Should Explanations Omit the Details? This is a repository copy of Should Explanations Omit the Details?. White Rose Research Online URL for this paper: http://eprints.whiterose.ac.uk/125496/ Version: Accepted Version Article: Bradley, DJ (2020) Should Explanations Omit the Details? British Journal for the Philosophy of Science, 71 (3). axy033. pp. 827-853. ISSN 0007-0882 https://doi.org/10.1093/bjps/axy033 © The Author(s) 2018. Published by Oxford University Press on behalf of British Society for the Philosophy of Science. This is a pre-copyedited, author-produced version of an article accepted for publication in The British Journal for the Philosophy of Science following peer review. The version of record Bradley, DJ (2018) Should Explanations Omit the Details? British Journal for the Philosophy of Science, Volume 71, Issue 3, September 2020, Pages 827–853 is available online at: https://doi.org/10.1093/bjps/axy033 eprints@whiterose.ac.uk https://eprints.whiterose.ac.uk/ Reuse Items deposited in White Rose Research Online are protected by copyright, with all rights reserved unless indicated otherwise. They may be downloaded and/or printed for private study, or other acts as permitted by national copyright laws. The publisher or other rights holders may allow further reproduction and re-use of the full text version. This is indicated by the licence information on the White Rose Research Online record for the item. Takedown If you consider content in White Rose Research Online to be in breach of UK law, please notify us by emailing eprints@whiterose.ac.uk including the URL of the record and the reason for the withdrawal request. mailto:eprints@whiterose.ac.uk https://eprints.whiterose.ac.uk/ 1 Should Explanations Omit the Details? Abstract There is a widely shared belief that the higher level sciences can provide better explanations than lower level sciences. But there is little agreement about exactly why this is so. It is often suggested that higher level explanations are better because they omit details. I will argue instead that the preference for higher level explanations is just a special case of our general preference for informative, logically strong, beliefs. I argue that our preference for informative beliefs entirely accounts for why higher level explanations are sometimes better に and sometimes worse に than lower level explanations. The result is a step in the direction of the unity of science hypothesis. 1. Introduction 2. Background: Is Omitting Details an Explanatory Virtue? 2.1. Anti-reductionist arguments 2.2. Reductionist argument 2.3 Logical strength 3. Bases, Links and Logical Strength ヴく F┌ﾐIデｷﾗﾐ;ﾉｷゲﾏ ;ﾐS FﾗSﾗヴげゲ Aヴｪ┌ﾏWﾐデ 5. Two Generalizations 6. Should the Base Really be Maximally Strong? 7. Anti-Reductionist Arguments Regarding the Base 8. Should the Antecedent of the Link Really be Maximally Weak? 1. Introduction It is widely believed that explanations can be improved by omitting details. But why is it good to omit details? One might think that it can be good to omit details because it can be good to provide less 2 information. I will argue to the contrary に explanations are always improved by adding information. And sometimes we can increase the information provided by omitting details. This looks paradoxical, but happens in the antecedent of a conditional; omitting details from the antecedent of a conditional logically strengthens the conditional, providing us with more information. In the background is the hypothesis of the unity of science (Carnap 1934, Nagel 1951, Oppenheim and Putnam 1958). LWデ けデｴW ｴｷｪｴWヴ ﾉW┗Wﾉ ゲIｷWﾐIWゲげ ヴWaWヴ デﾗ ;ﾉﾉ ゲIｷWﾐIWゲ ﾗデｴWヴ デｴ;ﾐ fundamental physics. One part of the hypothesis of the unity of science is that fundamental physics provides better explanations than higher level science. An important line of objection draws on examples to argue that omitting details improves an explanation, and that higher level explanations are better because they omit such details (Putnam 1967, Fodor 1974). I will argue that the wrong moral has been drawn from these examples. They show that logically strong explanations are better; tｴW┞ Sﾗﾐげデ ゲｴﾗ┘ デｴ;デ ｴｷｪｴWr level explanations are better. Thus, one objection to the unity of science hypothesis is undermined. Part 2 explains the background reductionist and anti-reductionist arguments; part 3 contains the core argument, introducing the distinction between links and bases and applying it to explanations that omit details; part 4 applies the distinction to functionalism, arguing that functional laws are logically weak, and therefore provide poor explanations; part 5 generalizes the account along two dimensions; part 6 develops the view that the base should be logically strong; part 7 defends the view that the base should be logically strong from G;ヴaｷﾐﾆWﾉげゲ ふヱΓΒヱぶ objections; part 8 defends the view that the link should be logically strong; part 9 concludes. 2. Background: Is Omitting Details an Explanatory Virtue? TｴW デﾗヮｷI ﾗa デｴｷゲ ヮ;ヮWヴ ｷゲ W┝ヮﾉ;ﾐ;デﾗヴ┞ ヴWS┌Iデｷﾗﾐく WWげﾉﾉ aﾗI┌ゲ ﾗﾐ デｴW W┝ヮﾉ;ﾐ;デｷﾗﾐ ﾗa W┗Wﾐデゲが ゲWtting aside W┝ヮﾉ;ﾐ;デﾗヴ┞ ヴWS┌Iデｷﾗﾐ ﾗa ﾉ;┘ゲく LWデげゲ ;ゲゲ┌ﾏW ┘W ｴ;┗W ; token event that is predicted with the same probability by both a lower level and a higher level explanation. Can we say anything in general about 3 which explanation is better? Anti-reductionists favour higher level explanations; reductionists favour lower level explanations.1 In this section I will explain the opposing arguments, then suggest how they can be reconciled. (Good-making features of explanations give us pro tanto reasons to believe them i.e. reasons which may by outweighed by other features. So all comparisons about which explanation is better should be understood ;ゲ ｴ;┗ｷﾐｪ ;ﾐ ｷﾏヮﾉｷIｷデ けﾗデｴWヴ デｴｷﾐｪゲ Wケ┌;ﾉげ Iﾉ;┌ゲWくぶ 2.1. Anti-reductionist arguments The driving force behind many anti-reductionist arguments are well-known examples: P┌デﾐ;ﾏげゲ Peg (Putnam 1967) Explanandum: A square peg with 1 inch sides fails to go through a round hole with a diameter of 1 inch. Higher level explanation: The peg is square Lower level explanation: A description of the position of every molecule of the peg and hole. G;ヴaｷﾐﾆWﾉげゲ Rabbit (Garfinkel 1981) Explanandum: Rabbit r gets eaten. Higher level explanation: The fox population is high Lower level explanation: Rabbit r passed through the capture space of fox f. Y;Hﾉﾗげゲ Pigeon (Yablo 1992) Explanandum: A pigeon trained to peck at red cards pecks at a scarlet card. 1 Cﾗﾏヮ;ヴW WWゲﾉ;ﾆW ヲヰヱヰく HW SｷゲI┌ゲゲWゲ ヴWS┌Iデｷﾗﾐ ;ゲ F┌ﾐS;ﾏWﾐデ;ﾉｷゲﾏぎ けデｴ;デ デｴWヴW ｷゲ ﾐﾗ SｷﾏWﾐゲｷﾗﾐ ﾗa explanatory depth along which the nonfundamental sciences can provide deeper explanations than those ヮヴﾗ┗ｷSWS H┞ a┌ﾐS;ﾏWﾐデ;ﾉ ヮｴ┞ゲｷIゲげく ヮくヲΑヴ DWヮデｴ ゲWWﾏゲ デﾗ HW ; ヮﾉ;IW-holder for an explanatory virtue. 4 Higher level explanation: The card is red Lower level explanation: The card is scarlet. The Glass (Jackson and Pettit 1992) Explanandum: The sealed glass, in which water was heated, cracked. Higher level explanation: Water was boiling Lower level explanation: Molecule A hit the glass with momentum greater than z. The Conductor (Jackson and Pettit 1992) Explanandum: The conductor was annoyed. Higher level explanation: Someone coughed Lower level explanation: Bob coughed. Thermodynamics (Strevens 2014)2 Explanandum: The gas filled the vacuum. Higher level explanation: The gas is at 100 Kelvin Lower level explanation: The gas consists of a billion molecules moving with velocities V1-V1,000,000,000 TｴWヴW ;ヴW SｷaaWヴWﾐIWゲ HWデ┘WWﾐ デｴWゲW W┝;ﾏヮﾉWゲ デｴ;デ ┘Wげﾉﾉ ;SSヴWゲゲ ﾉ;デWヴき aﾗヴ ﾐﾗ┘が ┘ｴ;デ ﾏ;デデWヴゲ ｷゲ ┘ｴ;デ they have in common. These examples are often taken to show that explanations should omit details, from which it seems to follow that higher level explanations can be better than lower level explanations3. 