(Chapter 5 of Across the Boundaries, forthcoming, from Oxford University Press) This chapter argues that previous accounts of extrapolation, either by reference to capacities or mechanisms, do not adequately address the challenges confronting extrapolation. It then begins the account of how the mechanisms-approach can be developed so as to do better. The central concept in this account is what I term comparative process tracing.
This essay defends the view that inductive reasoning involves following inductive rules against objections that inductive rules are undesirable because they ignore background knowledge and unnecessary because Bayesianism is not an inductive rule. I propose that inductive rules be understood as sets of functions from data to hypotheses that are intended as solutions to inductive problems. According to this proposal, background knowledge is important in the application of inductive rules and Bayesianism qualifies as an inductive rule. Finally, I consider a (...) Bayesian formulation of inductive skepticism suggested by Lange. I argue that while there is no good Bayesian reason for judging this inductive skeptic irrational, the approach I advocate indicates a straightforward reason not to be an inductive skeptic. (shrink)
This essay demonstrates a previously unnoticed connection between formal and statistical learning theory with regard to Nelson Goodman’s new riddle of induction. Discussions of Goodman’s riddle in formal learning theory explain how conjecturing “all green” before “all grue” can enhance efficient convergence to the truth, where efficiency is understood in terms of minimizing the maximum number of retractions or “mind changes.” Vapnik-Chervonenkis (VC) dimension is a central concept in statistical learning theory and is similar to Popper’s notion of degrees of (...) testability. I show that for a class inductive problems of which Goodman’s riddle is one example, a reliable inductive method minimizes the maximum number of mind changes exactly if it always conjectures the hypothesis from the set with lowest VC dimension consistent with the data. I also discuss the relevance of these results to language invariance and curve fitting. (shrink)
The naturalism versus interpretivism debate in social science is traditionally framed as the question of whether social science should attempt to emulate the methods of natural science. I argue that this manner of formulating the issue is problematic insofar as it presupposes an implausibly strong unity of method among the natural sciences. I propose instead that the core question of the debate is the extent to which reliable causal inference is possible in social science, a question that cannot be answered (...) by comparisons between social and natural science. I explore how some common arguments on both sides of the issue should be reexamined if the naturalism versus interpretivism debate is understood as I propose. (shrink)
I develop a critique of Hume’s infamous problem of induction based upon the idea that the principle of induction (PI) is a normative rather than descriptive claim. I argue that Hume’s problem is a false dilemma, since the PI might be neither a “relation of ideas” nor a “matter of fact” but rather what I call a contingent normative statement. In this case, the PI could be justified by a means-ends argument in which the link between means and end is (...) established solely by deductive reasoning. The means-ends argument is an elementary result from formal learning theory that you must be willing to make inductive generalizations if you want to be logically reliable in the types of examples Hume described. This justification of the PI avoids both horns of Hume’s dilemma. Since no contradiction ensues from rejecting logical reliability as an aim, the PI is contingent. Yet since the proof concerning the PI and logical reliability is not based on inductive reasoning, there is no threat of circularity. (shrink)
Any account of extrapolation from animal models to humans must confront two basic challenges: explain how extrapolation can be justified even when there are causally relevant differences between model and target, and explain how the suitability of a model can be established given only limited information about the target. We argue that existing approaches to extrapolation—either in terms of capacities or mechanisms—do not adequately address these challenges. However, we propose a further elaboration of the mechanisms approach that provides a better (...) treatment of this issue. The central concept in our proposal is what we term comparative process tracing. (shrink)
Nancy Cartwright’s most recent book, Hunting Causes and Using Them: Approaches to Philosophy and Economics (hereafter, HCUT), is a welcome and provocative addition to the current literature on causation. In HCUT, Cartwright further develops themes from her earlier work, especially Nature’s Capacities and their Measurement (1989) and The Dappled World (1999). One theme is that methodological issues having to with inferring and applying claims about cause and effect must be considered in tandem with metaphysical questions about what causation is. And (...) with regard to the latter issue, Cartwright insists that causation is not just one kind of thing but is instead a general category for various types of processes that often differ in important ways. From these two themes, it naturally follows that one should be skeptical that there is any method of causal inference that is applicable in all cases. Moreover, for any method, one ought