Common Cause Abduction: Its Scope and Limits ABSTRACT: This article aims to analyse the scope and limits of common cause abduction which is a version of explanatory abduction based on Hans Reichenbach’s Principle of the Common Cause. First, it is argued that common cause abduction can be regarded as a rational mechanism for inferring abductive hypotheses that aim to account for the surprising correlations of events. Three arguments are presented in support of common cause abduction: the argument from screening-off, the argument from likelihood, and the argument from simplicity. Second, it is claimed that common cause abduction is a defeasible reasoning, i.e., common cause abductive hypotheses are not always more plausible than separate cause abductive hypotheses. Finally, it is outlined what factors should be taken into account in order to use common cause abduction in a reasonable way. Keywords: abduction, common cause, reasoning, likelihood, simplicity, bayesianism. 1. Introduction More than a hundred years ago the American philosopher and logician Charles S. Peirce coined the puzzling concept of abduction in order to describe a kind of reasoning (argument)1 which aims to form an explanatory hypothesis to account for the surprising facts. Philosophers have struggled long and hard with the fundamental questions about abduction: Does abduction amount to a logically valid inference (argument) or to a mere act of guessing? If abduction is a logically valid inference, then abductive conclusion must be true if all the premises are true; but this cannot be true, since abduction is ampliative2, highly conjectural, 1 It is worth noticing that contemporary philosophers distinguish between the notion of argument and the notion of reasoning (inference). An argument is said to be a set of sentences divided into two parts: premises and conclusions; an argument is judged as valid or sound with respect to some principles of argument like modus ponens or modus tollens. On the other hand, the notion ‘reasoning’ or ‘inference’ is used to indicate the process of drawing conclusions from the premises, i.e., the process of extracting information from the premises. As it has been pointed by some philosophers, most notably by G. Harman (1986, pp. 1-6), the rules of argument do not become automatically the rules of reasoning (or rules for ‘a reasoned change in view’), although they may be relevant to them. Interestingly, Peirce (1931-1958, CP 6.456) had a different terminology: by ‘argument’ he meant a process of reasoning, while by ‘argumentation’ a set of premises and conclusions. For present purposes, these distinctions make little difference. 2 Abduction is an ampliative (synthetic) step of reasoning, i.e., its conclusion brings new information that is not contained—implicit or explicit—in the premises, and this new information is introduced by abduction as a kind of conjecture. 1 and non-monotonic3? On the other hand, if it is a mere kind of guessing, how is it possible that scientists armed with abductive mechanism ‘guessed’ so many true (realism), or empirically adequate (empiricism), theories about the world? These questions mark a tension between the conjectural, ampliative and non-monotonic character of abduction, on the one hand, and the possibility of a logical analysis of abduction (the possibility of constructing the logica docens for abduction), on the other hand. Philosophical opinions are sharply divided with respect to these questions. On the one hand, some philosophers argue, following Reichenbach (1938), Popper (1959), that if abduction constitutes the context of discovery, then it cannot be governed by rational rules, since the context of discovery cannot be logically analysed (in particular, as a logical argument); they add that, at best, abduction as a kind of guess can be analysed from a psychological point of view. On the other hand, it is argued that one can define rational rules for abduction that can be codified, for example, in various logics for abduction.4 Both strategies have their standard arguments, and each regards its own arguments as compelling—the debate resembles the trench warfare of the World War I. One way to avoid a stalemate in this debate is to acknowledge that one can tackle the fundamental questions about abduction either globally or locally. The global strategy aims to answer these questions in general, apart from the types of abduction one may specify, and apart from the various contexts in which abduction can be used; it aims to resolve the basic dilemmas about abduction, and then apply these solutions to all the contexts in which abduction can be used. On the other hand, a more modest local strategy acknowledges that the fundamental questions about abduction cannot be answered in general; at best, one may tackle them with respect to a type of abduction (e.g., explanatory or instrumental abduction) or even with respect to a type of abduction in a particular context (e.g., explanatory abduction in law or science).5 On this strategy, one can compare different answers to the core questions about abduction with respect to different types of abduction. It may happen then that one can define rational rules 3 Abduction is non-monotonic (defeasible) because an abductive conclusion drawn from a set of premises can be undercut if the premise set is supplemented with additional information; other words abduction, unlike deduction, lacks monotonicity because the set of abductive conclusions does not grow monotonically while the premise set grows. 