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abduction	## 1. Abduction: The General Idea You happen to know that Tim and Harry have recently had a terrible row that ended their friendship. Now someone tells you that she just saw Tim and Harry jogging together. The best explanation for this that you can think of is that they made up. You conclude that they are friends again. One morning you enter the kitchen to find a plate and cup on the table, with breadcrumbs and a pat of butter on it, and surrounded by a jar of jam, a pack of sugar, and an empty carton of milk. You conclude that one of your house-mates got up at night to make him- or herself a midnight snack and was too tired to clear the table. This, you think, best explains the scene you are facing. To be sure, it might be that someone burgled the house and took the time to have a bite while on the job, or a house-mate might have arranged the things on the table without having a midnight snack but just to make you believe that someone had a midnight snack. But these hypotheses strike you as providing much more contrived explanations of the data than the one you infer to. Walking along the beach, you see what looks like a picture of Winston Churchill in the sand. It could be that, as in the opening pages of Hilary Putnam's book Reason, Truth, and History, (1981), what you see is actually the trace of an ant crawling on the beach. The much simpler, and therefore (you think) much better, explanation is that someone intentionally drew a picture of Churchill in the sand. That, in any case, is what you come away believing. In these examples, the conclusions do not follow logically from the premises. For instance, it does not follow logically that Tim and Harry are friends again from the premises that they had a terrible row which ended their friendship and that they have just been seen jogging together; it does not even follow, we may suppose, from all the information you have about Tim and Harry. Nor do you have any useful statistical data about friendships, terrible rows, and joggers that might warrant an inference from the information that you have about Tim and Harry to the conclusion that they are friends again, or even to the conclusion that, probably (or with a certain probability), they are friends again. What leads you to the conclusion, and what according to a considerable number of philosophers may also warrant this conclusion, is precisely the fact that Tim and Harry's being friends again would, if true, best explain the fact that they have just been seen jogging together. (The proviso that a hypothesis be true if it is to explain anything is taken as read from here on.) Similar remarks apply to the other two examples. The type of inference exhibited here is called abduction or, somewhat more commonly nowadays, Inference to the Best Explanation. ### 1.1 Deduction, induction, abduction Abduction is normally thought of as being one of three major types of inference, the other two being deduction and induction. The distinction between deduction, on the one hand, and induction and abduction, on the other hand, corresponds to the distinction between necessary and non-necessary inferences. In deductive inferences, what is inferred is necessarily true if the premises from which it is inferred are true; that is, the truth of the premises guarantees the truth of the conclusion. A familiar type of example is inferences instantiating the schema > > All As are Bs. > > > a is an A. > > > Hence, a is a B. > But not all inferences are of this variety. Consider, for instance, the inference of "John is rich" from "John lives in Chelsea" and "Most people living in Chelsea are rich." Here, the truth of the first sentence is not guaranteed (but only made likely) by the joint truth of the second and third sentences. Differently put, it is not necessarily the case that if the premises are true, then so is the conclusion: it is logically compatible with the truth of the premises that John is a member of the minority of non-rich inhabitants of Chelsea. The case is similar regarding your inference to the conclusion that Tim and Harry are friends again on the basis of the information that they have been seen jogging together. Perhaps Tim and Harry are former business partners who still had some financial matters to discuss, however much they would have liked to avoid this, and decided to combine this with their daily exercise; this is compatible with their being firmly decided never to make up. It is standard practice to group non-necessary inferences into inductive and abductive ones. Inductive inferences form a somewhat heterogeneous class, but for present purposes they may be characterized as those inferences that are based purely on statistical data, such as observed frequencies of occurrences of a particular feature in a given population. An example of such an inference would be this: > > 96 per cent of the Flemish college students speak both Dutch and > French. > > > Louise is a Flemish college student. > > > Hence, Louise speaks both Dutch and French. > However, the relevant statistical information may also be more vaguely given, as in the premise, "Most