Reformed Philosophy

In the seminal work Epistemic Luck (2005), Duncan Pritchard provided the philosophical community with perhaps the most robust conception of luck to date, his modal account of luck (hereafter MAL). MAL’s chief critic has been Jennifer Lackey who in her related pieces “Critical Study: Pritchard’s Epistemic Luck” (2006) and “What Luck is Not” (2008) levels some strong and serious criticisms against Pritchard’s account. In what follows, a work in progress, I elucidate MAL and Lackey’s criticism of it, then provide what I take to be a viable defense.

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In Epistemic Luck, Duncan Pritchard notes that in most contemporary literature luck is often conflated with accidents, chance, or a loss of control; however, whatever luck is, Pritchard notes that such conceptions of luck do not sufficiently characterize it.  For example, if S is purposefully playing the lottery, it may be lucky if S wins, but it would be strange to call such a lottery win an accident.[1] The problem with conflating luck with chance, according to Pritchard, is that most of us would say luck requires an agent to be affected; chance, however, does not. It may be a matter of chance that a landslide did or did not occur on such and such a mountain, but most of us would not call such an event a matter of luck if no one was affected.[2] Pritchard notes that conflating luck with an absence of control is perhaps the most common characterization of luck due to an influential paper by Thomas Nagel in which he so defines a particular species of moral luck.[3] Such a characterization, however, has been criticized as at best a necessary condition on (moral) luck; it is, after all, out of our control that the sun rose this morning, but few of us would identify its rising as lucky.[4] What is more, typifying luck as a lack of control for epistemic luck, is doubly problematic given that many epistemologists would adhere to doxastic involuntarism for a whole host of perceptual beliefs; it seems reasonable to think that I have no control over whether or not I believe ‘I am now being appeared to redly’ when I am so appeared to, but few would identify such a belief as lucky. As such, Pritchard notes that though it may be intuitive to characterize luck in terms of accidents, chance, or a lack of control, “there is no straightforward way available of accounting for luck in these terms.”[5]

So, a more robust assessment of luck is needed. Regrettably, the philosophical literature has been scant and has not provide a much better answer (that is, after all, one of the reasons why Epistemic Luck is so seminal).  As such, Pritchard puts forward a modal account of luck (hereafter MAL) as an account of luck that appropriately tracks our intuitions across the relevant cases. MAL consists of two conditions:

L1: “If an event is lucky, then it is an event that occurs in the actual world but which does not occur in a wide class of the nearest possible worlds where the relevant initial conditions for that event are the same as in the actual world.”[6]

L2: “If an event is lucky, then it is an event that is significant to the agent concerned (or would be significant, were the agent to be availed for the relevant facts).”[7]

MAL seems to accurately identify paradigm cases such as lottery wins as lucky (contra an accident conception of luck), and it also seems to prevent sunrises, being appeared to redly, and isolated (insignificant to an appropriate agent) landslides, from being deemed lucky as well (contra chance and lack of control conceptions of luck). To be sure, Pritchard notes that there is an inherent vagueness to this conception of luck (What counts as the “relevant initial conditions?” How do we determine the closeness of worlds?), though we do seem to have a good intuitive grasp as to how the conditions are meant to function (e.g. that the “relevant initial conditions” should neither predetermine the given event nor should they make it inherently ‘chancy’). Pritchard is willing to let us be guided by our intuitions, and, given our current purposes, so am I.[8]

In her paper “Critical Study: Pritchard’s Epistemic Luck”, Jennifer Lackey raises an object to MAL through a counter example she identifies as Buried Treasure:

Buried Treasure: “Sophie, knowing that she had very little time left to live, wanted to bury on the island she inhabited a chest filled with all of her earthly treasures. As she walked around trying to determine the best site for proper burial, her central criteria were, first, that a suitable location must be on the northwest corner of the island, where she had spent many of her fondest moments in life, and secondly, that it had to be a spot where rose bushes could flourish, since these were her favorite flowers. As it happened, there was only one particular patch of land on the northwest corner of the island where the soil was rich enough for roses to thrive. Sophie, being excellent at detecting such soil, immediately located this patch of land and buried her treasure, along with seeds for future roses to bloom, in the one and only spot that fulfilled her two criteria. One month later, Vincent, a distant neighbour of Sophie’s, was driving in the northwest corner of the island, which was also his most beloved place to visit, and was looking for a place to plant a rose bush in memory of his mother who had died ten years earlier, since these were her favourite flowers. Being excellent at detecting the proper soil for rose bushes to thrive in, he immediately located the same patch of land as Sophie had found one month earlier. As he began digging a hole for the bush, he was astonished to discover a buried treasure in the ground.”[9]