4 Various logics and logical approaches to abduction have been proposed in the domain of artificial intelligence, cognitive science, philosophy of science and philosophical logic. For example, Aliseda (2006) has proposed a logical approach to abduction in terms of semantic tableaux; Meheus and Batens (2006) have defined logics for abduction based on ampliative adaptive logics; Carnielli (2006) has designed a logic for abduction based on a version of paraconsistent logic; Hintikka (1998) has proposed a logical approach to abduction in terms of his interrogative model of inquiry and interrogative logic. 5 So, for example, on the local strategy, either one focuses on the nature of explanatory abduction, or on the nature of various non-explanatory or instrumental abductions like abduction in the so-called ‘reverse’ mathematics or abduction in interpretation. Moreover, it is possible that the justification of explanatory abduction is highly context-dependent (e.g., explanatory abduction in science and in law may differ essentially). 2 for the explanatory abduction, but fail to do this for the abductive reasoning in ‘reverse’ mathematics. This article focuses on abduction from the perspective of the local strategy. It aims to scrutinise the nature of one version of the explanatory abduction, namely common cause abduction, which is based on Hans Reichenbach’s principle of the common cause. First, it is claimed that common cause abduction can be regarded as a rational and powerful rule for abductive explanatory inferences from the observed surprising correlations of events to the screening-off common cause abductive hypothesis that explains this observed correlation. Three arguments are presented to bolster this thesis: the argument form screening-off, the argument from likelihood, and the argument from simplicity. The upshot of these three arguments is that common cause abductive hypotheses appear to be more plausible than the separate cause abductive hypotheses. Second, it is argued that we should not be so optimistic about common cause abduction. I shall argue that it is not always true that the common cause abductive hypothesis is more plausible than the separate cause hypothesis. All of these three arguments appear to be defeasible. Third, it is claimed that the defeasible nature of common cause abduction does not imply that this kind of abduction is unreasonable. As a consequence, I shall outline some general remarks of how to use common cause abduction in a reasonable manner. 2. The Explanatory Abduction for the Correlation of Events Before diving into the body of discussion concerning the substantial theses of this article, I shall first clarify the concept of explanatory abduction by introducing its model, and then use this model to define the explanatory abduction for the correlation of events. The idea of explanatory abduction is inherently connected with Peirce’s conception of abduction. As it has been argued by Peirce, abduction aims to find an explanans that accounts for an explanandum which describes some surprising event or fact. One may say that abduction begins when ignorance comes, or that one’s ignorance ‘triggers’ abduction. This means that we reason abductively, when we are faced with unknown surprising circumstances or, broadly speaking, with a cognitive problem that cannot be resolved on the basis of our background knowledge. Following Kapitan (1997, pp. 477-478), Peirce’s conception of abduction may be characterised by the four theses: Inferential Thesis: Abduction is, or includes, an inferential process or processes. 3 Thesis of Purpose: The purpose of scientific abduction is both (i) to generate new hypotheses and (ii) to select hypotheses for further examination; hence, a certain aim of abduction is to recommend a course of action. Comprehension Thesis: Scientific abduction includes all the operations whereby theories are engendered. Autonomy thesis: Abduction is, or embodies, reasoning that is distinct from, and irreducible to, neither deduction nor induction. It is essential to Peirce’s conception that abduction is an inference that aims to create, select and conjecture hypotheses. Some philosophers suggested, albeit in different ways, that we can make sense of two epistemological kinds of abduction: creative abduction and abduction as inference to the best explanation (evaluative or selective abduction).6 Whereas creative abduction aims to generate hypotheses for further examination, abduction as inference to the best explanation leads to accepting a hypothesis on the grounds that it best explains some explanandum proposition. This distinction, however, does not comply with Peirce’s Thesis of Purpose which states that any kind of abduction encompasses both the selective and the creative part. The question arises: How can we represent explanatory abduction in order to make sense of Peirce’s theses? A very promising way is to adopt the so-called GW-model of abduction proposed by D. M. Gabbay and J. Woods (Gabbay and Woods 2005, pp. 39-73). In comparison to various formal and quasi-formal representations of Peirce’s idea of abduction presented in the literature, GW-model aims to provide a more general structure of abduction; it encompasses both the creative and the selective part, and it captures both the instances of explanatory and instrumental abductions. What is crucial for this model is that it is based on non-classical logic—the practical logic of cognitive systems.7 This logic is a principled description of the conditions under which agents employ resources in order to perform their cognitive tasks. It is a non-classical logic in the sense that it does not restrict logic to modelling arguments as 6 This distinction is to be found in Magnani (2001), Schurz (2008), Fetzer (2004). Some philosophers regard Peirce’s abduction as synonymous with inference to the best explanation; see, e.g., Harman (1965). 