to be very clear about the types of causal systems for which it is suited and, of equal importance, those for which it is not. Given Cartwright’s approach, such investigations will require careful attention to domain specific detail about the nature of the causal processes of interest. Cartwright pursues these ideas in the context of critical examinations of current approaches to causation, including Bayes nets and several approaches proposed by econometricians. I am quite sympathetic to Cartwright’s overall perspective on causation, but I take issue with some of her characterizations of particular approaches and several of her specific claims about their limitations. I focus on Cartwright’s claims concerning methods of causal inference that rely on Bayes nets, which among the methods she discusses is the one I know best. First, I argue that Cartwright’s discussion of this topic 1 is problematic insofar as it does not pay adequate attention to the distinct projects that might be pursued within a Bayes nets approach to causation.. (shrink)
This essay defends the view that inductive reasoning involves following inductive rules against objections that inductive rules are undesirable because they ignore background knowledge and unnecessary because Bayesianism is not an inductive rule. I propose that inductive rules be understood as sets of functions from data to hypotheses that are intended as solutions to inductive problems. According to this proposal, background knowledge is important in the application of inductive rules and Bayesianism qualifies as an inductive rule. Finally, I consider a (...) Bayesian formulation of inductive skepticism suggested by Lange. I argue that while there is no good Bayesian reason for judging this inductive skeptic irrational, the approach I advocate indicates a straightforward reason not to be an inductive skeptic. (shrink)
Howson's critique of my essay on Hume's problem of induction levels two main charges. First, Howson claims that I have attributed to him an error that he never made, and in fact which he warned against in the very text that I cite. Secondly, Howson argues that my proposed solution to Hume's problem is flawed on technical and philosophical grounds. In response to the first charge, I explain how Howson's text justifies attributing to him the claim that the principle of (...) induction is shown to be inconsistent by Goodman's riddle. In regards to the second, I show that Howson's objections rest on misunderstandings of formal learning theory and on conflating the problem of induction with the problem of unconceived alternatives. (shrink)
This article argues that a successful answer to Hume's problem of induction can be developed from a sub-genre of philosophy of science known as formal learning theory. One of the central concepts of formal learning theory is logical reliability: roughly, a method is logically reliable when it is assured of eventually settling on the truth for every sequence of data that is possible given what we know. I show that the principle of induction (PI) is necessary and sufficient for logical (...) reliability in what I call simple enumerative induction. This answer to Hume's problem rests on interpreting PI as a normative claim justified by a non-empirical epistemic means-ends argument. In such an argument, a rule of inference is shown by mathematical or logical proof to promote a specified epistemic end. Since the proof concerning PI and logical reliability is not based on inductive reasoning, this argument avoids the circularity that Hume argued was inherent in any attempt to justify PI. (shrink)
Critics of the ideal of value‐free science often assume that they must reject the distinction between epistemic and nonepistemic values. I argue that this assumption is mistaken and that the distinction can be used to clarify and defend the argument from inductive risk, which challenges the value‐free ideal. I develop the idea that the characteristic feature of epistemic values is that they promote, either intrinsically or extrinsically, the attainment of truths. This proposal is shown to answer common objections to the (...) distinction and provide a principled basis for separating legitimate from illegitimate influences of nonepistemic values in scientific inference. *Received June 2009; revised September 2009. †To contact the author, please write to: 503 S. Kedzie Hall, Michigan State University, East Lansing, MI 48824‐1032; e‐mail: steel@msu.edu. (shrink)
In order to make scientific results relevant to practical decision making, it is often necessary to transfer a result obtained in one set of circumstances—an animal model, a computer simulation, an economic experiment—to another that may differ in relevant respects—for example, to humans, the global climate, or an auction. Such inferences, which we can call extrapolations, are a type of argument by analogy. This essay sketches a new approach to analogical inference that utilizes chain graphs, which resemble directed acyclic graphs (...) (DAGs) except in allowing that nodes may be connected by lines as well as arrows. This chain graph approach generalizes the account of extrapolation I provided in my (2008) book and leads to new insights that integrate the contributions of the other participants of this symposium. More specifically, this approach explicates the role of “fingerprints,” or distinctive markers, as a strategy for avoiding an underdetermination problem having to do with spurious analogies. Moreover, it shows how the extrapolator’s circle, one of the central challenges for extrapolation highlighted in my book, is closely tied to distinctive markers and the Markov condition as it applies to chain graphs. Finally, the approach suggests additional ways in which investigations of a model can provide information about a target that are illustrated by examples concerning nanomaterials in sunscreens and Wendy Parker’s discussion of fingerprints in climate science. (shrink)