2 This is the closest I will get to engaging with a specific science. As my thesis is general, it would be distracting to spend too much time engaging with the details of a specific example. 3 See Putnam 1967 p.138, Fodor 1974 p. 103, Garfinkel 1981 p.56, Jackson and Pettit 1992 p.11, and also MacDonald (1992, p. 86, 90に92), Haug (2011, p.1150), Clarke (2016) and Batterman (forthcoming) among 5 But why is it good to omit details? I will briefly survey the literature and argue that no convincing reason has been given to think that omitting details is an explanatory virtue (where an explanatory virtue is a good-making feature of an explanation). First, perhaps details should be omitted when alternative details would have produced the same event. Such details would not make a difference to the outcome, and perhaps explanations should only mention features that a make a difference to the outcome.4 But now we need a specification of what the alternative details are. This suggests a contrastive theory of explanation (in the explanans at least), according to which A rather than B explains E. I will argue in section 7.2 that contrastive explanations do not imply that details are irrelevant. Second, Weslake (2010) suggests the following answer: Why believe that [omitting details] provides a genuine [virtue]? My central Iﾉ;ｷﾏぐｷゲ デｴ;デ ぷthat omitting details is a virtue] provides the best explanation for the truth of [the thesis that higher level explanations can give better explanations]. p.288 But this is circular if the ultimate aim is to explain why higher level explanations are better than lower level explanations. Grant that if omitting details is a virtue, then this explains why higher level explanations can give better explanations. But this is no argument that omitting details is a virtue. The reductionist denies that higher level explanations can give better explanations, so has no need of an explanation of it. Furthermore, we have been given no account of why omitting details is a virtue ふ┘Wげ┗W ﾗﾐﾉ┞ HWWﾐ デﾗﾉS デｴ;デ ; ヮヴWaWヴWﾐIW aﾗヴ ｴｷｪｴWヴ ﾉW┗Wﾉ W┝ヮﾉ;ﾐ;デｷﾗﾐゲ I;ﾐ HW W┝ヮﾉ;ｷﾐWS ｷa ﾗﾏｷデデｷﾐｪ others; see Sawyer 2002 for a helpful overview. Technically, it is said we should omit irrelevant details. But this ケ┌;ﾉｷaｷI;デｷﾗﾐ SﾗWゲﾐげデ ヴW;ﾉﾉ┞ ;SS ;ﾐ┞デｴｷﾐｪく Oa Iﾗ┌ヴゲW ┘W ゲｴﾗ┌ﾉS ﾐﾗデ ﾗﾏｷデ ヴWﾉW┗;ﾐデ SWデ;ｷﾉゲく Aﾐ┞┘;┞が I ┘ｷll argue that omitting details is not a fundamental virtue, so relevance plays no role in my account. 4 See Strevens 2004, 2009. 6 details is a ┗ｷヴデ┌Wぶく AﾐS WWゲﾉ;ﾆWげゲ ;IIﾗ┌ﾐデ ﾉW;┗Wゲ ﾗヮWﾐ デｴ;デ ┘W ﾏｷｪｴデ aｷﾐS ; HWデデWヴ W┝ヮﾉ;ﾐ;デｷﾗﾐ aﾗヴ デｴW benefits of higher level explanation に indeed this is what I will suggest. Third, perhaps explanations with fewer details can explain more actual events. Consider an attempt to explain some particular actual event E. Suppose T1 explains only E; T2 explains E and also (actual event) F. Someone might argue that the fact that T2 also explains F makes T2 a better explanation of E. But how could explaining F improve the quality of the explanation of E? Surely the fact that T2 also explains F has nothing to do with how well T2 explains E. “ﾗﾏWﾗﾐW Iﾗ┌ﾉS ヴWヮﾉ┞ デｴ;デ ┘W ゲｴﾗ┌ﾉSﾐげデ aﾗI┌ゲ ﾗﾐﾉ┞ ﾗﾐ Eき デｴW a;Iデ デｴ;デ Tヲ W┝ヮﾉ;ｷﾐゲ E-and-F, while T1 only explains E, makes T2 the better explanation. But then T2 predicts more evidence so is more empirically adequate. And of course empirical adequacy is an explanatory virtue. So we have no reason here to posit omitting details as an explanatory virtue beyond its role in empirical adequacy. Fourth, one might argue that less detailed explanations are less sensitive to the initial conditions, and that being less sensitive to the initial conditions is an explanatory virtue.5 WWげﾉﾉ ゲ;┞ that explanations that are relatively insensitive to the initial conditions are counterfactually robust. Counterfactual robustness does seem to be an explanatory virtue. In fact, I think it is. But why is counterfactual robustness an explanatory virtue? PWヴｴ;ヮゲ ｷデげゲ ; a┌ﾐS;ﾏWﾐデ;ﾉ a;Iデ ;Hﾗ┌デ W┝ヮﾉ;ﾐ;デｷﾗﾐ デｴ;デ Iﾗ┌ﾐデWヴa;Iデ┌;ﾉ ヴﾗH┌ゲデﾐWゲゲ ｷゲ ; ┗ｷヴデ┌Wく I have no objection to this view, but we should only posit fundamental facts when necessary. It will emerge that on my account, counterfactual robustness might be a virtue, but is not a fundamental virtue; counterfactual robustness is a good feature of an explanation to the extent that it indicates that the explanation is logically strong. 2.2. Reductionist arguments 5 Compare Woodward and Hitchcock (2003a, 2003b), White (2005) 7 “ﾗ a;ヴ Iげ┗W ;ヴｪ┌WS デｴ;デ ｷデげゲ not obvious why omitting details is a virtue of explanations. And there are powerful arguments that adding details improves explanations に details that might only be described using the concepts of a lower level science.6 Here are a few examples: Non-detailed: Socrates died because he drank poison Detailed: Socrates died because he drank hemlock. Non-detailed: Bob is crying because she is either happy or sad Detailed: Bob is crying because she is happy. Non-detailed: The building collapsed because it was structurally unsound Detailed: The building collapsed because tension in the concrete keystone caused a crack. In these cases the detailed explanations seem to be better, suggesting that lower level explanations are better. Furthermore, tｴW ヮヴWaWヴWﾐIW aﾗヴ SWデ;ｷﾉゲ ｷゲ Wﾏヮｴ;ゲｷ┣WS H┞ ﾗﾐW ゲデヴ;ﾐS ﾗa デｴﾗ┌ｪｴデ ｷﾐ デｴW けﾐW┘ ﾏWIｴ;ﾐｷゲデｷIげ ヮｴｷﾉﾗゲﾗヮｴ┞ ﾗa ゲIｷWﾐIW に Machamer, Darden, and Craver 2000, Darden and Craver 2002, Darden 2006 and Craver 2007 emphasize completeness and specificity as an explanatory virtue.7 Darden 2007 is perhaps the most explicit: A mechanism sketch is an incomplete model of a mechanism. It characterizes some ヮ;ヴデゲが ;Iデｷ┗ｷデｷWゲ ﾗヴ aW;デ┌ヴWゲ ﾗa デｴW ﾏWIｴ;ﾐｷゲﾏげゲ ﾗヴｪ;ﾐｷ┣;デｷﾗﾐが H┌デ ｷデ leaves 6 For other defences of reductionism see Kim (1992, 1993), Sober (1999) and Dizadji-Bahmani, Frigg and Hartmann (2010). 7 See also Churchland 1981, Ylikoskiand Kuorikoski 2010. For dissent see Levy & Bechtel (2013). 8 ｪ;ヮゲぐぷPへヴﾗHﾉWﾏ;デｷI;ﾉﾉ┞が ゲﾗﾏWデｷﾏWゲ ぷデｴW ｪ;ヮゲへ ;ヴW ﾏ;ゲﾆWS H┞ aｷﾉﾉWヴ デWヴﾏゲ デｴ;デ ｪｷ┗W the illusion that the explanation is complete when it is not. p.113 AﾐS EﾉゲデWヴ ふヱΓΒンぶ ┘ヴｷデWゲ デｴ;デ けデﾗ W┝ヮﾉ;ｷﾐ ｷゲ デﾗ ヮヴﾗvide a mechanism, to open up the black box and show the nuts and bolts, the cogs and wheWﾉゲ ﾗa デｴW ｷﾐデWヴﾐ;ﾉ ﾏ;IｴｷﾐWヴ┞げ ふヮくヲンぶく So we have a puzzle に sometimes extra details seem to improve an explanation and sometimes fewer details seem to improve an explanation. Michael Strevens (2011) puts his finger on the tension: On the one hand, we say that an explanation is deep when it goes far down toward the physical level, the level of detail at which ultimate causal underpinnings are found. On the other hand, we also say that an explanation is deep when it has a certain striking generality - when it attributes the phenomenon to be explained not to some very particular set of initial conditions, but to some high-level, abstract, often virtually mathematical state of affairs. He aptly calls this the Goldilocks problem (Strevens 2008) - that of characterizing what it is for an explanation to be just right in its level of detail. My approach dissolves this problem. Rather than conflicting desiderata, I will argue that there is only one desideratum, and the apparent tension comes from failing to distinguish the two parts of an explanation. 