¹ I have discussed this idea in: Spector, Horacio, “The Irrelevance of Ideal Morality to International Law,” Analisi e Diritto (2013): 209–224.Google Scholar

² Alchourron, Carlos and Bulygin, Eugenio, Normative Systems (Vienna: Springer-Verlag, 1971), 33.CrossRefGoogle Scholar

³ Knight, Frank, Risk, Uncertainty and Profit (New York: Augustus M. Kelley, 1964), 46.Google Scholar Note that “certainty” is opposed to both “uncertainty” and “risk” (just as “certain” is opposed both to “uncertain” and “risky”).

⁴ Beccaria, Cesare, An essay on crimes and punishments, 2nd ed., trans. Ingraham, Edward D. (Philadelphia: Philip H. Nicklin, 1819), available at http:/www.constitution.org/cb/crim_pun.htm Google Scholar

⁵ This is true of consequentialist models of weighing goods. See, for instance, Broome, John, Weighing Goods: Equality, Uncertainty and Time (Oxford: Blackwell, 1991).Google Scholar

⁶ Jarvis Thomson, Judith, “Imposing Risks,” in Rights, Restitution, and Risk: Essays in Moral Theory, ed. Parent, William (Cambridge, MA: Harvard University Press, 1986), 176.Google Scholar For readability reasons, I omitted the word “pure” in the quotation.

⁷ Nozick, Robert, Anarchy, State, and Utopia (New York: Basic Books, 1974)Google Scholar, 30 (footnote); Jarvis Thomson, Judith, The Realm of Rights (Cambridge, MA: Harvard University Press, 1990)Google Scholar, 153; Brennan, Samantha, “Thresholds for Rights,” Southern Journal of Philosophy 33, no. 2 (1995);CrossRefGoogle Scholar Alexander, Larry, “Deontology at the Threshold,” San Diego Law Review 37, no. 4 (2000);Google Scholar Zamir, Eyal and Medina, Barak, Law, Economics, and Morality (New York: Oxford University Press, 2010).CrossRefGoogle Scholar

⁸ Alexander, Larry, “Scalar Properties, Binary Judgments,” Journal of Applied Philosophy 25, no. 2 (2008): 97–99.CrossRefGoogle Scholar

⁹ Nozick, Anarchy, State, and Utopia, 107.

¹⁰ Maynard Keynes, John, A Treatise on Probability (New York: Cosimo, 2007);Google Scholar F. P. Ramsey, “Truth and Probability,” in Ramsey, F. P., Philosophical Papers, ed. Mellor, D. H. (Cambridge: Cambridge University Press, 1990);Google Scholar Finetti, Bruno de, Theory of Probability, Vol. 1 (New York: John Wiley and Sons, 1974).Google Scholar Prichard also embraced Keynes‘s epistemic approach: Prichard, H. A., Moral Obligation, Essays and Lectures (Oxford: Clarendon Press, 1949), 30.Google Scholar

¹¹ Bruno de Finetti, Theory of Probability, 3–4.

¹² In fact, decisional nonconsequentialism could also be understood in terms of the frequentist conception of probability by reinterpreting the doxastic operator B that I will use later on as a nonquantifiable operator that ranges over frequency-based probabilities.

¹³ Prichard, Moral Obligation, 29.

¹⁴ Ibid., 29–30. Prichard attributes this example to Collingwood.

¹⁵ Ibid., 30; italics in the original.

¹⁶ Parfit, Derek, On What Matters, Volume I (New York: Oxford University Press, 2011), 159.Google Scholar

¹⁷ I took the structure of the reasoning from: Kolodny, Niko and Macfarlane, John, “Ifs and Oughts,” The Journal of Philosophy 107, no. 3 (2010).CrossRefGoogle Scholar

¹⁸ Jackson, Frank, “Decision–Theoretic Consequentialism and the Nearest and Dearest Objection,” Ethics 101 (1991), 467.CrossRefGoogle Scholar

¹⁹ Ibid. Jackson’s supposition that a physical theory can leave the “passage to action” to a different discipline is very controversial. Such actions as experimentation and technical application must be determined by physics as well.

