cham. https://doi.org/10.1007/978-3-030-03487-0_4
Download citation
DOI: https://doi.org/10.1007/978-3-030-03487-0_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-03486-3
Online ISBN: 978-3-030-03487-0
eBook Packages: Religion and PhilosophyPhilosophy and Religion (R0)