2.3 Logical strength I suggest we focus on logical strength. My thesis is: Logical strength is an explanatory virtue.8 8 Compare Woodward and Hitchcock 2003b p.195 9 ふIげﾉﾉ デ;ﾆW ﾉﾗｪｷI;ﾉ ゲデヴWﾐｪデｴ デﾗ HW Wケ┌ｷ┗;ﾉWﾐデ デﾗ informativeness ｷくWく けA ｷゲ ﾏﾗヴW ｷﾐaﾗヴﾏ;デｷ┗W デｴ;ﾐ Bげ ﾏW;ﾐゲ that A entails B (and B does not entail A).) Usually adding details increases logical strength; but in the antecedent of a conditional the usual effects are reversed. More details means less information. This accounts for the tension. Positing a preference for logical strength explains our judgments about omitting details and higher level explanations. The issue is complicated by the fact that there are two ways of moving from a lower level to a higher level explanation. One way is to omit details; the other is to use a functional concept. Example: Start with the lower level explanation that someone died because they ingested cyanide. (A) We can generate a higher level explanation by omitting details of the chemical, and saying only that ingesting a substance in the cyano group (of which cyanide is a member) caused death. (B) Alternatively, we could say that ingesting a poison caused death, where けヮﾗｷゲﾗﾐげ ｷゲ ┌ﾐSWヴゲデﾗﾗS デﾗ ヴWaWヴ デﾗ ;ﾐ┞デｴｷﾐｪ デｴ;デ I;┌ゲWゲ Sｷゲデ┌ヴH;ﾐIWゲ ｷﾐ ﾗヴｪ;ﾐｷゲﾏゲ ｷくWく けヮﾗｷゲﾗﾐげ ｷゲ ; functional term. Higher level laws9 generated by omitting details in the antecedent (A) are logically stronger than lower level laws; the claim that all substances in the cyano group cause death is stronger than the claim that cyanide causes death. Higher level laws generated by using functional concepts (B) are logically weaker than lower level laws; the claim that poisons cause death is weaker than the claim that cyanide causes 9 I Sﾗﾐげデ ｴﾗﾉS デｴ;デ W┝ヮﾉ;ﾐ;デｷﾗﾐゲ ﾐWWS デﾗ Iﾗﾐデ;ｷﾐ ﾉ;┘ゲが ゲﾗ I ゲｴﾗ┌ﾉS ゲ;┞ けｪWﾐWヴ;ﾉｷ┣;デｷﾗﾐげが ﾗヴ けI;┌ゲ;ﾉ ゲデ;デWﾏWﾐデげが ﾗヴ ┘ｴ;デ I ヴW;ﾉﾉ┞ ┘;ﾐデ デﾗ ゲ;┞ぎ けﾉｷﾐﾆげく B┌デ I ┘ﾗﾐげデ ｷﾐデヴﾗS┌IW デｴｷゲ デWヴﾏｷﾐﾗﾉﾗｪ┞ ┌ﾐデｷﾉ デｴW ﾐW┝デ ゲWIデｷﾗﾐく 10 death. So I will argue that omitting details in the antecedent of the law improves the explanation (section 3) while moving to a functional law worsens the explanation (section 4). 3. Bases, Links and Logical Strength Explanations have two parts に a basis and a link.10 This division is explicit in Hempel and Oppenheim (1948) for whom けデｴW W┝ヮﾉ;ﾐ;ﾐゲ a;ﾉﾉゲ ｷﾐデﾗ デ┘ﾗ ゲ┌HIﾉ;ゲゲWゲき ﾗﾐW ﾗa デｴWゲW Iﾗﾐデ;ｷﾐゲぐゲWﾐデWﾐIWゲぐwhich state specific antecedent conditions; the other is a seデ ﾗa ゲWﾐデWﾐIWゲぐ┘ｴｷIｴ ヴWヮヴWゲWﾐデ ｪWﾐWヴ;ﾉ ﾉ;┘ゲげ p.137. The antecedent conditions are the basis, and the law is the link. It is widely agreed that explanations do not need to appeal to laws; but I will assume we need some kind of conditional to link the basis to the thing-to-be-explained.11 Now return to my claim that good explanations should be as informative as possible. How are conditionals logically strengthened? Conditionals are logically strengthened by weakening the antecedent.12 For example, けｷa ┞ﾗ┌ ヮﾉ;┞ ┘Wﾉﾉ デｴWﾐ ┞ﾗ┌ ┘ｷﾉﾉ ┘ｷﾐげ is logically strengthened by weakening the antecedent with a disjunct: けｷa ┞ﾗ┌ ヮﾉ;┞ ┘Wﾉﾉ ﾗヴ ヮﾉ;┞ ;Hﾗ┗W ;┗Wヴ;ｪW デｴWﾐ ┞ﾗ┌ ┘ｷﾉﾉ ┘ｷﾐげく So the most informative conditionals have the weakest antecedents i.e. have the fewest details in the antecedents. This is where details should be omitted に in the antecedent of the conditional. And this improves the explanation by making it more informative. This is why higher level explanations are sometimes better than lower level explanations. 10 See Schaffer (forthcoming) 11 Or at least, my account will only apply to explanations containing conditionals. 12 AﾐS H┞ ゲデヴWﾐｪデｴWﾐｷﾐｪ デｴW IﾗﾐゲWケ┌Wﾐデが デｴﾗ┌ｪｴ デｴｷゲ ┘ﾗﾐげデ ﾏ;デデWヴ ｴWヴWく 11 Consider J;Iﾆゲﾗﾐ ;ﾐS PWデデｷデげゲ example of the conductor who is annoyed because someone coughed. It is Bob who coughed, but anyone coughing would have annoyed the conductor. Should an explanation ﾗa デｴW IﾗﾐS┌Iデﾗヴげゲ ;ﾐﾐﾗ┞;ﾐIW include the fact that it was Bob who coughed? The anti- reductionist says けﾗﾏｷデ Bobげ; the reductionist says けinclude Bobげ. How to reconcile these conflicting intuitions? I suggest that we can accommodate both intuitions by noting that the most informative, logically strong, link SﾗWゲﾐげデ ﾏWﾐデｷﾗﾐ BﾗH. Logically weak link: If Bob coughs then the conductor is annoyed Logically strong link: If someone coughs then the conductor is annoyed By contrast, when it comes to the base, adding the lower level details increases logical strength. Logically weak basis: Someone coughed Logically strong basis: Bob coughed Putting these together, the most informative explanation is: Logically strong basis: Bob coughed Logically strong link: If someone coughs then the conductor is annoyed Result: The conductor is annoyed We can now explain what is correct about the intuition that details should be omitted; details should be omitted from the antecedent of the link. And we can explain the apparently conflicting intuition that details should be included in explanations; details should be included in the base. Notice that the result that good explanations are insensitive to initial conditions falls out of this account. The sensitivity of the explanation to the initial conditions depends on the antecedent of 12 the link. The more detailed the antecedent of the link, the more sensitive the explanation to initial conditions. This account recommends logically strong links, which means antecedents with fewer details, which means explanations which are insensitive to initial conditions.13 Also, I remain neutral on whether there are other explanatory virtues besides logical strength. I only claim that the virtue of omitting details can be reduced to the virtue of logical strength. One last point before concluding this section. So far I have argued that logical strength is an W┝ヮﾉ;ﾐ;デﾗヴ┞ ┗ｷヴデ┌Wく LWデげゲ ;ｪ;ｷﾐ ;ゲﾆ デｴW SWWヮWヴ ケ┌Wゲデｷﾗﾐぎ ┘ｴ┞ ｷゲ ﾉﾗｪｷI;ﾉ ゲデヴWﾐｪデｴ ;ﾐ W┝ヮﾉ;ﾐ;デﾗヴ┞ ┗ｷヴデ┌Wい I suggest: logical strength is a virtue of any belief に it is good to be informed. Thus the explanatory virtue of informativeness reduces to a virtue of any belief に that it be logically strong.14 There is a further question of course: why is logical strength a virtue of beliefs? I think there is an answer to be found, which I can only gesture at here. It is widely believed that belief aims at truth.15 So truth is a norm of belief. But there must also be other norms of belief に otherwise, the HWﾉｷWa デｴ;デ ヱЩヱЭヲ ┘ﾗ┌ﾉS HW ;ゲ ｪﾗﾗS ;ゲ ;ﾐ┞ HWﾉｷWa Iﾗ┌ﾉS HW ふHWI;┌ゲW ｷデ ｷゲ デヴ┌Wぶく Wｴ;デげゲ ﾉ;Iﾆｷﾐｪ ｷﾐ デｴW HWﾉｷWa デｴ;デ ヱЩヱЭヲ ｷゲ デｴ;デ ｷデげゲ ﾐﾗデ informative.16 It would be better to have a more informative belief (other things/virtues equal). Thus, it seems that logical strength is a virtue of a belief. Iげﾏ ﾐﾗデ ゲ;┞ｷﾐｪ デｴ;デ logical strength and truth are the only norms of belief. Presumably evidence is also part of the story, to name just one more. But it is very plausible that logical strength is a virtue of belief. There is more to say developing this thought, but the philosopher of science can rest content that a question about explanatory virtues has been reduced to a question about the norms of belief. 