Abstract
A triviality result for what Lewis (Mind 105: 303–313, 1996) called “the Desire by Necessity Thesis” and Broome (Mind 100(2): 265–267, 1991) called “the Desire as Expectation Thesis” is presented. The result shows that this thesis and three other reasonable conditions can be jointly satisfied only in trivial cases. Some meta-ethical implications of the result are discussed. The discussion also highlights several issues regarding Lewis’ original triviality result for “the Desire as Belief Thesis” that have not been properly understood in the literature.
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Notes
By “anti-Humean thesis” Lewis meant a thesis that allows a rational agent’s beliefs to restrict the agent’s desires in a way that is not captured by the standard rationality assumptions (see Lewis 1996 and Broome 1999, Chap. 5, for more detailed discussions). Others (for example, Weintraub 2007; Oddie 1994; Piller 2000) took Lewis’ result to be a challenge to moral cognitivism generally. I agree. Humean moral cognitivism (i.e. the position according to which moral judgments are beliefs but these beliefs do not constrain the desires of a morally motivated rational agent in any way) is logically possible, I believe, but seems to me completely unmotivated. Thus, although in the rest of the paper I will—most of the time—not be explicit about the implications of the discussion to the moral cognitivism anti-cognitivism debate, I believe that all of the implications of the discussion to the Humean anti-Humean debate (which I will discuss) are directly relevant to the cognitivism anti-cognitivism debate.
The demand that the constraint will still hold after any redistribution of the agent’s degrees of belief, is crucial. Without this demand, Lewis’ result does not hold. However, as will be explained later on in this section, this demand is philosophically motivated. At this point, it will be enough to think of the demand in the following way: if one takes some constraint on an agent’s attitudes at a given point in time to be normatively appealing, then after the agent changes some of these attitudes in a normatively permissible way (whatever the norm is: rationality, morality or anything else) the constraint must still hold, as a set of attitudes that is normatively permissible that has been updated in a normatively permissible way must lead to a normatively permissible set of attitudes. The same idea plays a significant role in Lewis’ discussions of the Principal Principle and Adam’s thesis (see Lewis 1976; 1980 and Lewis 1994). I will return to this point later on.
I thank an anonymous referee for pointing this out to me.
This derivation, however, holds only for the simple case—that is usually discussed in the literature—in which there are only two possible degrees of goodness, either 0 or 1. As noted, Lewis’ result holds also for the general case but I was not able to find an analogous simple derivation for the general case. Nothing substantive hangs on this.
See also Oddie (1994). Oddie did try to “save” the DBT by arguing that although it is true in every informational state, the moral propositions (the different \(\hbox {A}_{\mathrm{i}}^{*}\hbox {s}\)) may change from one informational state to another. The explanation he provides for this phenomenon is based on what Lewis called the Principal Principle, which will play a significant role in the result that will be presented in the next section. Nothing in what Oddie says can help him avoid my result.
Since from Jeffrey’s desirability axiom we get: \(\hbox {d(A)} = \sum \nolimits _{i= 1\ldots n } d(A_{i}^{*}A)(c(A_{i}^{*}{\vert } A)\) and by substituting each \(d(A_{i}^{*}A)\) with the corresponding i, we get Price’s thesis.
The derivation is similar to the derivation of Price’s thesis from the PMP, presented in footnote 9.
Of course, one can accept the DBT without accepting Adam’s Thesis. The point is, though, that by rejecting Adams’ Thesis it is possible to accept the DET without accepting the DBT.
This is a bit hard to swallow, as we are asked to believe that the question as to whether Adams’ Thesis is true or false, and whether conditionals express propositions or not, can settle the question of whether anti-Humeanism is possible or not. It follows from Broome’s analysis that if he were convinced that Adams’ Thesis is true, and that conditionals express propositions, he would stop being an anti-Humean (which he claims to be; see Broome 1999). This is, no doubt, a radical conclusion and I believe this is so regardless of the question as to whether anti-Humeanism is true or not. Both Humeans and anti-Humeans should resist the claim that what they are really arguing about is the nature of conditionals. This need not concern us now, however.
See Smith (2002) for an example of such a meta-ethical position.
This is, basically, the move Oddie (1994) makes.
Of course, Lewis—as he himself admitted in his 1996 paper—did not actually “prove” that there can be no other consistent anti-Humean thesis that may play the role the DBT was supposed to play. However, he proved that several promising candidates cannot play this role. Now, the DET on its own, as was just explained, cannot play this role and so, in the absence of any other alternative, we must—at least tentatively—adopt the conclusion that one must be either a moral realist or a Humean.
See Meachem (2010) for an alternative—and more precise—definition for admissibility.
Many readers, I suspect, will be tempted, at this point, to question the validity of the NDC and the NVC for their apparent commitment to the claim that the fairness of lotteries has no moral value. In the next section I will explain why the fairness of lotteries is not what is at issue here. For now, we can think of both the NDC and the NVC as conditions that sometimes hold. Even those who are committed to the claim that lotteries are sometimes more fair, and thus have higher moral value, than deterministic choices, must accept that in some cases this is not so. We can limit our attention, then, to those cases in which fairness considerations do not arise and thus the agent assigns a positive credence only to theories that respect the NVC and his own desires naturally respect the NDC.
But see Bradley (2007) for an example of how several different decision theoretic frameworks can be expressed in his generalization of Jeffrey’s framework.
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Acknowledgments
I thank Richard Bradley and two anonymous referees for helpful comments on earlier versions of this paper.
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Nissan-Rozen, I. A triviality result for the “Desire by Necessity” thesis. Synthese 192, 2535–2556 (2015). https://doi.org/10.1007/s11229-015-0666-8
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DOI: https://doi.org/10.1007/s11229-015-0666-8