7 This practical logic is an instance of the so-called Resource-Target Logic. This logic models a target-motivated and resource-dependent reasoning. A detailed analysis of this logic is to be found in Gabbay and Woods (2001). 4 relations between linguistic structures (propositions, sentences, etc.), but it extends logic to model in a principled way the behaviour of agents who employ inferences. So, this logic finds the structure of abduction as more complex than the relation between an explanandum and an explanans proposition. On GW-model, abduction is a presumptive solution to a cognitive agent’s ignorance problem (IP). IP may be defined as follows: Definition 2.1. (Ignorance Problem (IP)) IP exists for a cognitive agent iff he has a cognitive target T that cannot be attained from what he currently knows (his current knowledge base K) and from the accessible successor knowledge K* of K (the extension of K). 8 It is important to note that one’s ignorance problem is always a matter of degree; that is to say, our cognitive targets are more or less attainable from what we currently know and from our accessible successor knowledge. Abduction offers a presumptive solution to IP, i.e., it leads to a hypothesis H which, if an agent knew it, would together with K solve his IP; and from this fact he conjectures that H is true (Gabbay and Woods 2005, pp. 42-47). More schematically, let T indicate an agent’s cognitive target, Ris the attainment relation on T, K is the agent’s knowledge base, K* is a closely accessible successor of K, Rpresis the presumptive attainment relation on T, H is a hypothesis, K(H) is a knowledge base revised by H, C(H) is a conjecture that H, and HCis a discharge of H. Then, the schema for abduction runs as follows: 1. T! [declaration of T] 2. ¬(R(K, T)) [fact] 3. ¬(R (K*, T)) [fact] 4. Rpres(K(H), T) [fact] 5. H satisfies some conditions that assess H’s plausibility [fact] 6. Therefore, C(H) [conclusion] 7. Therefore, HC [conclusion] 8 It is important to notice that the accessible successor K* of K is an extended knowledge-base that should be available to a cognitive agent in a way that enables him to attain the cognitive target without proposing a conjecture. Suppose that you have forgotten what the concept ‘abduction’ means, but you want to explain it. Then you may extend your current knowledge-base K to the accessible successor K* by consulting the dictionary of philosophy or The Collected Papers of Charles S. Peirce. K* then attains your cognitive target, and you are no more faced with the ignorance problem. 5 The crucial fact about abduction that is implied by GW-model is that an agent who employs abduction as his response to IP does not attain his cognitive target on the basis of his knowledge K or K* (this is indicated by line 2 and 3 in the above schema). By employing abduction, he proposes H such that his knowledge K revised by H would attain T (line 4), and after evaluating H’s plausibility (line 5), he conjectures that H (line 6), and decides to act on the basis of H (line 7), e.g. he decides to test or examine H in scientific inquiry. Conjecturing that H, however, does not constitute knowledge; abduction lowers an agent’s epistemic aims with regard to T, since it does not offer knowledge that enables him to attain T, but only a conjecture that H is true. This general GW-model for abduction may serve as a point of departure for studying the nature of various kinds of abduction that respond to a variety of abductive ignorance problems. In what follows, I shall focus on one species of explanatory abduction, namely abduction defined as a presumptive solution to explanatory ignorance problems (EIP) concerning a correlation of events. In general, one may define EIP as follows: Definition 2.2. (Explanatory Ignorance Problem (EIP)) EIP exists for a cognitive agent iff he has a cognitive target that calls for explanation (E), and it can be explained neither on the basis of what he currently knows (his current knowledge base K) nor on the basis of his accessible successor knowledge K* of K. A majority of explanatory ignorance problems consists in finding an explanation for particular events, e.g., fossil evidence in biological sciences, a behaviour of the crime perpetrator in legal reasoning, physical phenomena. Much of past and current philosophical and logical theories of abduction center on finding rational rules for explanatory abduction for such EIP. The other, rather neglected, explanatory ignorance problems consist in finding an explanation not for particular events but for the correlations of events. There are many examples of interesting correlations of events that call for explanation in