The fact that Vincent found the buried treasure intuitively seems lucky even though it does not appear to meet L1; Vincent finds the treasure both in the actual world and, conceivable, in a wide range of nearby possible worlds. If one is not convinced of this the case, Lackey notes that it can be modified to make this more apparent with out doing damage to our initial intuition (e.g. the topography of the island is invariant; the only flower that Sophie and Vincent’s mother have ever liked is roses; Sophie has always had this specific detailed plan to bury her possessions once she was informed of her illness; etc.).[10] To be sure, Buried Treasure does not seem to be an isolated case. To make additional cases, all someone has to do, roughly, is pick a paradigmatic instance of luck and then “construct a case involving such an event in which both its central aspects are counterfactually robust, though there is no deliberate or other-wise relevant connection between them” then modifying the case as need be so that the lucky event is bound to happen in all (or most) nearby possible worlds.[11]

So what do cases like Buried Treasure mean for Pritchard’s account of luck? According to Lackey, such cases reveal that MAL is “fundamentally misguided.”[12] This diagnoses, I think, is a bit premature; Lackey certainly does not provide an argument for it. Lackey seems to assume that the closeness of possible worlds should be determined by whether, downstream of some relevant initial conditions, a given event was bound or determined to happen; but why should we think a thing like that? Pritchard does not defend a method for judging the closeness of worlds and neither does Lackey, so until we have reason to think the closeness of possible worlds should be judge how Lackey assumes it is not clear that Buried Treasure even offers a counter example to MAL let alone offers a reason to think that MAL fundamentally misguided.

In Buried Treasure, Lackey assumes that the closeness of a world is discerned by whether, downstream of some relevant initial conditions, a given event was bound or determined to happen. If there was no way a given event was not going to happen, then it cannot be modally improbable.  Given this reading of modality, we do not have to agree with Lackey that cases like Buried Treasure disprove MAL. One could simply object that Vincent’s treasure-find in Buried Treasure is not, contra our intuitions, an instance of luck; after all, as Heather Battally (2006) argued, someone defending MAL could “simply deny that Vincent’s discovery of buried treasure was lucky” pointing out that “there are no nearby possible worlds in which Vincent fails to dig in that precise spot, and no nearby possible worlds in which Vincent fails to discover buried treasure.”[13] So we could, like Battally, tacitly accept Lackey’s assumed method for ording possible worlds for MAL, and yet deny that Buried Treasure is an effective a counter-example. However, this reading of MAL has two strikes against it. First of all, if we were to pursue this proposal, we would be immediately pressed with the very real prospect of radical skepticism concerning luck ascriptions. It seems like the only way we could know if any given event is lucky, is if we were to be privy to the relevant causal details concerning the event’s modality (i.e. whether or not the event was ‘bound to happen’), a position we rarely, if ever, seem to be in. [14] Second of all, and more importantly, determining modality in terms of causality simply seems off the mark. Lackey in her criticism and Battally in her reply assume that modality is gauged by causality such that if a given event was bound or predetermined to happen (e.g. Vincent finding Sophia’s treasure) downstream of certain relevant initial conditions, it is not modally improbable and therefore, according to MAL, not an instance of luck. Such a conception of modality and subsequently such a conception of luck is simply not what is at issue in most (if not all) Gettier cases. Consider classic case once again:

