The property of rationality: a guide to what rationality requires?

Abstract

Can we employ the property of rationality in establishing what rationality requires? According to a central and formal thesis of John Broome’s work on rational requirements, the answer is ‘no’—at least if we expect a precise answer. In particular, Broome argues that (i) the property of full rationality (i.e. whether or not you are fully rational) is independent of whether we formulate conditional requirements of rationality as having a wide or a narrow logical scope. That is, (ii) by replacing a wide-scope requirement with a corresponding narrow-scope requirement (or vice versa), we do not alter the situations in which a person is fully rational. As a consequence, (iii) the property of full rationality is unable to guide us in determining whether a rational requirement has a wide or a narrow logical scope. We cannot resolve the wide/narrow scope debate by appealing to a theory of fully rational attitudes. This paper argues that (i), (ii) and (iii) are incorrect. Replacing a wide- with a corresponding narrow-scope requirement (or vice versa) can alter the set of circumstances in which a person is fully rational. The property of full rationality is therefore not independent of whether we formulate conditional requirements of rationality as having a wide or a narrow logical scope. As a consequence, the property of full rationality can guide us in determining what rationality requires—even in cases where we expect a precise answer.

Appendix

Kolodny’s counterargument. Kolodny (2007b, pp. 375–376) argues that Property equivalence and Theorem do not hold for what he calls ‘process requirements’.²⁸ I argue that Kolodny fails to show this.

Consider a simplified version of a narrow-scope conditional requirement, the wide-scope counterpart of which differs, according to Kolodny, in terms of its conditions of violation²⁹:

Necessarily, if, at t ₁, you believe that you ought to X, then rationality requires of you that, at t ₃, you intend to X,

where time t ₁ precedes t ₃. Expressed as a code constraint, this requirement reads as follows:

(NP):

For all w: B _t1[O(X)] → [I _t3(X) ∈ RP(w)],

where B stands for ‘you believe that’, O for ‘you ought to’, and I for ‘you intend to’. The corresponding wide-scope constraint reads as follows:

(WP):

For all w: {B _t1 [O(X)] → I _t3(X)} ∈ RP(w)

Kolodny thinks that there are situations in which you are fully rational under (WP), but not so under (NP). His argument runs as follows (2007b, pp. 375–376): suppose that, at t ₁, you believe that you ought to X without intending to X. However, at t ₂ (i.e. after t ₁ and before t ₃), you abandon your belief that you ought to X. Furthermore, at t ₃, you fail to intend to X. Kolodny argues that in this situation you cannot be fully rational under (NP). Yet (WP) does not imply this.

This is not correct. It is true that under (NP) you are not entirely rational. Since, at t ₁, you believe that you ought to X, ‘At t ₃, you intend to X’ is a required proposition. But this proposition turns out to be false. You are not fully rational. However, the same holds for (WP). If, at t ₁, you believe that you ought to X, and, at t ₃, you fail to intend to X, you are also not entirely as rationality requires you to be, since the required proposition ‘If, at t ₁, you believe you ought to X, then, at t ₃, you intend to X’ turns out to be false. This result holds despite the fact that, at t ₂, you drop your belief that you ought to X. Thus Kolodny’s example disproves neither Property equivalence nor Theorem.

Broome’s proof. Broome (2007a, pp. 369–370) provides us with a proof for his theorem (see Sect. 6). Although Theorem proves correct, Broome’s original proof does not. Here is why.

Consider only the final part of the proof. Here, Broome tries to establish that, necessarily, if you are fully rational under R ₂, you are also fully rational under R ₁ ³⁰:

[T]ake a world w where ‘You are rational’ is true under R ₂. I shall prove it is also true under R ₁. Since w satisfies all the requirements in R ₂(w), and R ₁(w) contains all the same requirements apart from the single one that differs, w satisfies all the requirements in R ₁(w) apart from, possibly, that final one.

Because (p → q) is in R ₂(w), and ‘You are rational’ is true at w under R ₂, (p → q) is true at w. Either p is true at w or it is not. If it is, then q is in R ₁(w): q is required at w according to R ₁. And this requirement is satisfied; q is true at w because both p and (p → q) are true there. On the other hand, if p is not true at w, there is no final requirement in R ₁(w) to be satisfied. Either way, w satisfies all the requirements in R ₁(w). ‘You are rational’ is therefore true at w under R ₁.

Broome argues as follows: if p is true at w, and you are fully rational under R ₂, then you also satisfy all requirements under R ₁. Under R ₂, (p → q) is a required proposition. At all p-worlds (p → q) is true if and only if q is true. This in turn guarantees that you also satisfy all requirements under R ₁. At all p-worlds, q is a required proposition under R ₁.

What about not-p-worlds? In those worlds, (p → q) is true in virtue of p’s being false. Hence, you are fully rational under R ₂. But what about R ₁? Broome argues that you are also fully rational under R ₁. His point is this: ‘if p is not true at w, there is no final requirement in R ₁(w) to be satisfied’. That is, if p is false at w, then q is not a required proposition.

Consequently, Broome’s proof relies on the following principle of requirement ‘avoidance’. Described as a constraint of a code, this principle reads as follows:

Avoidance. Necessarily For all w: {{[p ∈ w] → [q ∈ RP(w)]} & [¬p ∈ w]} → ¬[q ∈ RP(w)].

Less technically: whenever p implies that rationality requires you to q, then if not-p, you are not required to q.

Avoidance has been commonly assumed to hold true for requirements that are represented by a code satisfying (NC) (see, for example, Broome 2007b, p. 38, 2013a; Lord 2011; Hill 1973; Schroeder 2004, 2005, p. 362; and Vranas 2008). However, the logic of an (NC)-code fails to support Avoidance. So, to the extent that it relies on Avoidance, Broome’s proof contains a mistake.

(NC) depicts the following constraint of a code: necessarily, if w is a p-world, then q is a required proposition at w. The implication here is a material one. This is necessary, inter alia, to support an important aspect of (WC)-type requirements: if (p → q) is a required proposition at w, you can satisfy the corresponding requirement by ensuring that ‘not-p’ holds at w. However, it also implies that the logic of the (NC)-type requirements does not support Avoidance. In fact, Avoidance falls foul of the requirements of logic, as it represents the fallacy of denying the antecedent: the fact that p materially implies that q is a required proposition does not imply that if p is not true, then it is not the case that q is a required proposition.

The following example shows why it would not even be a good idea to inject Avoidance into the logic of requirements that (NC) represents. Suppose you believe that you ought to drive carefully. Suppose this implies materially that ‘You to intend to drive carefully’ is rationally required of you. At some point you drop your belief that you ought to drive carefully. This does not suffice to ensure that intending to drive carefully is no longer rationally required of you. For example: suppose that you, at the same time, intend to arrive home safe and sound, and you believe that a necessary condition of your doing so is that you drive carefully. Intending to drive carefully will still be rationally required of you—despite your having dropped the belief that you ought to drive carefully. This shows that Avoidance is not correct. Broome’s proof contains a mistake.³¹