13 So the preference for logical strength also explains the preference for the counterfactual dependence relations emphasized by Woodward and Hitchcock (2003a, 2003b). 14 Cﾗﾏヮ;ヴW LW┘ｷゲ けWｴ;デ I ｴ;┗W HWWﾐ ゲ;┞ｷﾐｪ ぷ;Hﾗ┌デ W┝ヮﾉ;ﾐ;デﾗヴ┞ ┗ｷヴデ┌Wゲへ ;ヮヮﾉｷWゲ ﾃ┌ゲデ ;ゲ ┘Wﾉﾉ デﾗ ;Iデゲ ﾗa ヮヴﾗ┗ｷSｷﾐｪ ｷﾐaﾗヴﾏ;デｷﾗﾐ ;Hﾗ┌デ ;ﾐ┞ ﾉ;ヴｪW ;ﾐS IﾗﾏヮﾉｷI;デWS ゲデヴ┌Iデ┌ヴWぐTｴW ｷﾐaﾗヴﾏ;デｷﾗﾐ ヮヴﾗ┗ｷSWSが ;ﾐS デｴW ;Iデ ﾗa ヮヴﾗ┗ｷSｷﾐｪ ｷデが can be satisfactory or not in preciseﾉ┞ デｴW ゲ;ﾏW ┘;┞ゲくげ ふヱΓΒヶ ヮくヲヲΑ-8) Lewis is talking about pragmatics here, but I think the same applies to objective norms. 15 See Whiting 2012 for discussion and references. 16 Cﾗﾏヮ;ヴWぎ けScience does not aim, primarily, at high probabilities. It aims at a high informative content, well backed by experienceげ. (Popper 1954, p.146, original Italics.) 13 LWデげゲ ﾐﾗ┘ work through the consequences for functional explanations. 4. F┌ﾐIデｷﾗﾐ;ﾉｷゲﾏ ;ﾐS FﾗSﾗヴげゲ Aヴｪ┌ﾏWﾐデ A functional property is a property that is characterized in terms of what it does. That is, functional properties are individuated by their causal profile.17 FﾗSﾗヴげゲ ふヱΓΓΑぶ ;ヴｪ┌ﾏWﾐデ aﾗヴ a preference for functional explanations is especially interesting: ぷTｴWへ a┌ﾐIデｷﾗﾐ;ﾉｷゲデぐゲデｷﾉﾉ ﾐWWSゲ デﾗ W┝ヮﾉ;ｷﾐ ┘ｴ┞ ┘W ゲｴﾗ┌ﾉSぐヮヴWaWヴ ｴｷｪｴWヴ ﾉW┗Wﾉ IﾉﾗゲWS laws (pain leads to avoidance) to lower level open laws (states that are RI v R2 v ... lead to avoidance), all else equal. Why are we prepared to buy closed laws at the cost of reifying high level properties? My story is that this policy complies with an injunction that all of our inductive practice illustrates: Prefer the strongest claim compatible with the evidence, all else equal. p. 159 I have been arguing for something like the claim that Fodor makes in the final sentence, though I would put it as follows: logical strength is an explanatory virtue. But I want to argue that Fodor has got the implications for functionalism the wrong way round. Fodor suggests that functional links are logically stronger than lower level links. I will argue that functional links are logically weaker than lower level links. In fact functional links ;ヴW デヴｷ┗ｷ;ﾉが ﾉW;Sｷﾐｪ ゲﾗﾏW デﾗ ┘ﾗヴヴ┞ デｴ;デ デｴW┞ Sﾗﾐげデ ゲ┌IIWWS ;ゲ explanations at all. Ironically, Fodor himself had expressed this worry with a characteristically clear and colourful example that has become common currency18: 17 B┞ けa┌ﾐIデｷﾗﾐ;ﾉｷゲﾏげ I ﾏW;ﾐ デｴW ‘;ﾏゲW┞-Carnap-Lewis theory described by Lewis (1970, 1972). This should be Sｷゲデｷﾐｪ┌ｷゲｴWS aヴﾗﾏ ﾗデｴWヴ ┌ゲWゲ ﾗa けa┌ﾐIデｷﾗﾐ;ﾉｷゲﾏげ Wくｪく “ｴﾗemaker (2003), which I set aside 18 Fodor goes on to give an answer by appealing to Turing machines, but this seems to restrict the scope of functionalism so much that it would not apply to any special sciences に with the possible exception of computing. 14 The second problem isぐ; ﾉ┌ヴﾆｷﾐｪ ゲ┌ゲヮｷIｷﾗﾐ デｴ;デ a┌ﾐIデｷﾗﾐ;ﾉぐW┝ヮﾉ;ﾐ;デｷﾗﾐぐｷゲ ﾃ┌ゲデ デﾗﾗ easy. Moliere had a finger on it: In virtue of what did the morphine put Jones to sleep?...In virtue of its having dormative power. In what does having this dormative power consist? It consists in being the cause of a certain kind of effect; viz. in causing sleep. Fodor (1981) p.12 Italics original The poor explanation of Jones being put to sleep is something like: Basis: Jones took something with a dormative power Link: Substances with dormative powers cause sleep (i.e. if someone takes a substance with a dormative power then it puts them to sleep) Result: Jones was put to sleep And the link tells us nothing about the world. It is analytic に a Carnap-sentence (see Carnap 1963 p.964, Lewis 1970, 1972).19 Thus functional links are logically weak, and FﾗSﾗヴげゲ ;aaｷヴﾏ;デｷﾗﾐ デｴ;デ ┘W ゲｴﾗ┌ﾉS prefer logically stronger explanations ends up counting against functionalism. 20 (And we can explain the intuitive unsatisfactoriness of the functional link in terms of its being uninformative に this fits with my position that informativeness is an explanatory virtue.) LWデげゲ ｷﾐ┗Wゲデｷｪ;デW ┘ｴWデｴWヴ ┘W Iﾗ┌ﾉS ｴ;┗W ;ﾐ ｷﾐaﾗヴﾏ;デｷ┗W a┌ﾐIデｷﾗﾐ;ﾉ link. We could start with a link that mentions a realizer e.g. Link: If something aｷヴWゲ ´-opioid receptors then it puts people to sleep 19 I Sﾗ ﾐﾗデ ｷﾐデWﾐS デﾗ HW IﾗﾏﾏｷデデWS デﾗ ┘ｴ;デ ｷゲ ﾗaデWﾐ I;ﾉﾉWS け;ﾐ;ﾉ┞デｷI a┌ﾐIデｷﾗﾐ;ﾉｷゲﾏげ ;ﾐS ｷゲ Sｷゲデｷﾐｪ┌ｷゲｴWS aヴﾗﾏ けヮゲ┞Iｴﾗ-a┌ﾐIデｷﾗﾐ;ﾉｷゲﾏげ ふゲWW LW┗ｷﾐ ヲヰヱヶぶく 20 Despite being analytic, I argue that functional explanations can be useful in [auth] 15 And we could logically strengthen the explanation by adding a disjunct to the antecedent of the link: Link: If something aｷヴWゲ ´-opioid receptors or k-opiod receptors then it puts people to sleep Dﾗﾐげデ a┌ﾐIデｷﾗﾐ;ﾉ links have exactly this disjunctive structure, making them logically stronger than links without the disjunction? No. Functional links do not have the structure above, in which adding a disjunct to the antecedent provides additional information about the realizers in the actual world. Functional properties are individuated by their causal powers, and are independent of the actual realizers. We can use disjunctions to state something extensionally equivalent to a functional link if we refer to other possible worlds21: Link: If something fires H receptors in humans in possible world 1 or fires J receptors in humans in possible world 2 ﾗヴぐ then it puts them to sleep This link is non-analytic but still necessary に it is true in all possible worlds, so it is maximally weak and uninformative.22 So as far as the virtue of logical strength goes, it is just as bad an explanation as a functional explanation. 21 “WW CﾗｴWﾐ ヲヰヰヲぎ けデｴe dispositions a thing has depends crucially on the operative laws of nature: in worlds where the laws of nature are different, none of the [actual realizers] need serve as the basis for the disposition fragility. Consequently, we must take into account the (perhaps infinitely many) low-level configurations that ゲWヴ┗W ;ゲ デｴW H;ゲｷゲ aﾗヴ デｴW Sｷゲヮﾗゲｷデｷﾗﾐ ;デ W;Iｴ ┘ﾗヴﾉS ┘ЭっЭ を ;ゲ ┘Wﾉﾉげく ヮくΒヰ (Cohen here assumes that the causal profiles of properties are not essential to them. Thanks to a referee for emphasizing this.) 22 Fodor (1974) puts great stock in the distinction between infinite lists of realizers and functional properties, but the link is maximally weak either way. And this is another problem with the 1997 Fodor quote above. Fodor implies that higher level closed laws are logically stronger than lower level open laws; it seems to me that they must be extensionally equivalent, and so equally strong. 16 The views I wish to defend are now on the table. I have argued that logical strength is an explanatory virtue. This accounts for our intuitions in examples where omitting details looks virtuous に explanations can be improved by omitting details if (and only if23) doing so makes the explanation logically stronger. The result is that higher level links formed by omitting details from lower level links provide better explanations; higher level links formed by using functional predicates provide worse explanations. It remains to generalize from these examples and respond to objections. 