people living in Chelsea are rich." (There is much discussion about whether the conclusion of an inductive argument can be stated in purely qualitative terms or whether it should be a quantitative one--for instance, that it holds with a probability of .96 that Louise speaks both Dutch and French--or whether it can sometimes be stated in qualitative terms--for instance, if the probability that it is true is high enough--and sometimes not. On these and other issues related to induction, see Kyburg 1990 (Ch. 4). It should also be mentioned that Harman (1965) conceives induction as a special type of abduction. See also Weintraub 2013 for discussion.) The mere fact that an inference is based on statistical data is not enough to classify it as an inductive one. You may have observed many gray elephants and no non-gray ones, and infer from this that all elephants are gray, because that would provide the best explanation for why you have observed so many gray elephants and no non-gray ones. This would be an instance of an abductive inference. It suggests that the best way to distinguish between induction and abduction is this: both are ampliative, meaning that the conclusion goes beyond what is (logically) contained in the premises (which is why they are non-necessary inferences), but in abduction there is an implicit or explicit appeal to explanatory considerations, whereas in induction there is not; in induction, there is only an appeal to observed frequencies or statistics. (I emphasize "only," because in abduction there may also be an appeal to frequencies or statistics, as the example about the elephants exhibits.) A noteworthy feature of abduction, which it shares with induction but not with deduction, is that it violates monotonicity, meaning that it may be possible to infer abductively certain conclusions from a subset of a set S of premises which cannot be inferred abductively from S as a whole. For instance, adding the premise that Tim and Harry are former business partners who still have some financial matters to discuss, to the premises that they had a terrible row some time ago and that they were just seen jogging together may no longer warrant you to infer that they are friends again, even if--let us suppose--the last two premises alone do warrant that inference. The reason is that what counts as the best explanation of Tim and Harry's jogging together in light of the original premises may no longer do so once the information has been added that they are former business partners with financial matters to discuss. ### 1.2 The ubiquity of abduction The type of inference exemplified in the cases described at the beginning of this entry will strike most as entirely familiar. Philosophers as well as psychologists tend to agree that abduction is frequently employed in everyday reasoning. Sometimes our reliance on abductive reasoning is quite obvious and explicit. But in some daily practices, it may be so routine and automatic that it easily goes unnoticed. A case in point may be our trust in other people's testimony, which has been said to rest on abductive reasoning; see Harman 1965, Adler 1994, Fricker 1994, and Lipton 1998 for defenses of this claim. For instance, according to Jonathan Adler (1994, 274f), "[t]he best explanation for why the informant asserts that P is normally that ... he believes it for duly responsible reasons and ... he intends that I shall believe it too," which is why we are normally justified in trusting the informant's testimony. This may well be correct, even though in coming to trust a person's testimony one does not normally seem to be aware of any abductive reasoning going on in one's mind. Similar remarks may apply to what some hold to be a further, possibly even more fundamental, role of abduction in linguistic practice, to wit, its role in determining what a speaker means by an utterance. Specifically, it has been argued that decoding utterances is a matter of inferring the best explanation of why someone said what he or she said in the context in which the utterance was made. Even more specifically, authors working in the field of pragmatics have suggested that hearers invoke the Gricean maxims of conversation to help them work out the best explanation of a speaker's utterance whenever the semantic content of the utterance is insufficiently informative for the purposes of the conversation, or is too informative, or off-topic, or implausible, or otherwise odd or inappropriate; see, for instance, Bach and Harnish 1979 (92f), Dascal 1979 (167), and Hobbs 2004. As in cases of reliance on speaker testimony, the requisite abductive reasoning would normally seem to take place at a subconscious level. Abductive reasoning is not limited to everyday contexts. Quite the contrary: philosophers of science have argued that abduction is a cornerstone of scientific methodology; see, for instance, Boyd 1981, 1984, Harre 1986, 1988, Lipton 1991, 2004, and Psillos 1999. According to Timothy Williamson (2007), "[t]he abductive methodology is the best science provides" and Ernan McMullin (1992) even goes so far to call abduction "the inference that makes science." To illustrate the use of