The naturalism versus interpretivism debate the in philosophy of social science is traditionally framed as the question of whether social science should attempt to emulate the methods of natural science. I show that this manner of formulating the issue is problematic insofar as it presupposes an implausibly strong unity of method among the natural sciences. I propose instead that what is at stake in this debate is the feasibility and desirability of what I call the Enlightenment ideal of social science. (...) I argue that this characterization of the issue is preferable, since it highlights the central disagreement between advocates of naturalism and interpretivism, makes connections with recent work on the topics of causal inference and social epistemology, while avoiding unfruitful comparisons between the social and natural sciences. (shrink)
Nelson Goodman’s new riddle of induction forcefully illustrates a challenge that must be confronted by any adequate theory of inductive inference: provide some basis for choosing among alternative hypotheses that fit past data but make divergent predictions. One response to this challenge is to distinguish among alternatives by means of some epistemically significant characteristic beyond fit with the data. Statistical learning theory takes this approach by showing how a concept similar to Popper’s notion of degrees of testability is linked to (...) minimizing expected predictive error. In contrast, formal learning theory appeals to Ockham’s razor, which it justifies by reference to the goal of enhancing efficient convergence to the truth. In this essay, I show that, despite their differences, statistical and formal learning theory yield precisely the same result for a class of inductive problems that I call strongly VC ordered , of which Goodman’s riddle is just one example. (shrink)
The likelihood principle (LP) is a core issue in disagreements between Bayesian and frequentist statistical theories. Yet statements of the LP are often ambiguous, while arguments for why a Bayesian must accept it rely upon unexamined implicit premises. I distinguish two propositions associated with the LP, which I label LP1 and LP2. I maintain that there is a compelling Bayesian argument for LP1, based upon strict conditionalization, standard Bayesian decision theory, and a proposition I call the practical relevance principle. In (...) contrast, I argue that there is no similarly compelling argument for or against LP2. I suggest that these conclusions lead to a restrictedly pluralistic view of Bayesian confirmation measures. (shrink)
This reply to Erik Weber’s commentary agrees that mechanisms are important for causal inference in social science, but argues that Weber makes the mistake that was the main focus of my original essay: inferring that since a problem cannot be solved without mechanisms, it can be solved with them. As it stands, this inference is invalid since the problem might be unsolvable with or without mechanisms. Any claim about the usefulness of mechanisms for some purpose requires an adequate account of (...) how mechanisms can actually fulfill that function, which Weber has not provided with regard to the issues he discusses. (shrink)
Woodward present an argument for the Causal Markov Condition (CMC) on the basis of a principle they dub ‘modularity’ ([1999, 2004]). I show that the conclusion of their argument is not in fact the CMC but a substantially weaker proposition. In addition, I show that their argument is invalid and trace this invalidity to two features of modularity, namely, that it is stated in terms of pairwise independence and ‘arrow-breaking’ interventions. Hausman & Woodward's argument can be rendered valid through a (...) reformulation of modularity, but it is doubtful that the argument so revised provides any substantially new insight regarding the basis of the CMC. Introduction The CMC versus Hausman & Woodward's conclusion Hausman & Woodward's argument Modularity and independent error terms Conclusion Appendix: D-separation. (shrink)
The faithfulness condition (FC) is a useful principle for inferring causal structure from statistical data. The usual motivation for the FC appeals to theorems showing that exceptions to it have probability zero, provided that some apparently reasonable assumptions obtain. However, some have objected that, the theorems notwithstanding, exceptions to the FC are probable in commonly occurring circumstances. I argue that exceptions to the FC are probable in the circumstances specified by this objection only given the presence of a condition that (...) I label homogeneity, and furthermore that this condition typically does not obtain in the FC’s intended domain of application. (shrink)
This article examines methodological individualism in terms of the theory that invariance under intervention is the signal feature of generalizations that serve as a basis for causal explanation. This theory supports the holist contention that macro-level generalizations can explain, but it also suggests a defense of methodological individualism on the grounds that greater range of invariance under intervention entails deeper explanation. Although this individualist position is not threatened by multiple-realizability, an argument for it based on rational choice theory is called (...) into question by experimental results concerning preference reversals. Key Words: methodological individualism • mechanisms • explanation • invariance • preference reversal. (shrink)
