Abstract
Reasons transmit. If one has a reason to attain an end, then one has a reason to effect means for that end: reasons are transmitted from end to means. I argue that the likelihood ratio (LR) is a compelling measure of reason transmission from ends to means. The LR measure is superior to other measures, can be used to construct a condition specifying precisely when reasons transmit, and satisfies intuitions regarding end-means reason transmission in a broad array of cases.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
For statements of various versions of a principle of reason transmission, see Darwall (1983), Raz (2005), Schroeder (2009), Bedke (2009), and Kolodny (forthcoming). Many have taken such a principle for granted, but Korsgaard (1997) and others have argued that Humeans cannot account for the normativity of reason transmission, while Humeans respond by arguing that a principle of reason transmission is a brute norm (Beardman 2007) or constitutive of an agent’s desire for an end (Finlay 2008). What follows remains neutral on the source of the normativity of reason transmission.
Cartwright’s complete definition takes into account the expected probabilities of all state descriptions KJ consistent with L by multiplying both conditional probabilities in the inequality by p(KJ) summed over all J (see her 1979 for details). From here on I will drop the added notation for the sake of simplicity.
I was first introduced to the idea of a probabilizing condition for reason transmission in a colloquium talk by Niko Kolodny. His associated paper will not appear in print for some time (personal communication).
Moreover, anytime p(M) > p(M|E), then PR < 0, and according to PR, M is not a means for E, and so reasons do not transmit from E to M.
To relate this to my case of high p(M) below (Sect. 4.4): simply because Deb has a high prior probability for studying does not mean that Deb has little reason to study. That would be perverse. Indeed, Deb evidently has plenty of reasons for studying. The PR measure simply indicates that whatever reasons Deb has for studying, these reasons are comprised only modestly from reasons transmitted from her desire to do well on the logic exam.
Is PP necessary to characterize reason transmission? Necessity in this context—the requirement that a means render the probability of the end at least greater than 0—is prima facie such a weak condition that it is hardly worth mentioning. Nevertheless, there is some reason to think that PP is in fact not necessary to characterize transmission of reasons from end to means. Any situation in which one thinks that reasons transmit from end to means and yet p(E|M) = 0 would show that PP is not necessary to characterize reason transmission from ends to means. Futility, for instance, might be characterized this way. One might think that a more egalitarian distribution of the world’s resources would be a means toward achieving world peace, even if one thinks that world peace is impossible to achieve. That is, p(E|M) = 0 despite thinking that M is a means for E.
This is widely accepted—see, e.g., Darwall (1983), Schroeder (2009), and Bratman (2009). The LR, PP, and PR measure all return the result that reasons transmit from the end of winning the lottery to the means of buying a lottery ticket. Of course such reasons can be outweighed by countervailing reasons, such as the costs associated with doing M or norms constraining M.
That is, in order to consider e as evidence for H, both p(H|e) > p(H) and p(H|e) > x must be the case. Achinstein suggests that a natural threshold value for x is 0.5.
Proof: applying Bayes’ Theorem to LR results in:
-
(1)
[p(E|M)p(M)/p(E)]/[p(~E|M)p(M)/p(~E)] (from LR and Bayes’ Theorem)
-
(2)
[p(E|M)/p(E)]/[p(~E|M)/p(~E)] (from (1), p(M) terms cancel)
Since the prior probability of M, p(M), appears in both the numerator and the denominator of (1), and (1) is equivalent to LR, p(M) cancels out in LR to give (2). Thus the degree of reason transmission as measured by LR is not sensitive to p(M).
-
(1)
I use ‘background context’ here as shorthand for the state descriptions KL of situation L which include the complete set of means relevant to E not including M.
Properly stratifying the population from which we determine the relevant probabilities also resolves a concern raised by Kolodny (forthcoming), who considers a boxer who always ‘telegraphs’ his intention to punch by gritting his teeth: “In spite of inadvertently warning his opponent, he nevertheless sometimes connects. So the probability, conditional on telegraphing, of connecting is positive. However, intuitively, no reason transmits to telegraphing”. If we let E = ‘hit opponent’ and T = ‘telegraph’, then p(E|T) > 0, and so PP prima facie returns the wrong verdict. This is why Kolodny adds his effectiveness clause to PP (discussed in Sect. 2): telegraphing does not help to bring about hitting the opponent. Kolodny also notes that p(E|T) > p(E|~T), which contradicts a seemingly attractive measure of probability raising (such a measure is defended in the probabilistic causality literature). However, recall the single constraint stipulated on determining the relevant probabilities: they must be calculated from the largest population which is homogeneous with respect to the complete set of means relevant to the end but not including the particular means in question. To determine if telegraphing is a means for landing a punch, we should calculate the probabilities among all boxers (stratified by other means for E); calculating the relevant probabilities for this particular boxer would be to over-stratify the relevant population. Since telegraphing warns one’s opponent amongst boxers generally, we have p(E|T) < p(E|~T), and so the measure that Kolodny was opposed to is saved. LR also returns the correct verdict: since p(T|E) is zero or nearly so, while p(T|~E) is a bit larger, since there are some non-hitting ends which raise the probability of telegraphing (such as training a boxer, feigning a punch with a friend, goofing around with the kids, etc.), LR < 1, which is exactly what intuition says about the case, with no added clauses: whatever reasons a boxer has to land a punch do not transmit to telegraphing. Another nice thing about LR is that it is symmetric—that is, an LR measure can show a countermean—an LR < 1 implies that reasons to hit transmit to not telegraphing.