abduction in science, we consider two examples. At the beginning of the nineteenth century, it was discovered that the orbit of Uranus, one of the seven planets known at the time, departed from the orbit as predicted on the basis of Isaac Newton's theory of universal gravitation and the auxiliary assumption that there were no further planets in the solar system. One possible explanation was, of course, that Newton's theory is false. Given its great empirical successes for (then) more than two centuries, that did not appear to be a very good explanation. Two astronomers, John Couch Adams and Urbain Leverrier, instead suggested (independently of each other but almost simultaneously) that there was an eighth, as yet undiscovered planet in the solar system; that, they thought, provided the best explanation of Uranus' deviating orbit. Not much later, this planet, which is now known as "Neptune," was discovered. The second example concerns what is now commonly regarded to have been the discovery of the electron by the English physicist Joseph John Thomson. Thomson had conducted experiments on cathode rays in order to determine whether they are streams of charged particles. He concluded that they are indeed, reasoning as follows: > > > As the cathode rays carry a charge of negative electricity, are > deflected by an electrostatic force as if they were negatively > electrified, and are acted on by a magnetic force in just the way in > which this force would act on a negatively electrified body moving > along the path of these rays, I can see no escape from the conclusion > that they are charges of negative electricity carried by particles of > matter. (Thomson, cited in Achinstein 2001, 17) > > > The conclusion that cathode rays consist of negatively charged particles does not follow logically from the reported experimental results, nor could Thomson draw on any relevant statistical data. That nevertheless he could "see no escape from the conclusion" is, we may safely assume, because the conclusion is the best--in this case presumably even the only plausible--explanation of his results that he could think of. Many other examples of scientific uses of abduction have been discussed in the literature; see, for instance, Harre 1986, 1988 and Lipton 1991, 2004. Abduction is also said to be the predominant mode of reasoning in medical diagnosis: physicians tend to go for the hypothesis that best explains the patient's symptoms (see Josephson and Josephson (eds.) 1994, 9-12; see also Dragulinescu 2016 on abductive reasoning in the context of medicine). Last but not least, abduction plays a central role in some important philosophical debates. See Shalkowski 2010 on the place of abduction in metaphysics (also Bigelow 2010), Krzyzanowska, Wenmackers, and Douven 2014 and Douven 2016a for a possible role of abduction in the semantics of conditionals, and Williamson 2017 for an application of abduction in the philosophy of logic. Arguably, however, abduction plays its most notable philosophical role in epistemology and in the philosophy of science, where it is frequently invoked in objections to so-called underdetermination arguments. Underdetermination arguments generally start from the premise that a number of given hypotheses are empirically equivalent, which their authors take to mean that the evidence--indeed, any evidence we might ever come to possess--is unable to favor one of them over the others. From this, we are supposed to conclude that one can never be warranted in believing any particular one of the hypotheses. (This is rough, but it will do for present purposes; see Douven 2008 and Stanford 2009, for more detailed accounts of underdetermination arguments.) A famous instance of this type of argument is the Cartesian argument for global skepticism, according to which the hypothesis that reality is more or less the way we customarily deem it to be is empirically equivalent to a variety of so-called skeptical hypotheses (such as that we are beguiled by an evil demon, or that we are brains in a vat, connected to a supercomputer; see, e.g., Folina 2016). Similar arguments have been given in support of scientific antirealism, according to which it will never be warranted for us to choose between empirically equivalent rivals concerning what underlies the observable part of reality (van Fraassen 1980). Responses to these arguments typically point to the fact that the notion of empirical equivalence at play unduly neglects explanatory considerations, for instance, by defining the notion strictly in terms of hypotheses' making the same predictions. Those responding then argue that even if some hypotheses make exactly the same predictions, one of them may still be a better explanation of the phenomena predicted. Thus, if explanatory considerations have a role in determining which inferences we are licensed to make--as according to defenders of abduction they have--then we might still be warranted in believing in the truth (or probable truth, or some such, depending--as will be seen below--on the version of abduction one assumes) of one of a number of hypotheses that all make the same predictions. Following Bertrand Russell (1912, Ch. 2), many epistemologists have invoked abduction in arguing against Cartesian skepticism, their key claim being that even though, by construction, the skeptical hypotheses make the same predictions as the hypothesis that reality is more or less the way we ordinarily take it to be, they are not equally good explanations of what they predict; in particular, the skeptical hypotheses have been said to be considerably less simple than the "ordinary world" hypothesis. See, among many others, Harman 1973 (Chs. 8 and 11), Goldman 1988 (205), Moser 1989 (161), and Vogel 1990, 2005; see Pargetter 1984 for an abductive response specifically to skepticism regarding other minds. Similarly, philosophers of science have argued that we are warranted to believe in Special Relativity Theory as opposed to Lorentz's version of the aether theory. For even though these theories make the same predictions, the former is explanatorily superior to the latter. (Most arguments that have been given for this claim come down to the contention that Special Relativity Theory is ontologically more parsimonious than its competitor, which postulates the existence of an aether. See Janssen 2002 for an excellent discussion of the various reasons philosophers of science have adduced for preferring Einstein's theory to Lorentz's.) ## 2. Explicating Abduction Precise statements of what abduction amounts to are rare in the literature on abduction. (Peirce did propose an at least fairly precise statement; but, as explained in the supplement to this entry, it does not capture what most nowadays understand by abduction.) Its core idea is often said to be that explanatory considerations have confirmation-theoretic import, or that explanatory success is a (not necessarily unfailing) mark of truth. Clearly, however, these formulations are slogans at best, and it takes little effort to see that they can be cashed out in a great variety of prima facie plausible ways. Here we will consider a number of such possible explications, starting with what one might term the "textbook version of abduction," which, as will be seen, is manifestly defective, and then going on to consider various possible refinements of it. What those versions have in common--unsurprisingly--is that they are all inference rules, requiring premises encompassing explanatory considerations and yielding a conclusion that makes some statement about the truth of a hypothesis. The differences concern the premises that are required, or what exactly we are allowed to infer from them (or both). In textbooks on epistemology or the philosophy of science, one often encounters something like the following as a formulation of abduction: ABD1 Given evidence E and candidate explanations H1,..., Hn of E, infer the truth of that Hi which best explains E. An observation that is frequently made about this rule, and that points to a potential problem for it, is that it presupposes the notions of candidate explanation and best explanation, neither of which has a straightforward interpretation. While some still hope that the former can be spelled out in purely logical, or at least purely formal, terms, it is often said that the latter must appeal to the so-called theoretical virtues, like simplicity, generality, and coherence with well-established theories; the best explanation would then be the hypothesis which, on balance, does best with respect to these virtues. (See, for instance, Thagard 1978 and McMullin 1996.) The problem is that none of the said virtues is presently particularly well understood. (Giere, in Callebaut (ed.) 1993 (232), even makes the radical claim that the theoretical virtues lack real content and play no more than a rhetorical role in science. In view of recent formal work both on simplicity and on coherence--for instance, Forster and Sober 1994, Li and Vitanyi 1997, and Sober 2015, on simplicity and Bovens and Hartmann 2003 and Olsson 2005, on coherence--the first part of this claim has become hard to maintain; also, Schupbach and Sprenger (2011) present an account of explanatory goodness directly in probabilistic terms. Psychological evidence casts doubt on the second part of the claim; see, for instance, Lombrozo 2007, on the role of simplicity in people's assessments of explanatory goodness and Koslowski et al. 2008, on the role of coherence with background knowledge in those assessments.) Furthermore, many of those who think ABD1 is headed along the right lines believe that it is too strong. Some think that abduction warrants an inference only to the probable truth of the best explanation, others that it warrants an inference only to the approximate truth of the best explanation, and still others that it warrants an inference only to the probable approximate truth. The real problem with ABD1 runs deeper than this, however. Because abduction is ampliative--as explained earlier--it will not be a sound rule of inference in the strict logical sense, however abduction is explicated exactly. It can still be reliable in that it mostly leads to a true conclusion whenever the premises are true. An obvious necessary condition for ABD1 to be reliable in this sense is that, mostly, when