Classic Case: Smith and Jones are applying for the same job. Smith has very strong evidence for thinking that Jones will get the job (e.g. the employer tells Smith that he will hire Jones, etc.), and for thinking that Jones has 10 coins in his pocket (e.g. Jones emptied his pockets in front of Smith and then clearly, slowly, in good lighting, and perhaps even counting out loud, placed 10 coins in his pocket). As such, Smith forms a belief in the general proposition that ‘the man who gets the job has 10 coins in his pocket.’ As it turns out however, Smith gets the job and he happens to also have 10 coins in his pocket. Thus, Smith’s belief seems to be justified and true, but doesn’t seem like knowledge.[15]

Even if we were to discover that somehow the events of Classic Case were causally predetermined such that Smith was bound to end up with the belief ‘the man who gets the job has 10 coins in his pocket’, this would not dissolve the case.  Even though Smith’s belief in this case would not be luckily true according to Lackey and Battally’s causal reading how possible worlds should be ordered in MAL (hereafter causal-MAL), we would still have a Gettier case; so even if the causal-MAL is explicating some sort of luck, it is not the kind of luck we are currently interested in.

Lackey’s criticism of MAL, by my lights, seems ill founded; however, we are left unsure as to how to understand Pritchard’s ‘possible world’ and ‘close possible world’ talk. Again, MAL is vague at this juncture, and Pritchard is willing to let us be guided by our intuitions; however, for the sake of diligence, let me gesture towards what I take to be more or less correct approximation of how such talk should be understood for MAL. I take it that Pritchard, offering no metaphysical context for his possible world talk, is taking ‘in all close possible worlds X’ to simply mean something like ‘it could so easily have been the case that X’. As such, what we take to be close possible worlds is not so much wed to metaphysics as it is to what we conceptually take to be the likelihood or aptness of the proposed event given the fixed initial conditions.

Contra Battally, I think we do intuitively think that Vincent’s finding of Sophia’s treasure is lucky even though it goes against causal-MAL; however, contra Lackey, I do not think this shows MAL to be fundamentally misguided. The reason we think Vincent is lucky to find the treasure is not based on the event’s causal indeterminacy but instead it is simply based on the fact that planting roses does not usually yield treasure – planting roses is not apt for finding treasure. Instead of determining modality in MAL in terms causality we should, I think, determine modality in terms of something like aptness.[16] Consider Buried Treasure once again. We could indeed evaluate modal improbability in terms of the causal-context provided in Buried Treasure, which does seem to yield the result that Vincent’s specific instance of rose-planting that yielded treasure was not modally improbable. As such, given that we take Vincent’s finding the buried treasure to be lucky, this seems to be contra MAL. However, we can instead evaluate modal improbability in terms of the likelihood or aptness of any given rose-planting event yielding treasure, in which case the fact that Vincent found treasure by planting roses is terribly modally improbability and intuitively lucky (in accord with MAL). In other words, take X_n to be the set of all rose-planting events, of which X₁, Vincent’s specific rose-planting event, is one of them. Even if X₁ was predetermined to happen via some story of causal relations, we can still judge X₁ as modally improbable in light of X_n. We take rose-planting to be an inapt method for finding buried treasure (no one, barring special cases, would plant roses in hopes of making such a find), and so, insofar as this plays a large role in our luck ascriptions in Buried Treasure, we have reason to determine the modal improbability of X₁ in terms of X_n and not how Lackey is assuming. Of course, Lackey might reply with a case like Buried Treasure Addendum:

Buried Treasure Addendum: The people in Vincent and Sophia’s world have a subconscious desire to bury their treasure in locations that have such and such a smell; these locations just so happen to perfectly correspond to places with soil suitable for planting roses. After generations and generations of people with this subconscious desire, almost every place in the world suitable for planting roses has treasure buried there. Planting roses, then, is an activity that is very apt for finding treasure, though, we should add, no one is aware of this – no one has discovered the correspondence between rose-soil and treasure. What is more, all of this is in addition to the circumstances outlined in Buried Treasure (e.g. Vincent and Sophia live on an island with only one place suitable for roses (which, we shall assume, was one of the very few such places without treasure already when it came time for Sophia to bury hers), both Sophia and Vincent’s mother have always only like roses, Sophia and Vincent had planned on taking their respective actions long in advance, etc.).