physics, chemistry, biological sciences, legal investigation, and in everyday reasoning. For example, there is a significant correlation between cancer and yellow fingers (Arntzenius 1990, p. 78), or a correlation between two lamps that go out suddenly in your room (Reichenbach 1956, p. 157). But, what does it mean that events are correlated? What do we mean when we say, for example, that there is a correlation between having a cancer and having yellow fingers? This question finds 6 an interesting probabilistic answer. Probabilistically, one may define (positive) correlation between events A and B as follows: Definition 2.3. ((Positive) Correlation of Events)9 The events A and B are said to be (positively) correlated if the joint probability of A and B, P(A&B), is greater than the product of the single probabilities P(A) and P(B), i.e., if P(A&B) > P(A) × P(B) This condition can be equivalently stated as follows: if two events A and B have some positive probability of occurrence, i.e., P(A) ≠ 0 and P(B) ≠ 0, then there is a positive correlation between events A and B if P(A|B) > P(A), or if P(B|A) > P(B). As it is easy to observe, the probabilistic definition of a correlation of events does not state that a correlation of events A and B means ‘An event A occurs whenever an event B occurs’. This would be too much. On the other hand, correlation does not mean a mere coincidence. It says that to find a correlation of events A and B is to observe that the occurrence of both A and B is more probable than their independent occurrence. So, we say that there is a (positive) correlation between cancer and yellow fingers if the probability of having a cancer among people with yellow fingers is greater than the probability of having a cancer in general, say in some population. When one observes a correlation between events A and B one intuitively admits that the occurrence of both events is not independent. Other words, the idea of correlation among events is the idea of probabilistic dependence. Having the definition of the correlation of events at hand, we can now define an explanatory ignorance problem concerning such correlations: Definition 2.4. (Explanatory Ignorance Problem Concerning Correlations of Events (EIP )) COR EIP exists for a cognitive agent iff his cognitive target consists in finding an explanation COR for a correlation of events (E ), and it can be explained neither on the basis of what he COR currently knows (his current knowledge base K) nor on the basis of the accessible successor knowledge K* of K. 9 It is also possible to define probabilistically a negative correlation of events. It runs as follows: The events A and B are said to be negatively correlated if the joint probability of A and B, P(A&B), is less than the product of the single probabilities P(A) and P(B), i.e., if P(A&B) < P(A) × P(B). In a simple way a negative correlation may ¬ ¬ be transformed into a positive one just by replacing A by A, or B by B. 7 What is then the explanatory abductive response to EIP ? To state precisely COR explanatory abduction for E , we must first introduce some important distinctions. First, it COR is important to recognise that explanations may come at least in two sorts: causal and non- causal explanations. A causal explanation of an event provides information about its causal history. An example of non-causal explanation is the reason-based explanation which says that an explanation provides a reason to believe the explanandum. There is a controversy in the literature about explanation as to whether we can make a theoretically significant distinction between causal and non-causal explanations. On the one hand, it is claimed that there is no such thing as non-causal explanation; the only relevant explanation is causal explanation, and all the alleged non-causal explanations are reducible to causal ones (Lewis 1986). On the other hand, it is argued that there are strong reasons for making room for both causal and non-casual explanations; causal explanation is not the whole story that can be said about explanation. For example, it is claimed that while empirical science is the kingdom of causal explanations, mathematics and other formal sciences require non-causal explanations (e.g., a mathematician may explain why Fermat’s theorem is true, but his explanation does not cite causes) (Lipton 2004; Kitcher 1989). Putting this fundamental and interesting discussion aside, I shall, rather modestly, ask: what model of explanation should we assume for the explanatory abduction that aims to account for E ? My answer is that the model should be COR causal. But this is not to say that all kinds of the explanatory abduction should be based on the causal model of explanation; again, ‘reverse’ mathematics might be the kingdom of non- causal abductive explanations. The first reason for applying the causal model to the case of abductive explanation of E is that such an abductive explanation should be asymmetric in COR the sense that the proposed explanans should explain the explanandum but cannot itself be explained by the explanandum. This reason is obvious, since abduction aims to resolve the ignorance problem by inventing conjecture which itself cannot be explained abductively by the phenomena that call for explanation. The required asymmetry in abductive mechanism can be established by characterising abductive hypotheses as causal hypotheses, since the relation of causal dependency is, at least on the predominant view, asymmetric. The second more particular reason is that causal explanations for the surprising correlation of events provide more ‘explanatory relevant’ reasons. For example, if one observes a surprising correlation, say that two lamps go out suddenly in the room, one provides a better understanding of the correlation by conjecturing a cause of the correlation than by conjecturing a law-like statements from which the correlation can be derived. 