²⁰ Smith, Michael, “The Right, the Good and Uncertainty,” in Horgan, Terry and Timmons, Mark, eds., Metaethics after Moore (Oxford: Clarendon Press, 2006), 145.Google Scholar Smith disagrees with Jackson. He thinks that “the story from the inside of an agent” is not the business of ethics, but rather “the story of rational decision-making as outlined in the diagram above, the story that is formalized — or anyway partially formalized — in decision theory.” This seems like a semantic dispute. Decision theory in ethical contexts is the business of ethics.

²¹ Smith, Holly M., “Subjective Rightness,” Social Philosophy and Policy 27, no. 2 (2010): 74.CrossRefGoogle Scholar

²² In this respect, I follow Williams’s approach. See Williams, Bernard, “Ought and Moral Obligation,” in Moral Luck (Cambridge: Cambridge University Press, 1981), 114–23.CrossRefGoogle Scholar Although there are more complex ways to analyze the logical form of “ought,” I think that this simplification does not imply any significant explanatory cost related to the risk sensitivity of moral obligation.

²³ Prichard argued that the subjective “ought” does not dictate an obligation to do something, but “to perform an activity of a totally different kind, that of setting or exerting ourselves to do something.” He claimed that what we directly do is our intending (not intending) to do something, everything else being a more or less likely result of what we intend or do not intend. This is a plausible claim. However, I do not want to consider here the probability that the agent’s intention to do x will actually bring about his doing x. This would demand expository complexities that exceed the scope of this essay. Cf. Prichard, Moral Obligation, 34–35; italics added.

²⁴ I discuss the problem of “epistemic obligations” later on.

²⁵ Hill, Thomas, “The Hypothetical Imperative,” Philosophical Review 82, no. 4 (1973): 429–50;CrossRefGoogle Scholar Greenspan, 1975 Greenspan, Patricia, “Conditional Oughts and Hypothetical Imperatives,” The Journal of Philosophy 72, no. 10 (1975): 259–76;CrossRefGoogle Scholar Alchourron, Carlos, “Detachment and Defeasibility in Deontic Logic,” Studia Logica 57 (1996): 5–18;CrossRefGoogle Scholar Broome, John, “Normative Requirements,” Ratio 12, no. 4 (1999): 398–419;CrossRefGoogle Scholar Dancy, Jonathan, Practical Reality (Oxford: Oxford University Press, 2000), 49–76;Google Scholar Jay Wallace, R., “Normativity, Commitment, and Instrumental Reason,” Philosophers’ Imprint 1, no. 3 (2001).Google Scholar For an application to judicial reasoning, see: Zuleta, Hugo, Normas y justificacion (Madrid, Barcelona, Buenos Aires: Marcial Pons, 2008).Google Scholar

²⁶ Greenspan, Patricia S., “Conditional Oughts and Hypothetical Imperatives,” The Journal of Philosophy 72, no. 10 (1975): 265;CrossRefGoogle Scholar Vorobej, Mark I., “Conditional Obligation and Detachment,” Canadian Journal of Philosophy 16, no. 1 (1986): 16.CrossRefGoogle Scholar

²⁷ Chisholm, Roderick, “Contrary to Duty Imperatives and Deontic Logic,” Analysis 24 (1963): 33–36.CrossRefGoogle Scholar

²⁸ Jackson, “Decision–Theoretic Consequentialism and the Nearest and Dearest Objection,” 463.

²⁹ Jackson, “Consequentialism and the Nearest and Dearest Objection,” Ethics 101, no. 3 (1991);Google Scholar Zimmerman, Michael J., Living under Uncertainty. The Moral Significance of Ignorance (Cambridge: Cambridge University Press, 2008)CrossRefGoogle Scholar; Persson, Ingmar, From Morality to the End of Reason (Oxford: Oxford University Press, 2013), chap. 10.CrossRefGoogle Scholar

³⁰ Von Neumann, John and Morgenstern, Oskar, Theory of Games and Economic Behavior (Princeton, NJ: Princeton University Press, 1953),Google Scholar chap. I; Arrow, Kenneth J., “Exposition of the Theory of Choice Under Uncertainty,” in Essays in the Theory of Risk-Bearing (Amsterdam: North-Holland, 1971).Google Scholar

³¹ Frank Jackson, “Decision-Theoretic Consequentialism and the Nearest and Dearest Objection,” 462–63.

³² Michael J. Zimmmerman, Living under Uncertainty, 17–42.

³³ Ibid., 19.

³⁴ Ibid., 19.

³⁵ Ibid., 20.

³⁶ Ibid., 18.

