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Abstract

I extend theories of nonmonotonic reasoning to account for reasons allowing free choice. My approach works with a wide variety of approaches to nonmonotonic reasoning and explains the connection between reasons for kinds of action and reasons for actions or subkinds falling under them. I use an Anderson–Kanger reduction of reason statements, identifying key principles in the logic of reasons.

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Notes

  1. To avoid commitments about the metaphysical nature of reasons (see, e.g., Alvarez 2010, 2016; Hyman 2015), we might say more cautiously that reasons are specified by premises of practical reasoning.

  2. This problem appears originally in Aristotle, who speaks “of the man who, though exceedingly hungry and thirsty, and both equally, yet being equidistant from food and drink, is therefore bound to stay where he is” (De Caelo II 13 295b32–35; Buridan comments on this passage in his unpublished Expositio Textus De Caelo, where his example concerns a dog (Rescher 1959, p. 154)). A version of the puzzle reappears in al-Ghazali, who summarizes the position of “the philosophers” (primarily Avicenna): “Indeed, if in front of a thirsty person there are two glasses of water that are similar in every respect in relation to his purpose [of wanting to drink], it would be impossible for him to take either\(\ldots \)” (Al-Ghazali 2000, I, 41, pp. 32–39). It appears most poetically in Dante: “Between two foods alike in appetite, and like afar, a free man, I suppose, would starve before either of them he would bite” (Paradiso III, Canto IV, quoted in Rescher 1959, p. 152). The fabled donkey first appears in the writings of Buridan’s critics.

  3. Mill’s formulation suggests another way to understand the distinction between perfect and imperfect obligations, as narrow-scope and wide-scope obligations, respectively. Where x is some person or action, perfect obligations have the form \(\exists x OA(x)\), and imperfect obligations have the form \(O \exists x A(x)\) (with no commitment to \( \exists x OA(x)\)). Assuming constant domains, \(\exists x OA(x)\) implies \(O \exists x A(x)\). But the reverse does not hold. So, the situation described can recur for any de dicto obligation, whether or not it would traditionally be considered imperfect.

  4. Jonathan Dancy suggested the idea of applying Prichard’s question to reasons. The example is Buridan’s: “Debeo tibi denarium” (1977, p. 83).

  5. In speech, we would normally express the thoughts leading to the puzzle by using emphasis: I have no reason to give you Blackie. This is not equivalent to the sentence without emphasis, for it sets up a contrast class (Rooth 1992).

  6. Where the disjunction represents different epistemic possibilities rather than freedom to choose, in contrast, the disjunction or existential quantifier has wide scope. We can read I have reason to give you Blackie or Tawny—I’m not sure which as (I have reason to give you Blackie) or (I have reason to give you Tawny). Fox (2012, 2015) makes an analogous point with respect to imperatives; compare the two readings of Buy some teak or mahogany—whichever you prefer as opposed to whichever is in stock. See also Kaufmann (2012).

  7. This framing ignores a limitation of Horty’s system, which relies on the default logic of Reiter (1980); a default such as \(A \rightarrow B\) never appears as the conclusion of an argument. Gelfond et al. (1991) and Brewka (1992) have investigated expanding default logic to allow defaults to be derived from other defaults. As Horty’s system stands, the equivalent point would be that, in a default theory with the single default \(A \rightarrow (B \vee C)\), the defaults \(A \rightarrow B\) and \(A \rightarrow C\) would be inadmissible; they could enlarge the set of consequences.

  8. Assume for the sake of simplicity that each object in the domain has a constant in the language designating it.

  9. Note that material implication and counterfactual conditionals violate (38)a, b, and c and so are not suitable candidates for this connective.

  10. The most attractive accounts of nonmonotonic reasoning for my purpose are therefore based on pivotal valuation accounts (e.g., circumscription (McCarthy 1980; Lifschitz 1994), KLM (Kraus et al. 1990), or commonsense entailment (Asher 1995; Morreau 1997a)), since they automatically satisfy (40)b (Makinson 2005). Disjunctive Antecedents can however be added to theories based on pivotal rule accounts such as default logic (Reiter 1980; Horty 2012) or theories using maxfamily operations (Makinson and Torre 2000).

  11. I am again abstracting away from a limitation of Horty’s system, since default logic, as Reiter and Horty develop it, is purely sentential. A natural quantificational extension, however, would make \(\forall x (A \leadsto B)\) and \(A \leadsto \forall x B\) equivalent, where x is not free in A.

  12. It might seem more faithful to Cicero’s words to interpret him as saying something higher-order, familiar from Chisholm (1964), and interestingly elaborated in Rett (2016): If OA, then, for some B, B and B is a reason for A. On (41d), this becomes, if OA, then there is some B such that B and \(B | \!\!\!\approx A \leadsto \alpha \). But then, provided that \(OA, B | \!\!\!\approx A \leadsto \alpha \), OA defeasibly implies \(A \leadsto \alpha \). Presumably, if B is a reason for A, it doesn’t undermine A’s being a duty. Cutting out the intermediate step thus allows us to avoid higher-order quantification without any cost. I set aside here, incidentally, issues concerning the connection between reasons and motivational states. (See, e.g., Manne 2014).

  13. This would again require extending H to include embedded defaults, as in Brewka (1992).

  14. I am grateful to Jonathan Drake, Daniel Muñoz, and two anonymous referees for their comments on earlier drafts of this paper. I have learned much from Jonathan Dancy; his reading of Prichard in a seminar on practical space inspired the paper’s central idea. I am also grateful to conference participants at Washington University, especially, Jonathan Kvanvig, whose comments on my talk helped to shape the paper. Finally, I owe thanks to the Classical Theism Project for supporting this work.

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    Daniel Bonevac

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Bonevac, D. Free choice reasons. Synthese 196, 735–760 (2019). https://doi.org/10.1007/s11229-017-1540-7

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