If we think Vincent is lucky in Buried Treasure Addendum we have a counter-example to the reading of MAL in which we judge modality in terms of aptness (hereafter apt-MAL); however, I think we can comfortably deny that Vincent is lucky here. Finding the buried treasure may seem lucky to Vincent, which it surely would, but this does not mean it was a truly lucky event. Becoming violently ill may seem terribly unlucky to the first person who ate a Jack-O’-Lantern mushroom (also known as Omphalotus olearius; a mushroom that tastes and smells good), but that doesn’t mean that it is – as a matter of fact, when you eat Jack-O’-Lantern mushrooms you get sick. Hence, quintessentially lucky events (which Lackey takes finding buried treasure to be) are not necessarily lucky.

Does apt-MAL more accurately than causal-MAL track our luck ascriptions in Gettier cases? I think so. Consider Classic Case once more. Of the set of beliefs formed by testimony, perception, and logical inference, the vast majority of them are true for reasons directly related to the given testimony, perception and logical inference – testimony, perception, and logical inference are generally apt for arriving at true beliefs. As such, the fact that Smith’s belief happens to be true for reasons unrelated to his potential employer’s testimony, his perception of Jones’s 10 coins, and his logical inference is very modally improbable, which, given this is significant to Smith, means apt-MAL is rightly ascribing luck in this case. Just to be sure, consider the Goldman’s Fake Barn Case once again:

Goldman’s Fake Barn Territory: “Henry is driving in the country with his son. For the boy’s edification Henry identifies various objects on the landscape as they come into view. ‘That’s a cow’, says Henry, ‘That’s a tractor’, ‘That’s a silo’, ‘That’s a barn’, etc. Henry has no doubt about the identity of these objects; in particular, he has no doubt that the last-mentioned object is a barn, which indeed it is. Each of the identified objects has features characteristic of its type. Moreover, each object is fully in view, Henry has excellent eyesight, and he has enough time to look at them reasonably carefully, since there is little traffic to distract him…Suppose we are told that, unknown to Henry, the district he has just entered is full of paper-mâché facsimiles of barns. These facsimiles look from the road exactly like barns, but are really just façades, without back walls or interiors, quite incapable of being used as barns. They are so cleverly constructed that travelers invariably mistake them for barns. Having just entered this district, Henry has not encountered any facsimiles; the object he sees is a genuine barn. But if the barn on that site were a facsimile, Henry would mistake it for a barn.”[17]

Given the set of barn-identification beliefs Henry would make in Fake Barn Territory where Henry cannot distinguish between real barns and barn façades, it is modally improbable that what Henry would identify as a barn would actually be a barn. Henry is not apt at discerning barns in Fake Barn Territory. In contrast, if we had a story that made Henry’s identification of the real barn as a barn predetermined, causal-MAL would erroneously deny that this case exhibited luck. Hence, it looks like apt-MAL tracks luck-ascriptions in Gettier cases where causal-MAL does not.[18]

[2] Ibid.

[3] Ibid., 127. See Thomas Nagel, Mortal Questions, 2nd ed. (Cambridge, UK: Cambridge University Press, 1979), 25.

[4] Pritchard, Epistemic Luck, 126. Also see D. Statman, “Moral and Epistemic Luck,” Ratio 4 (1991): 146. Statman, “Moral and Epistemic Luck,” 146; M. J. Zimmerman and Daniel Statman, eds., “Luck and Moral Responsibility,” in Moral Luck (Albany, NY: State University of New York Press, 1993); John Greco, “A Second Paradox Concerning Responsibility and Luck,” Metaphilosophy 26 (1995): 81-96; Andrew Latus, “Moral and Epistemic Luck,” Journal of Philosophical Research 25: 167.

[5] Pritchard, Epistemic Luck, 127.

[6] Ibid., 128.

[7] Ibid., 132.