5. Two Generalizations We need to make two generalizations to cover the examples discussed in the literature. The first generalization extends our analysis to two other types of explanation. Like Hempel and Oppenheim, we focussed on causal explanations, which have antecedent conditions as bases and some kind of causal connection as links; but there are also metaphysical and logical explanations. Metaphysical explanations have relatively fundamental states as bases and grounding principles ;ゲ ﾉｷﾐﾆゲく Fﾗヴ W┝;ﾏヮﾉWが デｴW ﾉｷﾐﾆ けｷa デｴWヴW ;ヴW ﾏﾗﾉWI┌ﾉWゲ ;ヴヴ;ﾐｪWS デ;HﾉW-wise then there is a デ;HﾉWげが IﾗﾏHｷﾐWS ┘ｷデｴ デｴW H;ゲW デｴ;デ molecules are arranged table-wise, explains that there is a table. Logical explanations have minor premises as bases and material conditionals as links. For W┝;ﾏヮﾉWが デｴW ;ゲゲ┌ﾏヮデｷﾗﾐ デｴ;デ けｷa A デｴWﾐ Bげが IﾗﾏHｷﾐWS ┘ｷデｴ デｴW ;ゲゲ┌ﾏヮデｷﾗﾐ デｴ;デ Bが W┝ヮﾉ;ｷﾐゲ A. Basis Link Causal/nomological Antecedent conditions Law/generalization Logical Minor premise Material conditional Metaphysical Relatively fundamental state Grounding principle Recall P┌デﾐ;ﾏげゲ ﾗヴｷｪｷﾐ;ﾉ W┝;ﾏヮﾉWぎ 23 I ｴ;┗Wﾐげデ ;ヴｪ┌WS aﾗヴ デｴｷゲ けﾗﾐﾉ┞ ｷaげく TｴWヴW ﾏ;┞ HW ゲﾗﾏW ﾗデｴWヴ ヴW;ゲﾗﾐ デﾗ ﾗﾏｷデ SWデ;ｷﾉゲが デｴﾗ┌ｪｴ I Sﾗﾐげデ デｴｷﾐﾆ デｴWre is. 17 Linkぎ Ia ｷデげゲ ; ヱ ｷﾐIｴ ゲケ┌;ヴW ﾗHﾃWIt then it does not fit through circular holes with diameter 1 inch Although Putnam was defending higher level laws, he does not use a law of nature に it is not a law of ﾐ;デ┌ヴW デｴ;デ ヱ ｷﾐIｴ ゲケ┌;ヴWゲ Sﾗﾐげデ aｷデ デｴヴﾗ┌ｪｴ ヱ ｷﾐIｴ ｴﾗﾉWゲく Nor is it merely a counterfactual-supporting generalization. It is much more like a grounding principle. To be more precise, it seems to follow from principles of geometry as applied to actual space, so perhaps we need to add mathematical principles to the list of causal, metaphysical and logicalく TｴW W┝;Iデ ヮヴｷﾐIｷヮﾉWゲ ┘ﾗﾐげデ ﾏ;デデWヴ ｴWヴW though; what matters is that we need some kind of conditional in the explanation, and conditionals can be strengthened by weakening the antecedent. And this is why explanations that describe the overall shapes of the peg and board can be better than those that describe the positions of the molecules. Moving from cauゲ;ﾉ デﾗ ﾏWデ;ヮｴ┞ゲｷI;ﾉ ﾗヴ ﾉﾗｪｷI;ﾉ W┝ヮﾉ;ﾐ;デｷﾗﾐゲ SﾗWゲﾐげデ Iｴ;ﾐｪW デｴｷゲく The second generalization is needed because the concepts of the base can differ from the concepts of the antecedent of the link. Consider the explanation: Basis: The card is scarlet Link: If the card is red then the pigeon pecks Result: The pigeon pecks Logic does not connect scarletness with redness. We need grounding principles24. These could be packed into the link, but it is clearer to separate them. We would end up with something like: Basis: The card is scarlet Grounding principle: Scarlet is a determinate of red 24 See Schaffer (forthcoming). 18 Link: If the card is red then the pigeon pecks Result: The pigeon pecks So the second generalization extends the account to explanations which require a grounding principle. The main point remains に omitting details from the antecedent of the link improves the explanation. One might now argue that explanations are better without grounding principles. I ┘ﾗﾐげデ ;ヴｪ┌W that they are; but if they are, and assuming bases should contain lower level concepts (perhaps because they are more informative) it follows that links should contain lower level concepts. The result would be that explanations in terms of the lowest level science are best. This is the explanatory reductionist position that the best explanations are given in terms of the lowest level science. For example, assuming that redness comes in just two varieties に scarlet and maroon に the reductionist a;┗ﾗ┌ヴゲ けｷa デｴW I;ヴS ｷゲ ゲI;ヴﾉWデ ﾗヴ ﾏ;ヴﾗﾗﾐ デｴWﾐ デｴW ヮｷｪWﾗﾐ ヮWIﾆゲげ ﾗ┗Wヴ けｷa デｴW I;ヴS ｷゲ ヴWS デｴWﾐ デｴW ヮｷｪWﾗﾐ ヮWIﾆゲげく25 What anti-reductionist arguments are there for preferring links that use higher level concepts? There are three main arguments for favouring higher level links: they avoid disjunctive predicates, illuminate generalities and are better at speaking to our interests (see Pereboom & Kornblith, 1991, Fodor 1974, 1997, Sober 1999, Clapp 2001, Batterman 200226). These arguments all require further discussion, but none of them seem very strong. Wｴ;デげゲ wrong with disjunctive predicates? Why is it better to use a single predicate that just ties a bow around the disjunction? And if the disjunction is heterogenous, is there really any generality to be illuminated, 25 A different argument for this conclusion is given by Sider (2011), who argues that explanations should be given in joint-carving terms: さデｴWﾗヴｷWゲざ H;ゲWS ﾗﾐ Hｷ┣;ヴヴWが ﾐﾗﾐ-joint-carving classifications are unexplanatoryげ p.23 Aゲゲ┌ﾏｷﾐｪ デｴ;デ ﾉﾗ┘Wヴ ﾉW┗Wﾉ IﾗﾐIWヮデゲ I;ヴ┗W ;デ デｴW ﾃﾗｷﾐデゲ HWデデWヴ デｴ;ﾐ ｴｷｪｴWヴ ﾉW┗Wﾉ IﾗﾐIWヮデゲが “ｷSWヴげゲ ヮﾗゲｷデｷﾗﾐ supports explanatory reductionism. I Sﾗﾐげデ デｴｷﾐﾆ ﾐﾗﾐ-joint-carving explanations are unexplanatory; I think they are not as good as joint-carving explanations. 26 Batterman (2000, 2002, forthcoming) argues that the question the reductionist cannot answer is: (MR) How can systems that are heterogeneous at some (typically) micro-scale exhibit the same pattern of behavior at the macro-scale? This strikes me as analogous to the one over many argument for Platonism: how can two different objects, a and b, have the same property F? I am inclined to give the nominalist answer: in virtue of a being F and b being F. I think a similar nominalist stylW ;ﾐゲ┘Wヴ ;ヮヮﾉｷWゲ デﾗ B;デデWヴﾏ;ﾐげゲ Iｴ;ﾉﾉWﾐｪWく 19 as opposed to an illusion of a generality created by a higher level concept? If there is a genuine ｪWﾐWヴ;ﾉｷデ┞が ┘ｴ┞ I;ﾐげデ デｴ;デ HW ｷﾉﾉ┌ﾏｷﾐ;デWS H┞ a lower level conditional connecting one effect with multiple causes? As for speaking to our interests, this is sensitive to the interests of the agent in question. It is hard to see that there are any morals to be drawn regarding objective explanatory virtues (I expand on objective vs. pragmatic virtues in the next section). But I will remain officially neutral on this debate about whether higher or lower level links are better; I claim only that logically strong links are better. 6. Should the Base Really be Maximally Strong? These final three sections defend my account in more detail. This section defends the view that bases should be maximally strong, and the next (7) discusses G;ヴaｷﾐﾆWﾉげゲ objections. The final section (8) defends the view that links should be maximally strong from the problem of disjunctive explanations. On my account, bases should contain as many details as possible, so details should be provided all the way down to the level of fundamental physics. This might appear odd. But I think it can be independently motivated. Suppose an unusually curious Ancient Greek wants to know why Socrates died. She is told that he drank poison. Not fully satisfied, she asks which poison was drunk; a reasonable question, she is told he drank hemlock. But our unusually curious Ancient Greek is still not satisfied. What is the process by which hemlock killed Socrates? Surely another reasonable question, though not one any AﾐIｷWﾐデ GヴWWﾆ Iﾗ┌ﾉS ｴ;┗W ;ﾐゲ┘WヴWSく B┌デ ﾉWデげゲ ヮヴWデWﾐS ; ﾏﾗSWヴﾐ Hｷﾗﾉﾗｪｷゲデ ;ヴヴｷ┗Wゲ ;ﾐS W┝ヮﾉ;ｷﾐゲ デｴ;デ hemlock contains coniine, which disrupts the workings of the central nervous system. Will our curious Ancient Greek be satisfied? Perhaps not. She now asks what the process is by which coniine disrupts the central nervous system. A chemist arrives to explain how coniine paralyzes muscles by blocking the nicotinic receptors which cause muscular contraction. And how does it do that, our curious Ancient Greek now asks. A physicist is now needed to explain the interaction between the coniine and the nicotinic receptors. So we have rapidly descended to physics to explain why Socrates died, and at each 20 step the explanation has improved. At what point is our curious Ancient Greek satisfied? Perhaps