Abstract
The paper identifies a key pragmatic principle that is responsible for the information-sensitivity of deontic modals. Information-sensitivity has been extensively discussed in the recent linguistic and philosophical literature, in connection with a decision problem known as the Miners’ puzzle (Kolodny and MacFarlane 2010). I argue that the so-called Ellsberg paradox (Ellsberg 1961) is a more general source of information-sensitivity. Then I outline a unified pragmatic solution to both puzzles on the basis of a well-known decision procedure (MiniMax).
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.
In the standard modal semantics (Kratzer 2012), the consequent of such an entailment is a proposition in the ordering source, while the antecedent is the proposition in the scope of the deontic modals. Roughly, the more consequent-propositions in the ordering source follow from the antecedent-proposition, the more deontically valuable the antecedent-proposition is.
- 2.
In decision-theoretic terms, complex acts and outcomes are obtained by putting together the information in the estimated desirability matrix of a decision problem. More precisely, we could gather the information on a specific row of a matrix (which corresponds to an act), or by considering for deliberation a combination of rows (acts) of the matrix (cf. Jeffrey 1965/1983). For completeness, the outcomes—seen as entailments of the acts—should be weighted with the probabilities of the relevant conditions, but we shall leave this information implicit.
- 3.
It is natural to stipulate that acts, viewed as propositions, should be non-empty, and thus should have at least one element (i.e., world).
- 4.
- 5.
Notation: \(R\), \(B\), and \(Y\) stand for red, blue, and yellow balls. \(R > B\) means that there are more red balls than blue ones, or that \(R\) is more probable than \(B\). Because the outcomes of the acts are equal, the probabilistic relation \(>\) translates into a preference relation \(\succ \) (but not vice-versa). So \(R > B\) means that choosing red is more probable than choosing blue, but can also read as saying that the former is preferable to the latter. Finally, the disjunctions should be interpreted as inclusive, unless either ... or-phrases are used. E.g. opting for \(R \vee B\) brings about the prize if any of the red or blue balls is then randomly drawn. (The same could be expressed in terms of conjunction, if we interpreted the letters as bets on colours, because e.g. choosing blue or yellow will amount to betting on blue and yellow.).
- 6.
A version of the puzzle can be stated even if we assume that the deontic necessity modal ought to requires a strict preference relation. To do this, we assume that one of the following should hold: \(B>Y\), \(Y>B\), or \(Y=B\). We then formulate three conditionals having these three statements as antecedents. For instance, we’ll have the new conditional: If \(Y=B\), we ought to be indifferent between the three options. (The other two conditionals will be like (6)-(7), but formulated in terms of the strict relation, \(>\).) It then follows by disjunctive syllogism that we ought to choose \(B\), \(Y\), or \(R\), which contradicts (3).
- 7.
Complementarity does not hold in (E) either. Complementarity requires that if \(A \succ B\), then \(\lnot A \preceq \lnot B\), where \(\succ , \preceq \) etc. are preference relations. Yet \(R \succ B\), but \(\lnot R = B \vee Y \succ \lnot B = R \vee Y\), and so complementarity is violated.
- 8.
For experimental evidence that the pattern of reasoning is robust see references in Camerer and Weber (1992, 332ff.).
- 9.
- 10.
In Nasta (2015b) I call this property instability and show that it holds of preferences and deontic commitments in general.
- 11.
E.g. in (M), blocking shaft \(A\) dominates the other two acts under the condition that the miners are in shaft \(A\).
- 12.
This decision procedure is closely related to the minimax regret rule invoked in rational choice theory; see Levi (1980, 144ff.) for discussion and references.
- 13.
I discuss more extensively the role of disjunction in settings (M) and (E) in Nasta (2015a).
- 14.
See von Fintel (2012, pp.28–29) for relevant evidence of this type. This evidence suggests that conditionals admit of implicit restrictors which are sensitive to local pragmatic implications. Such local pragmatic (coherence-based) implication exists in several other linguistic domains (cf. Simons 2014).
- 15.
- 16.