[8] To be sure, such an understanding ‘possible world’ and ‘close possible world’ talk is metaphysically thin; everything rides on what we take to be ‘the relevant initial conditions’. In other words, given we should understand modality here in terms of aptness (where ‘in all close possible worlds X’ simply means something like ‘it could so easily have been X’) the main philosophical work is being done by what conditions we take to be fixed. For example, in the Bible from the book of Luke chapter 8, we read a story of a woman being healed upon touching the fringe of Jesus’ clothes. Taking this much as true, was it lucky that the woman was healed? If the relevant initial conditions are simply that of how apt the touching of the fringe of cloth is to heal you in close possible worlds, then it seems like this event was lucky. However, if given a Christian metaphysics, there is something special about this Jesus character such that touching the fringe of his garments cannot be conflated with touching the fringe of garments in general – how apt the touching of Jesus’ garments is to heal someone is a relevant initial condition. As such, luck ascriptions will, it seems, vary according to metaphysics. Even so, there seems to be enough consistency with our intuitions from case to case that I, along with Pritchard, am willing to continue to follow our intuitions as to what counts as the relevant initial conditions from case to case.

[9] Jonathan L. Kvanvig, “Epistemic Luck,” Philosophy and Phenomenological Research 77, no. 1 (2008): 285.

[10] Jennifer Lackey, “Critical Study: Pritchard’s Epistemic Luck,” Philosophical Quarterly 56, no. 223 (2006): 286.

[11] Ibid.

[12] Ibid., 287.

[13] Heather Battaly, “Comments on Wayne Riggs’s “On Luck and Value”,” in  (presented at the Epistemic Value, The University of Stirling, 2006), 2. This is the general strategy that Pritchard himself has informally endorsed. See Duncan Pritchard, “Luck,” March 19, 2009.

[14] Given a deterministic universe, nothing much, it seems, would be deemed truly lucky on this view of luck (see Schaffer, “Deterministic Chance?”). This fact is all the more pressing given that any of the Reformed hold to such a view of the universe. Fore more on this aspect of the Reformed view see Karl Barth, Church Dogmatics (London, UK: T. & T. Clark Publishers, 2004), Paragraph 49; John Calvin, Calvin: Institutes of the Christian Religion, ed. John T. McNeill, vol. 2 (London, UK: Westminster John Knox Press, 1960), 949-950; General Assembly of the Presbyterian Church, The Westminster Confession of Faith together with The Larger Catechism and The Shorter Catechism with the Scripture Proofs, 3rd ed. (Lawrenceville, GA: Committee for Christian Education & Publications, 1990), Chapter 5 of the Confession; Larger Catechism Questions 12, 14, and 18; Robert L. Reymond, A New Systematic Theology Of The Christian Faith, 2nd ed. (Nashville, TN: Thomas Nelson Publishers, 1998), 356-372; ESV Classic Reference Bible (Wheaton, IL: Crossway Bibles, 2006), Proverbs 16:33.

[15] Edmund Gettier, “Is Justified True Belief Knowledge?,” Analysis 23: 122. Though the notion of justification used in this case is internalistic, this should not distract us now from the task at hand; a structurally identical case could be constructed that employed an externalistic notion of justification.

[16] I have Alan Millar to thank for pointing out to me the various ways of assessing modality. Alan Millar, Personal Conversation (University of Stirling, 2009).

[17] Alvin I. Goldman, “Discrimination and Perceptual Knowledge,” The Journal of Philosophy 73, no. 20 (November 18, 1976): 772-773; Linda Zagzebski, “The Inescapability of Gettier Problems,” The Philosophical Quarterly 44, no. 174 (January 1994): 66.  Notably Ducan Pritchard (forthcoming) does not consider Fake Barn to be a case to be a Gettier case, because the protagonist (Henry in our case) does not make a “cognitive error” Alan Millar, Duncan Pritchard, and Adrian Haddock, Value of Knowledge (Oxford, UK: Oxford University Press, 2009), 34. According to Pritchard, in order for a Gettier case to be a Gettier case a cognitive error has to be committed by the protagonist in question. This is, I think, a rather arbitrary qualification on what counts as a Gettier case – historically, a Gettier case has been any case in which the conditions of a given standard analysis of knowledge seem to be met without being sufficient

[18] To be sure, whether or not set-MAL accurately tracks luck ascriptions in Gettier-cases depends on what we take to be relevant initial conditions. Again, as noted above, I am willing, with Pritchard, to let our intuitions guide us.