only once we have descended to the level of fundamental laws, where we are faced with phenomena that cannot be further explained. And only then is the explanation good enough to satisfy the curious Ancient Greek. Someone might object that this continual movement towards further details does not improve the explanation. After all, the behaviour of the curious Ancient Greek is not realistic; real people do not have either the time or the interest to pursue explanations into such details. We can block this objection using two distinctions. First, distinguish an ideal explanatory text, which contains all the information that could be relevant to explaining the event, from the non-ideal explanations that we actually give, and which are explanatory in virtue of conveying information about some portion of the ideal text.27 Ideal explanatory texts are theoretical infinitely long sentences that cannot be made better or worse; we are discussing the virtue of a given explanation. Second, distinguish the virtues that make a given explanation objectively better from pragmatic features that make an explanation useful. 28 My account says that a given explanation objectively improves as it expands and moves closer to the ideal explanatory text; I allow that more details can pragmatically worsen a given explanation. For example, given explanations are subject to pragmatic principles of conversation.29 Giving too much ｷﾐaﾗヴﾏ;デｷﾗﾐ aﾉﾗ┌デゲ デｴW ゲWIﾗﾐS ｴ;ﾉa ﾗa GヴｷIWげゲ ふヱΓΑヵ ヮくヴヵぶ ﾏ;┝ｷﾏ ﾗa ケ┌;ﾐデｷデ┞ぎ けDﾗ ﾐﾗデ ﾏ;ﾆW ┞ﾗ┌ヴ IﾗﾐデヴｷH┌デｷﾗﾐ ﾏﾗヴW ｷﾐaﾗヴﾏ;デｷ┗W デｴ;ﾐ ｷゲ ヴWケ┌ｷヴWSげく AﾐS ┘ｴ;デ ｷゲ ヴWケ┌ｷヴWS SWヮWﾐSゲ on what the subject wants to know.30 This accounts for the intuition that extra details can worsen the explanation. 27 Railton 1981 p.240 28 For related comments about objective virtues, see Clapp 2001 p.135, Haug, 2011 p.1147; but also Pereboom & Kornblith, 1991 p.127 for dissent. 29 HWヴW ┘W I;ﾐ ;ヮヮﾉ┞ デｴW W;ヴﾉｷWヴ LW┘ｷゲ ケ┌ﾗデW ;ﾐS ;ﾐ W┝デヴ; ゲWﾐデWﾐIW ;Hﾗ┌デ ヮヴ;ｪﾏ;デｷIゲぎ けWｴ;デ I ｴ;┗W been saying [about explanatory virtues] applies just as well to acts of providing information about any large and IﾗﾏヮﾉｷI;デWS ゲデヴ┌Iデ┌ヴWぐTｴW ｷﾐaﾗヴﾏ;デｷﾗﾐ ヮヴﾗ┗ｷSWSが ;ﾐS デｴW ;Iデ ﾗa ヮヴﾗ┗ｷSｷﾐｪ ｷデが I;ﾐ HW ゲ;デｷゲa;Iデﾗヴ┞ ﾗヴ ﾐﾗデ ｷﾐ precisely the same ways. There is nﾗ ゲヮWIｷ;ﾉ ゲ┌HﾃWIデぎ ヮヴ;ｪﾏ;デｷIゲ ﾗa W┝ヮﾉ;ﾐ;デｷﾗﾐげ ふヱΓΒヶ ヮくヲヲΑ-8) 30 Tｴｷゲ ゲWWﾏゲ デﾗ HW LW┘ｷゲげゲ ふヱΓΒヶ; ヮくヲヲΑぶ Sｷ;ｪﾐﾗゲｷゲ ﾗa ┘ｴ;デげゲ ┘ヴﾗﾐｪ ┘ｷデｴ デｴW ﾏｷIヴﾗ-W┝ヮﾉ;ﾐ;デｷﾗﾐ ﾗa P┌デﾐ;ﾏげゲ peg. 21 Equally, a curious subject who wants to know more details will find a more detailed explanation more useful. Thus, Elliott Sober (1999), resヮﾗﾐSｷﾐｪ デﾗ P┌デﾐ;ﾏげゲ Iﾉ;ｷﾏ デｴ;デ ﾏｷIヴﾗ- properties are not explanatory writes: Perhaps the micro-details do not interest Putnam, but they may interest others, and for perfectly legitimate reasons. Explanations come with different levels of detail. When someone tells you more than you want to hear, this does not mean that what is said fails to be an explanation (p. 547). I would add: when someone tells you more than you want to hear, the given explanation objectively improves as it gets closer to the ideal explanatory text. The objector might continue31: けObjection: “┌ヮヮﾗゲW ┘W ;SS デﾗ デｴW W┝ヮﾉ;ﾐ;デｷﾗﾐ ﾗa “ﾗIヴ;デWゲげ SW;デｴ デｴ;デ ｴW ｴWﾉS デｴW cup with his left hand. This addition makes the explanation more informative, but surely does not impro┗W デｴW W┝ヮﾉ;ﾐ;デｷﾗﾐくげ In response, I maintain that the additional information does improve the explanation, and this can be demonstrated by consideration of cases where the additional information is needed for the explanation to succeed. Suppose you know that anyone who drinks hemlock with their right hand is given the antidote by Dexter, a deity who loves the right-handed. Knowing that Socrates is right-handed, you are puzzled as to why the hemlock killed Socrates. Where was Dexter? Your puzzlement is resolved only when you have the additional information that Socrates drank with his left hand this time. Generally, given the right background knowledge, anything can explain anything に a kind of explanation holism. It follows that for any given piece of information and any phenomenon, there are states of background knowledge where that piece of information explains that phenomenon. So the more information in the base, the more states of background knowledge allow the explanation to succeed, and the objectively better the explanation. 31 Thanks to Ben Wolfson for pressing this point. 22 The opposing intuition can be accounted for by the pragmatics. We have limited time and interest, so only want to hear information that is needed for the explanation to succeed given our background knowledge at the moment of explanation. But there is always more to know. 32 7. Anti-Reductionist Arguments Regarding the Base My position is that the base should contain as much information ;ゲ ヮﾗゲゲｷHﾉWく Aﾉデｴﾗ┌ｪｴ ｴW SﾗWゲﾐげデ ┌ゲW the link/base distinction, Garfinkel (1981) gives one of the most detailed arguments in the literature for removing information from the base, so it is worth going through his reasoning in detail.33 I will describe two arguments for removing information from the base, offer responses, then apply the ヴWゲヮﾗﾐゲWゲ デﾗ G;ヴaｷﾐﾆWﾉげゲ W┝;ﾏヮﾉWく 7.1. Lower level bases that omit information Suppose we boil water in a sealed glass container until the glass cracks. Compare the following bases: Basis 1: Molecule A hit the glass with momentum greater than z. Basis 2: The water was boiling. Basis 2 seems better. I agree. One might argue that basis 2 is better because it has less information than basis 1. Counterexample? No. Basis 2 is not less informative than basis 1. (Neither entails the other.) B;ゲｷゲ ヱげゲ explanation in terms of molecule A omits any information about the other molecules に molecule A could have been moving freakishly fast by chance. So basis 1 is lower level but omits information. Basis 2, by saying the water was boiling, includes the information that the other molecules were moving fast as well. So this 32 Cﾗﾏヮ;ヴW LW┘ｷゲ ふヱΓΒヶ;ぶぎ けYour explanatory information is only partial. Yes. And so is any serving of explanatory information we will ever get . . . There is ;ﾉ┘;┞ゲ ﾏﾗヴW デﾗ ﾆﾐﾗ┘くげ ヮくヲンΑ 33 If we interpret Garfinkel as arguing that we should omit details from the antecedent of the link then I agree with him. 23 is not a case in which an explanation with less information is better. In fact neither is more informative than the other. To devise a case where the higher level explanation that uses the cﾗﾐIWヮデ ﾗa けHﾗｷﾉｷﾐｪげ is less informative, the lower level explanation would have to provide the details of the trajectories of many molecules に at least enough to necessitate that the water is boiling. So we need to compare basis 2 with something like: Basis 3: Molecule A is at position L1 with momentum x1, Molecule B is at position Lヲ ┘ｷデｴ ﾏﾗﾏWﾐデ┌ﾏ ┝ヲぐ Basis 3 provides at least as much information as basis 2, making the explanation at least as good on my account. And this seems intuitively correct に for example, explanations with basis 3 are just as counterfactually robust as explanations with basis 2. Extra details appear to make the explanation worse only when we make explicit some details (about molecule A) and fail to say anything about the other details (the rest of the molecules). 