8 Second, one has to specify a model for assessing causal explanations’ plausibility (as indicated in line 5 of the GW-model). At least, two options are possible. First, one may want to assess a proposed abductive causal explanation on whether it is the best explanation from a set of possible explanations. This is, however, untenable. Such a model is susceptible to the infamous ‘bad lot’ argument, due to B. van Fraassen (1989, p.143). It may be stated as follows: suppose an abducer has invented a set of hypotheses that offer potential explanations of some phenomenon, and then he has sorted out the best explanation from the set. Selecting the best explanation from the set of possible explanations involves the belief that the possible true hypothesis is to be found in that selected lot of hypotheses. But, the best explanation may well be the best from the bad lot, say from the lot containing false explanations. One way of avoid this problem would be to insist that this model presupposes a principle of privilege which states that nature predisposed scientists to formulate the right set of possible hypotheses. This is untenable as well. The second more promising option is to assume that the assessment of causal explanation’s plausibility is contrastive. Instead of asking whether a causal explanation is the best of the possible ones, we ask whether it is more plausible than its rival; we do not ask whether it should be favoured over all possible explanations. It might occur, then, that an explanatory hypothesis H is favourable over H , but not over H . 1 2 3 Being endowed with the specifications stated above, the explanatory abduction for E runs as follows: COR Definition 2.5. (Explanatory Abduction for the Correlation of Events) Let E indicate an COR agent’s cognitive target consisting in finding a causal explanation for a correlation of events, R is the attainment relation on E , K is the agent’s knowledge base, K* is a closely COR accessible successor of K, Rpres is the presumptive attainment relation on E , H is a COR E hypothesis that explains the correlation, K(H ) is a knowledge base revised by H , C(H ) is a E E E conjecture that H , H* is H ’s rival, and HC is a discharge of H . Then the schema for E E E E E explanatory abduction for the correlation of events runs as follows: 1. E ! [declaration of E ] COR COR 2. ¬(R(K, E )) [fact] COR 3. ¬(R(K*, E )) [fact] COR 4. Rpres(K(H ), E ) [fact] E COR 5. H is more plausible than H* [fact] E E 6. Therefore, C(H ) [conclusion] E 9 7. Therefore, HC[conclusion] E One may find many significant instances of EIP in cases of scientific discoveries. COR One of the classic examples discussed in the textbooks of philosophy of science is the famous Semmelweis’ case (Hempel 1966, pp. 3-6; Lipton 2004, pp. 74-76). Ignaz Semmelweis was a Hungarian physician who discovered the cause of childbed fever working during 1844-1849 at the Vienna hospital. Semmelweis observed that a much higher percentage of women in the First Maternity Division contracted childbed fever than in the Second Division. When he was searching for the cause of the increasing mortality rate of women who contracted childbed fever, he noticed a surprising correlation between the symptoms of those who contracted childbed fever and the symptoms of his colleague’s disease. Semmelweis’ colleague Kolletschka who was performing autopsies in the First Maternity received a puncture wound from a scalpel, and died displaying the same symptoms as the victims of childbed fever. Other words, in this case the probability of the occurrence of both these events was greater than the probability to be expected if they occurred independently, i.e.: P(symptoms of childbed fever in the First Maternity Division & symptoms of Kolletschka’s disease) > P(symptoms of childbed fever in the First Maternity Division) × P(symptoms of Kolletschka’s disease) Furthermore, Semmelweis was faced with EIP , since any of the theories that had explained COR childbed fever before and during Semmelweis’ time failed to explain this specific correlation. For example, a popular in Semmelweis’ time theory which explained a childbed fever by postulating some ‘atmospheric-cosmic-telluric changes’, though providing a plausible explanation for the disease of women in the First Maternity Division, was unable to explain Kolletschka’s disease. The question that arises in cases like Semmelweis’ one is whether one can find an interesting inferential rule that enables us to make rational causal abductive explanations for explanatory targets like the surprising correlations of events. In other words, one can ask: Is there a kind of logica docens for abduction that aims to explain such correlations? In the next section, I shall propose an inferential rule for such abduction, namely Reichenbach’s Principle of the Common Cause. 10