The causal Markov condition (CMC) plays an important role in much recent work on the problem of causal inference from statistical data. It is commonly thought that the CMC is a more problematic assumption for genuinely indeterministic systems than for deterministic ones. In this essay, I critically examine this proposition. I show how the usual motivation for the CMC—that it is true of any acyclic, deterministic causal system in which the exogenous variables are independent—can be extended to the indeterministic case. (...) In light of this result, I consider several arguments for supposing indeterminism a particularly hostile environment for the CMC, but conclude that none are persuasive. Introduction Functional models and directed graphs The causal Markov theorem The causal Markov theorem and genuine indeterminism Are the exogenous variables independent? EPR Conclusion. (shrink)
Pluralism is often put forth as a counter-position to reductionism. In this essay, I argue that reductionism and pluralism are in fact consistent. I propose that there are several potential goals for reductions and that the proper form of a reduction should be considered in tandem with the goal that it aims to achieve. This insight provides a basis for clarifying what version(s) of reductionism are currently defended, for explicating the notion of a fundamental level of explanation, and for showing (...) how one can be both a reductionist and a pluralist. (shrink)
Several authors have claimed that mechanisms play a vital role in distinguishing between causation and mere correlation in the social sciences. Such claims are sometimes interpreted to mean that without mechanisms, causal inference in social science is impossible. The author agrees with critics of this proposition but explains how the account of how mechanisms aid causal inference can be interpreted in a way that does not depend on it. Nevertheless, he shows that this more charitable version of the account is (...) still unsuccessful as it stands. Consequently, he advances a proposal for shoring up the account, which is founded on the possibility of acquiring knowledge of social mechanisms by linking together norms or practices found in a society. Key Words: causality • social mechanisms • interpretation • anthropology. (shrink)
Disputes between advocates of Bayesians and more orthodox approaches to statistical inference presuppose that Bayesians must regard must regard stopping rules, which play an important role in orthodox statistical methods, as evidentially irrelevant.In this essay, I show that this is not the case and that the stopping rule is evidentially relevant given some Bayesian confirmation measures that have been seriously proposed. However, I show that accepting a confirmation measure of this sort comes at the cost of rejecting two useful ancillaryBayesian (...) principles. (shrink)
In a recent article, Elliot Sober responds to challenges to a counter-example that he posed some years earlier to the Principle of the Common Cause (PCC). I agree that Sober has indeed produced a genuine counter-example to the PCC, but argue against the methodological moral that Sober wishes to draw from it. Contrary to Sober, I argue that the possibility of exceptions to the PCC does not undermine its status as a central assumption for methods that endeavor to draw causal (...) conclusions from statistical data. 1 The PCC and the counter-example 2 Making non-stationary time series stand still 3 Sober's alternative. (shrink)
Critics of Bayesianism often assert that scientists are not Bayesians. The widespread use of Bayesian statistics in the field of radiocarbon calibration is discussed in relation to this charge. This case study illustrates the willingness of scientists to use Bayesian statistics when the approach offers some advantage, while continuing to use orthodox methods in other contexts. The case of radiocarbon calibration, therefore, suggests a picture of statistical practice in science as eclectic and pragmatic rather than rigidly adhering to any one (...) theoretical position. (shrink)
I use an explanation of Yanomami warfare given by the anthropologist Brian Ferguson as a case study to compare the merits of the causal and unification approaches to explanation. I argue that Ferguson's insistence on explaining actual occurrences and patterns of Yanomami warfare together with his claim that all of his generalizations are statistical raises difficulties for the unification approach, because of its commitment to "deductive chauvinism." Moreover, I show that there are serious difficulties involved in comparing the "unifying power" (...) of Ferguson's explanations to those of his competitors. I show that the causal approach can provide a rich analysis of Ferguson's explanation while avoiding these difficulties. (shrink)
In a recent essay (1995), Andrew Wayne charges that Bayesian attempts to account for the rule that, ceteris paribus, diverse evidence confirms better than narrow evidence are inadequate. I reply to these criticisms and argue that, on the contrary, one of the Bayesian approaches considered by Wayne does an excellent job of explaining why, and under what circumstances, diverse evidence is valuable.