7.2. Contrast One might think that explanations with extra details invoke the wrong contrast class. I will argue that the contrast class is separable from the details provided. LWデげゲ grant that explanation is contrastive.34 That is, p rather than q explains x rather than y35. Hold fixed that we want to explain why the ヮｷｪWﾗﾐ ヮWIﾆWS ヴ;デｴWヴ デｴ;ﾐ SｷSﾐげデ ヮWIﾆ. If we are offered the explanation of the scarlet card, we can contrast this with an explanation in terms of a maroon card. That is (leaving the link implicit): 34 WﾗﾗS┘;ヴSげゲ ｷﾐデWヴ┗Wﾐデｷﾗﾐｷゲデ ﾏﾗSWﾉ ﾗa W┝ヮﾉ;ﾐ;デｷﾗﾐ ｷゲ ﾐ;デ┌ヴ;ﾉﾉ┞ デｴﾗ┌ｪｴデ ﾗa ;ゲ Iﾗﾐデヴ;ゲデｷ┗Wく 35 Schaffer 2005 defends contrastive causation. The difference between contrastive causation and contrastive W┝ヮﾉ;ﾐ;デｷﾗﾐ ┘ﾗﾐげデ ﾏ;デデWヴ ｴWヴWく Iデ ;ﾉゲﾗ SﾗWゲﾐげデ ﾏ;デデWヴ ｷa W┝ヮﾉ;ﾐ;デｷﾗﾐ ヴW;ﾉﾉ┞ ｷゲ Iﾗﾐデヴ;ゲデｷ┗W に I am conceding the point to the objector. 24 Failed microexplanation Basis: The card is scarlet rather than maroon Result: The ヮｷｪWﾗﾐ ヮWIﾆWS ヴ;デｴWヴ デｴ;ﾐ SｷSﾐげデ ヮWIﾆ This purported explanation fails. The pigeon would have pecked at any shade of red. But it is a mistake to infer that any detailed explanation in terms of scarlet fails. We just have to make sure that the relevant contrast class is one that does allow the scarletness to explain. And this in turn requires that the contrast class contains only possibilities where the pigeon does not peck.36 For example: Successful microexplanation Basis: The card is scarlet rather than turquoise Result: TｴW ヮｷｪWﾗﾐ ヮWIﾆWS ヴ;デｴWヴ デｴ;ﾐ SｷSﾐげデ ヮWIﾆ 7.3く G;ヴaｷﾐﾆWﾉげゲ SｷゲI┌ゲゲｷﾗﾐ LWデげゲ ﾐﾗ┘ ;ヮヮﾉ┞ these two points デﾗ G;ヴaｷﾐﾆWﾉげゲ SｷゲI┌ゲゲｷﾗﾐく Garfinkelげゲ ゲデヴ;デWｪ┞ ｷゲ デﾗ ;ヴｪ┌W aﾗヴ デｴW failure of the microexplanation of why a rabbit was eaten. My reply is that he makes both the illicit moves above. Garfinkel first mentions that the micro level contains a huge amount of information, and then explicitly omits most of it: けデｴW ﾗ┗Wヴ;ﾉﾉ ﾐ;デ┌ヴW ﾗa デｴW ﾏｷIヴﾗﾉW┗Wﾉ ｷゲ ; ｴ┌ｪW-dimensional determinism37, which, given the complete description of all the equations of interaction between 36 See Franklin-Hall (2016 section 5). 37 OﾐW ﾏｷｪｴデ SWﾐ┞ デｴ;デ デｴW ﾏｷIヴﾗﾉW┗Wﾉ ｷゲ SWデWヴﾏｷﾐｷゲデｷIが H┌デ ｷデ ┘ﾗﾐげデ ﾏ;デデWヴ ｴWヴWく 25 individual foxes and individual rabbits and given a complete specification of foxes and rabbits, tells us the individual destiny of every one of them at every future time. Extracting from this mass デｴW S;デ; ヴWﾉW┗;ﾐデ デﾗ ヴ;HHｷデ ヴが ┘W ﾉW;ヴﾐ デｴ;デぐデｴW microexplanation is therefore something like: Rabbit r was eaten because he passed through the capture space of fox f.げ p.55 Italics added. By extracting from the mass of data, Garfinkel has omitted information from the lower level description. Second, once Garfinkel has focussed on the rabbitげゲ passing through the capture space of f, he invokes the conデヴ;ゲデ Iﾉ;ゲゲ ﾗa デｴW ヴ;HHｷデ ヮ;ゲゲｷﾐｪ デｴヴﾗ┌ｪｴ ゲﾗﾏW ﾗデｴWヴ aﾗ┝げゲ I;ヮデ┌ヴW ゲヮ;IW ;ﾐS IﾗﾐIﾉ┌SWゲぎ けThe object of the macroexplanation is why the rabbit was eaten rather than not eaten, while all the microexplanation tells us is why the rabbit was eaten by fox aぐヴ;デｴWヴ デｴ;ﾐ H┞ ゲﾗﾏW ﾗデｴWヴ aﾗ┝げ ヮく ヵヶ So Garfinkel correctly rejects: Failed microexplanation Basis: Rabbit r passed through the capture space of fox f1 rather than fox f2 Result: Rabbit r was eaten rather than not eaten In response, we can give a microexplanation that a) gives at least as much information as the macroexplanation, and b) has a contrast class (involving a small fox population) that explains why the rabbit was eaten rather than not eaten: 26 Successful microexplanation Basis: Rabbit r was at location l10 and foxes f1ぐf200 were at l1ぐﾉヲヰ0 respectively rather than rabbit r was at location l10 ;ﾐS aﾗ┝Wゲ aヱぐa9 were at l1ぐﾉ9 respectively. Result: Rabbit r was eaten rather than not eaten These points can be adapted to the other examples (though having conceded to the objector that explanation is contrastive, we have to modify some of the basesき ┘Wげﾉﾉ ;ﾉゲﾗ ﾉW;┗W the grounding principles of section 5 implicit, along with the links): Peg: Failed microexplanation Basis: The peg was square with structure S1 rather than square with structure S2. Result: The peg got stuck rather than going through the hole Successful microexplanation Basis: The peg was square with structure S1 rather than round with structure S3. Result: The peg got stuck rather than going through the hole Glass: Failed microexplanation 27 Basis: Molecule A was the first38 to hit the glass with momentum greater than z rather than molecule B was the first to hit the glass with momentum greater than z Result: The glass cracked rather than stayed intact Successful microexplanation Basis: Molecule A hit the glass with momentum greater than z rather than no molecule hit the glass with momentum greater than z Result: The glass cracked rather than stayed intact Conductor: Failed microexplanation Basis: Bob coughed and Alice SｷSﾐげデ rather than Alice coughed and Bob SｷSﾐげデ39. Result: The conductor is annoyed rather than serene Successful microexplanation Basis: Bob coughed rather than no-one coughed. Result: The conductor is annoyed rather than serene Thermodynamics: Failed microexplanation 38 This reference to the first molecule to hit the glass ensures that the contrasts are incompatible. (Molecule A hitting the glass with momentum greater than z is compatible with molecule B hitting the glass with momentum greater than z.) Thanks to x and y 39 Why not just: Bob coughed rather than Alice coughed? Because these possibilities are compatible, so do not form a contrast. 28 Basis: The gas had initial state A with velocities V1-V1,000,000,000 rather than initial state B with (different) velocities V1-V1,000,000,000. Result: The gas filled the vacuum rather than stayed in one corner Successful microexplanation Basis: The gas had initial state A with (non-zero) velocities V1-V1,000,000,000 rather than a billion stationary molecules. Result: The gas filled the vacuum rather than stayed in one corner 8. Should the Antecedent of the Link Really be Maximally Weak? Compare the following explanations: Good explanation Base: Sandy is a man Weak link: If Sandy is a man then Sandy does not get pregnant. Result: Sandy does not get pregnant けProblematicげ explanation Base: Sandy is a man Disjunctive link: If Sandy is a man or Sandy takes birth control pills then Sandy does not get pregnant. Result: Sandy does not get pregnant According to my account, the disjunctive link is logically stronger than the weak link, so better than the weak link, and this looks counter-intuitive. 29 The most important response dialectically is that competing theories of explanation face a similar problem. After all, if omitting details is a virtue, then adding disjunctions should improve the explanation. So most theories of explanation struggle to explain where this Disjunctive Explanation goes wrong: Disjunctive Explanation40 Base: Sandy is a man or Sandy takes birth control pills Disjunctive link: If Sandy is a man or Sandy takes birth control pills then Sandy does not get pregnant. Result: Sandy does not get pregnant Weslake (ms) calls this the problem of disjunctive explanations41 and shows it is a problem for Hempel and Oppenheim (1948), Kitcher (1981), Woodward (2003), Woodward and Hitchcock (2003b), and Strevens (2004; 2009). My account does say something about why the Disjunctive Explanation is worse than the Good Explanation に the base is logically weak.42 So this example supports my theory over alternatives. The problem case for me is where the base is held fixed and a disjunction is added to the link. Repeating from above: けProblematicげ explanation 40 We should also distinguish this case from one where the disjunct is irrelevant: Non-problematic explanation Base: Sandy is a man Strong link: If Sandy is a man or the Sun is yellow then Sandy does not get pregnant. Result: Sandy does not get pregnant I suggest we require conditionals in causal explanations to be stronger than the material conditional, which ensures this this link is false, so fails as an explanation (assuming that only the truth can explain). 