On the one hand, it is easy to check that MiniMax gets a good prediction for the conjunctive act of blocking both shafts in (M), and for the act of choosing a red ball in (E). On the other hand, it is much more difficult to come up with a sharp comparison between the disjunctive acts \(B_a \vee B_b\), \(B_a \vee B_n\), and \(B_b \vee B_n\). The latter two acts guarantee that either no miner will be saved or nine miners will be saved or all of them will be saved (\(S_0 \vee S_9 \vee S_{10}\)), whilst the former act guarantees that either zero or ten miners will be saved (\(S_0 \vee S_{10}\)). A first problem is that in order to estimate the desirabilities of the acts we have to come up with probabilities for the disjuncts. And even after doing that, it is not clear that there will be only one obvious way of choosing between the estimated desirabilities thus obtained.
References
Camerer, C., Weber, M.: Recent developments in modeling preferences: uncertainty and ambiguity. J. Risk Uncertainty 5, 325–370 (1992). (cit. on p. 5)
Cariani, Fabrizio, Kaufmann, M., Kaufmann, S.: Delib- erative modality under epistemic uncertainty. Linguist. Philos. 36, 225–259 (2013). doi:10.1007/s10988-013-9134-4. (cit. on p. 9)
Carr, J.: Subjective Ought. ms. MIT (2012). (cit. on p. 9)
Charlow, Nate: What we know and what to do. Synthese 190, 2291–2323 (2013). doi:10.1007/s11229-011-9974-9. (cit. on p. 9)
Ellsberg, D.: Risk, ambiguity, and the Savage axioms. The Quarterly Journal of Economics, pp. 643–669 (cit. on pp. 1, 3) (1961)
Fishburn, P.C.: The axioms of subjective probability. Stat. Sci. 1(3), 335–358 (1986). (cit. on p. 3)
Goble, L.: Utilitarian deontic logic. Philos. Stud. 82(3), 257–317 (1996). (cit. on p. 9)
Halpern, J.Y.: Reasoning About Uncertainty. MIT Press, Cambridge (2005). (cit. on p. 3)
Jeffrey, R.C.: The logic of decision, 2nd edn. University of Chicago Press, Chicago (1965/1983) (cit. on p. 3)
Kolodny, N., John, M.: Ifs and oughts. J. Philos. 107(3), 115–143 (2010). (cit. on pp. 1, 2, 9)
Kratzer, A.: Modals and Conditionals. Oxford University Press, Oxford (2012). doi:10.1093/acprof:oso/9780199234684.001.0001. (cit. on p. 2)
Lassiter, D.: Gradable epistemic modals, probability, and scale structure. In: Li, N., Lutz, D. (eds.) Semantics and Linguistic Theory (SALT), vol. 20, pp. 197–215. CLC Publications, Ithaca (2010). (cit. on p. 5)
Lassiter, D.: Measurement and Modality: the Scalar Basis of Modal Semantics. Ph.D. thesis, New York University (2011) http://semanticsarchive.net/ Archive/WMzOWU2O/ (cit. on p. 9)
Levi, I.: The Enterprise of Knowledge. MIT Press, Cambridge (1980). (cit. on p. 6)
Nasta, A.: Disjunctive deontic modals. ms. Pittsburgh/East Anglia (2015a) (cit. on p. 7)
Nasta, A.: Unstable preferences, unstable deontic modals. ms. Pittsburgh/East Anglia (2015b) (cit. on p. 5)
Simons, Mandy: Local pragmatics and structured contents. Philos. Stud. 168, 21–33 (2014). doi:10.1007/s11098-013-0138-2. (cit. on p. 8)
von Fintel, K.: The best we can (expect to) get? Challenges to the classic semantics for deontic modals. In: 85th Annual Meeting of the American Philosophical Association, Chicago (2012). http://web.mitedu/fintel/fintel-2012-apa-ought.pdf (cit. on p. 8)
Yalcin, S.: Proabability operators. Philos. Compass 5(11), 916–937 (2010). doi:10.1111/j.1747-9991.2010.00360.x. (cit. on p. 5)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Nasta, A. (2015). Deontic Modals with Complex Acts. In: Christiansen, H., Stojanovic, I., Papadopoulos, G. (eds) Modeling and Using Context. CONTEXT 2015. Lecture Notes in Computer Science(), vol 9405. Springer, Cham. https://doi.org/10.1007/978-3-319-25591-0_27
Download citation
DOI: https://doi.org/10.1007/978-3-319-25591-0_27
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-25590-3
Online ISBN: 978-3-319-25591-0
eBook Packages: Computer ScienceComputer Science (R0)