³⁷ Ibid., 33–34.

³⁸ Ibid., 74.

³⁹ Ibid., 87.

⁴⁰ Ibid., 88.

⁴¹ Ibid., 94. Other rights in contract law might be interpreted in subjectivist fashion (e.g., contractors’ right to a good faith performance of the contract by the other party.)

⁴² Ibid., 99.

⁴³ This notion has nothing to do with the Continental expression “subjective rights”; in English all rights are subjective in the latter sense.

⁴⁴ Ibid., 96.

⁴⁵ Nozick, Anarchy, State, and Utopia, 105.

⁴⁶ Ibid., 106.

⁴⁷ Nozick offers different interpretations of the epistemic condition an agent must have in order to be permitted to cross the jurisdictional borders of another individual (ibid., 106–7).

⁴⁸ Ibid., 103.

⁴⁹ Ibid., 107.

⁵⁰ Ibid., 107; italics added.

⁵¹ Ibid., 7.

⁵² Cicero, De Officiis, Bk I, paragraph 18.

⁵³ Ross, W. D., The Right and the Good (Oxford: Clarendon Press, 1930), 19.Google Scholar

⁵⁴ Ibid., 18.

⁵⁵ Although his enterprise is different from mine, it is relevant to point out that Ralph Wedgwood proposes an expectational semantic analysis for deontic propositions. See Wedgwood, Ralph, “Objective and Subjective ‘Ought’,” in Charlow, Nate and Chrisman, Matthew eds., Deontic Modality (Oxford: Oxford University Press, 2015).Google Scholar

⁵⁶ Jackson, Frank and Smith, Michael, “Absolutist Moral Theories and Uncertainty,” The Journal of Philosophy 53 (2006): 271;Google Scholar Huemer, Michael, “Lexical Priority and the Problem of Risk,” Pacific Philosophical Quarterly 91 (2010): 333; 337.CrossRefGoogle Scholar

⁵⁷ Jackson and Smith, “Absolutist Moral Theories and Uncertainty,” 272.

⁵⁸ Ibid., 273.

⁵⁹ Ibid., 275.

⁶⁰ Aboodi, Ron, Borer, Adi, and Enoch, David, “Deontology, Individualism, and Uncertainty: A Reply to Jackson and Smith,” The Journal of Philosophy 105, no. 5 (2008).CrossRefGoogle Scholar They acknowledge that other deontological theories might be affected by the paradox.

⁶¹ Ibid., 264.

⁶² Jackson and Smith, “Absolutist Moral Theories and Uncertainty,” 278.

⁶³ Ibid., 270.

⁶⁴ Hume did not subscribe to this law. For Hume’s actual view, see my article “Hume’s Theory of Justice,” Rationality, Markets and Morals 5 (2014): 47–63 (freely available on the web).

⁶⁵ Nozick, Anarchy, State, and Utopia, 75.

⁶⁶ W. D. Ross, The Right and the Good, 19–20.

⁶⁷ Consequentialists might reject risk neutrality, but I doubt that they could do so without sliding into some form of nonconsequentialism. Rivera Lopez acknowledges: “I do not know any (consequentialist) argument for abandoning moral risk neutrality and endorsing a degree of moral risk aversion,” but he nonetheless thinks “that some degree of risk aversion is defensible on consequentialist grounds.” Rivera López, Eduardo, “The Moral Murderer. A (More) Effective Counterexample to Consequentialism,” Ratio 25 (2012): 313–14.CrossRefGoogle Scholar

⁶⁸ Parfit, Derek, Reasons and Persons (Oxford: Oxford University Press, 1984), 25;Google Scholar Frank Jackson, “Decision–Theoretic Consequentialism and the Nearest and Dearest Objection,” 468; John Broome, Weighting Goods, 124–26; Michael J. Zimmmerman, Living under Uncertainty, 19; Ingmar Persson, From Morality to the End of Reason, chap. 10; Rivera López, Eduardo, “Probabilities in Tragic Choices,” Utilitas 20, no. 3 (2008): 326.CrossRefGoogle Scholar

⁶⁹ Brandt, Richard B., Ethical Theory. The Problems of Normative and Critical Ethics (Englewood Cliffs, NJ: Prentice-Hall, 1959), 415–19.Google Scholar

⁷⁰ I am indebted to Marcelo Sancinetti for this example.