Proof:
(1)
if M is SM for E then p(M|~E)p(~E)/p(M) = 0
(SM, Bayes’ Theorem)
(2)
p(M|~E)p(~E)/p(M) = 0 iff p(M|~E) = 0 or p(~E) = 0
(by definition)
(3)
if M is SM for E then [p(M|~E) = 0 or p(~E) = 0]
(from 1 and 2)
(4)
if p(M|~E) = 0, then LR is undefined
(division by zero)
(5)
p(~E) = 0 iff p(E) = 1
(by definition)
(6)
if M is SM for E then [LR is undefined or p(E) = 1]
(from 3, 4, 5)
(7)
if M is SM for E and if p(E) ≠ 1, then LR is undefined
(from 6)
Some might think that epistemic modesty should render us wary of any specific probability. I have much sympathy with this view, but a full discussion of it would take this paper far afield.
Raz’s (2005) facilitative principle is: “When we have an undefeated reason to take an action, we have reason to perform any one (but only one) of the possible (for us) alternative plans that facilitate its performance”.
Commenting on this case, Bedke (2009) writes “Unlike Broome, however, I am inclined to think that I do have some reason to kill myself in this case. It is just massively outweighed.” A virtue of LR is that one can share Broome’s intuition that, contra Bedke, one does not have any reason to kill oneself at all, and yet avoid Broome’s conclusion that there is a problem with a principle akin to Raz’s facilitative principle.
This is axiomatic. Immediately below I argue that the two conditional probabilities are in fact equal in this case.
Proof: rearrange (iv) as follows.
-
(iv)
p(M|E)p((MvB)|~E) > p((MvB)|E)p(M|~E)
We know that p(M|E) = p((MvB)|E), because necessarily p((MvB)|E) ≥ p(M|E), and conditioning on E does not raise the probability of (MvB) compared with M alone. So (iv) reduces to p((MvB)|~E) > p(M|~E). We have noted that there are non-E ends, like destroying all traces of my letter, which raise the probability of B, so in fact it is true that p((MvB)|~E) > p(M|~E).
-
(iv)
But not both! Because:
p((F & B)|E) ≪ p((F & B)|~E)
There are some non-E ends—such as playing hide and seek, or chasing one’s disobedient puppy—that make entering the house sequentially via both doors more probable than does the end of entering the house simpliciter.
References
Achinstein, P. (2001). The book of evidence. Oxford: Oxford University Press.
Beardman, S. (2007). The special status of instrumental reasons. Philosophical Studies, 134, 255–287.
Bedke, M. (2009). The iffiest oughts: a guise of reasons account of end-given conditionals. Ethics, 119, 672–698.
Bratman, M. (2009). Intention, practical rationality, and self-governance. Ethics, 119, 411–443.
Broome, J. (2005). Have we reason to do as rationality requires? A comment on Raz. Journal of Ethics and Social Philosophy, 1(1). www.jesp.org. Accessed on 23 Feb 2012.
Cartwright, N. (1979). Causal laws and effective strategies. Nous, 13, 419–437.
Cartwright, N. (1989). Nature’s capacities and their measurement. Oxford: Oxford University Press.
Darwall, S. (1983). Impartial reason. Ithaca, NY: Cornell University Press.
Finlay, S. (2008). Motivation to the means. In D. K. Chan (Ed.), Moral psychology today: Values, rational choice, and the will. Berlin: Springer.
Fitelson, B. (1999). The plurality of Bayesian measures of confirmation and the problem of measure sensitivity. Philosophy of Science, 66, S362–S378.
Kant, I. (1996). Groundwork of the metaphysics of morals (1785), In M. J. Gregor and A. Wood (Eds.), The Cambridge edition of the works of Immanuel Kant, practical philosophy. Cambridge, MA: Cambridge University Press.
Kolodny, N. (forthcoming). Toward a principle of instrumental transmission. In D. Star (Ed.), Oxford handbook and reasons and normativity. Oxford University Press.
Korsgaard, C. (1997). The normativity of instrumental reason. In G. Cullity & B. Gaut (Eds.), Ethics and practical reason. Cambridge, MA: Cambridge University Press.
Raz, J. (2005). The myth of instrumental rationality. Journal of Ethics and Social Philosophy, 1, 1–28. www.jesp.org. Accessed on 23 Feb 2012.
Ross, A. (1941). Imperatives and logic. Theoria, 7, 53–71.
Schroeder, M. (2009). Means-end coherence, stringency, and subjective reason. Philosophical Studies, 143, 223–248.
Skyrms, B. (1980). Causal necessity. New Haven, CT: Yale University Press.
Acknowledgments
Niko Kolodny first introduced to me to a principle of reason transmission during his colloquium talk at University of California, San Diego (2009); I have since benefited from detailed correspondence with Kolodny. Nancy Cartwright gave meticulous feedback on an earlier version of this paper, and I am grateful for support from the Social Sciences and Humanities Research Council of Canada.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Stegenga, J. Probabilizing the end. Philos Stud 165, 95–112 (2013). https://doi.org/10.1007/s11098-012-9916-5
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11098-012-9916-5