41 AIデ┌;ﾉﾉ┞ WWゲﾉ;ﾆWげゲ W┝;ﾏヮﾉW ｷゲ ゲﾉｷｪｴデﾉ┞ ﾏﾗヴW IﾗﾏヮﾉｷI;デWSが H┌デ I デ;ﾆW ｷデ デｴW ヮﾗｷﾐデ ｷゲ デｴW ゲ;ﾏWく 42 Objecction: But this is balanced by the virtue that the link is logically strﾗﾐｪく ‘Wヮﾉ┞ぎ YWゲが Iげ┗W ;ゲゲ┌ﾏWS デｴW base is the trumping consideration. Perhaps there is a non-extreme exchange rate. And perhaps the exchange rate is context-sensitive. I set aside these complications. 30 Base: Sandy is a man Disjunctive link: If Sandy is a man or Sandy takes birth control pills then Sandy does not get pregnant. Result: Sandy does not get pregnant One possible ヴWゲヮﾗﾐゲW ｷゲ デﾗ ;SS ; a┌ヴデｴWヴ W┝ヮﾉ;ﾐ;デﾗヴ┞ ┗ｷヴデ┌W デｴ;デ ヴ┌ﾉWゲ ﾗ┌デ Sｷゲﾃ┌ﾐIデｷ┗W ﾉｷﾐﾆゲき ┘Wげﾉﾉ consider a couple of ways to do that below. But I offer a different response: I maintain that this disjunctive link does improve the explanation. Why might someone thinﾆ デｴ;デ ｷデ SﾗWゲﾐげデい I can think of four reasons. First, someone might object that the disjunctive link is not law-like, holding that explanations must be law-like. But the claim that explanations must be law-ﾉｷﾆW ｷゲ ｴｷｪｴﾉ┞ Iﾗﾐデヴﾗ┗Wヴゲｷ;ﾉく Iげﾏ ｷﾐIﾉｷﾐWS to a more liberal view に for example, Jenkins and Nolan (2008) give compelling arguments that there can even be backwards explanations. (Still, those who demand that links must be law-like can add this as a restriction and accept the rest of my account.). Second, perhaps natural properties (Lewis 1983) in links explain better, and the disjunction けSandy is a man or Sandy デ;ﾆWゲ Hｷヴデｴ Iﾗﾐデヴﾗﾉ ヮｷﾉﾉゲげ ｷゲ ﾐﾗデ naturalく B┌デ I Sﾗﾐげデ デｴｷﾐﾆ デｴW preference for natural links can be maintained. Many intuitively good explanations are non-natural. For example, functional explanations are non-natural43. The explanation that someone died because they were poisoned is non-natural because so many different substances realize poisons.44 Furthermore, some think it is costly to wheel in metaphysically substantive concepts like naturalness.45 (Still, those who demand that links must be natural can add this as a restriction and accept the rest of my account.) Third, we might be misled by focussing only on the link and ignoring the base. Franklin-Hall (2016) argues that interventionists are pushed towards disjunctive explanations, with the result that 43 My earlier objection to functional explanations is that they are logically weak, not that they are non-natural. 44 Objection: Poisons are unified at the relevant (higher) level. What unifies poisons is their ability to disturb organisms. Response: But on such a liberal account of unification, being a man and taking birth controls are unified, as both prevent pregnancy. 45 See Weslake (ms) for a detailed discussion. 31 けデｴW ｷﾐデWヴ┗Wﾐデｷﾗﾐｷゲデ ｷゲ ヴWIﾗﾏﾏWﾐSｷﾐｪ ┗Wヴ┞ ヮWI┌ﾉｷ;ヴが ;ﾐS ｷﾐ ゲﾗﾏW ヴWゲヮWIデゲ ┗Wヴ┞ ┌ﾐｷﾐaﾗヴﾏ;デｷ┗Wが explanations, those that don't go any way towards specifying the particular circumstance that brought ;Hﾗ┌デ デｴW WaaWIデ デﾗ HW W┝ヮﾉ;ｷﾐWSげ (p.573). But on my account the link is not in the business of specifying the particular circumstances に that is for the base. Fourth, dissatisfaction with disjunctive links may be due to the pragmatics. Recall that the ideal explanatory text contains every sentence that could be used in an explanation of the event. When we ask for explanations, we will not be happy to be given the ideal explanatory text, because we Sﾗﾐげデ ｴ;┗W デｴW デｷﾏW ﾗヴ Iﾗｪﾐｷデｷ┗W I;ヮ;Iｷデ┞ デﾗ ｴ;ﾐSﾉW ｷデ に we want the information that is relevant to usく TｴW W┝ヮﾉ;ﾐ;デｷﾗﾐゲ ;Hﾗ┗W ｴ;┗W デｴW H;ゲW けSandy ｷゲ ; ﾏ;ﾐげく Tｴｷゲ ﾐ;デ┌ヴ;ﾉﾉ┞ ｷﾐ┗ﾗﾆWゲ ; I;ゲW ┘ｴWヴW デｴW explainer に the person doing the explaining に knows Sandy is a man. If this explainer gives us the disjunctive link, they have violated GヴｷIWげゲ ふヱΓΑヵ ヮくヴヶぶ maxim: be relevant. They would violate the same maxim as someone who told you Bill was in the library or the pub, while knowing that Bill was at the pub. But we can fill out the story so that the disjunctive link does not violate any pragmatic rules. Suppose an alien does not know whether men can get pregnant, SﾗWゲﾐげデ ﾆﾐﾗ┘ ┘ｴWデｴWヴ Sandy is a man or a woman, and is very interested in how pregnancy works, and why Sandy is not pregnant. They read a book on human biology. The first chapter tells them that men cannot get pregnant and women can. The second chapter tells them that women can avoid getting pregnant by taking birth control pills. When they learn that Sandy is a man, the explanation is complete. Would the explanation have been improved by omitting the second chapter of the book? Surely not. The second chapter gives the alien further knowledge about the causal dependencies associated with pregnancy; it gives the alien counterfactual knowledge about what would have happened if Sandy had turned out to be a woman taking birth control pills. So the disjunctive link is more useful to the alien than the weak link. So there a number of reasons the disjunctive link might look problematic, but I think they can all be answered. 32 9. Conclusion I have criticized the contemporary consensus that higher level explanations are better in virtue of omitting details. I agree that omitting details can be a virtue, but this is because omitting details can make an explanation logically stronger; logical strength is a fundamental explanatory virtue. So higher level explanations are better than lower level explanations when logically stronger and worse when logically weaker, other things equal. The situation is simpler for bases; in all the cases typically discussed, bases are improved by moving from higher level to lower level concepts, and this is because doing so increases logical strength. One of the main arguments for anti-reductionism is the claim that omitting details makes an explanation better. If, as I have argued, it is logical strength that makes an explanation better, then this argument for anti-reductionism is undercut. Acknowledgments Thanks to Jonathan Schaffer and Robbie Williams for comments on a draft of this paper, to Roman Frigg, Lara Franklin-Hall, Michael Weisberg and Ben Wolfson, and to the participants at the Workshop on Theoretical Virtues at Leeds 2017, especially Lina Jansson, Juha Saatsi, Jonathan Tallant and Pekka Väyrynen. This work was funded by EU Marie Curie Re-integration grant #656441. DARREN BRADLEY School of Philosophy, Religion and History of Science University of Leeds Leeds LS2 9JT UK d.j.bradley@leeds.ac.uk References 33 Batterman, R. W. 2000aく さA けMﾗSWヴﾐげ ふЭ VｷIデﾗヴｷ;ﾐいぶ Aデデｷデ┌SW デﾗ┘;ヴSゲ “IｷWﾐデｷaｷI UﾐSWヴゲデ;ﾐSｷﾐｪくざ Monist 83 (2): 228に57. Batterman, R. (2000b). Multiple Realizability and Universality. British Journal for the Philosophy of Science 51 (1):115-145. Batterman, R. 2002. The Devil in the Details: Asymptotic Reasoning in Explanation, Reduction, and Emergence. Oxford: Oxford University Press. Batterman (2017). Autonomy of Theories: An Explanatory Problem. 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