it is true that H best explains E, and E is true, then H is true as well (or H is approximately true, or probably true, or probably approximately true). But this would not be enough for ABD1 to be reliable. For ABD1 takes as its premise only that some hypothesis is the best explanation of the evidence as compared to other hypotheses in a given set. Thus, if the rule is to be reliable, it must hold that, at least typically, the best explanation relative to the set of hypotheses that we consider would also come out as being best in comparison with any other hypotheses that we might have conceived (but for lack of time or ingenuity, or for some other reason, did not conceive). In other words, it must hold that at least typically the absolutely best explanation of the evidence is to be found among the candidate explanations we have come up with, for else ABD1 may well lead us to believe "the best of a bad lot" (van Fraassen 1989, 143). How reasonable is it to suppose that this extra requirement is usually fulfilled? Not at all, presumably. To believe otherwise, we must assume some sort of privilege on our part to the effect that when we consider possible explanations of the data, we are somehow predisposed to hit, inter alia, upon the absolutely best explanation of those data. After all, hardly ever will we have considered, or will it even be possible to consider, all potential explanations. As van Fraassen (1989, 144) points out, it is a priori rather implausible to hold that we are thus privileged. In response to this, one might argue that the challenge to show that the best explanation is always or mostly among the hypotheses considered can be met without having to assume some form of privilege (see Schupbach 2014 for a different response, and see Dellsen 2017 for discussion). For given the hypotheses we have managed to come up with, we can always generate a set of hypotheses which jointly exhaust logical space. Suppose H1,...,Hn are the candidate explanations we have so far been able to conceive. Then simply define Hn+1 := !H1 [?] ... [?] !Hn and add this new hypothesis as a further candidate explanation to the ones we already have. Obviously, the set {H1,...,Hn+1} is exhaustive, in that one of its elements must be true. Following this in itself simple procedure would seem enough to make sure that we never miss out on the absolutely best explanation. (See Lipton 1993, for a proposal along these lines.) Alas, there is a catch. For even though there may be many hypotheses Hj that imply Hn+1 and, had they been formulated, would have been evaluated as being a better explanation for the data than the best explanation among the candidate explanations we started out with, Hn+1 itself will in general be hardly informative; in fact, in general it will not even be clear what its empirical consequences are. Suppose, for instance, we have as competing explanations Special Relativity Theory and Lorentz's version of the aether theory. Then, following the above proposal, we may add to our candidate explanations that neither of these two theories is true. But surely this further hypothesis will be ranked quite low qua explanation--if it will be ranked at all, which seems doubtful, given that it is wholly unclear what its empirical consequences are. This is not to say that the suggested procedure may never work. The point is that in general it will give little assurance that the best explanation is among the candidate explanations we consider. A more promising response to the above "argument of the bad lot" begins with the observation that the argument capitalizes on a peculiar asymmetry or incongruence in ABD1. The rule gives license to an absolute conclusion--that a given hypothesis is true--on the basis of a comparative premise, namely, that that particular hypothesis is the best explanation of the evidence relative to the other hypotheses available (see Kuipers 2000, 171). This incongruence is not avoided by replacing "truth" with "probable truth" or "approximate truth." In order to avoid it, one has two general options. The first option is to modify the rule so as to have it require an absolute premise. For instance, following Alan Musgrave (1988) or Peter Lipton (1993), one may require the hypothesis whose truth is inferred to be not only the best of the available potential explanations, but also to be satisfactory (Musgrave) or good enough (Lipton), yielding the following variant of ABD1: ABD2 Given evidence E and candidate explanations H1,..., Hn of E, infer the truth of that Hi which explains E best, provided Hi is satisfactory/good enough qua explanation. Needless to say, ABD2 needs supplementing by a criterion for the satisfactoriness of explanations, or their being good enough, which, however, we are still lacking. Secondly, one can formulate a symmetric or congruous version of abduction by having it sanction, given a comparative premise, only a comparative conclusion; this option, too, can in turn be realized in more than one way. Here is one way to do it, which has been proposed and defended in the work of Theo Kuipers (e.g., Kuipers 1984, 1992, 2000). ABD3 Given evidence E and candidate explanations H1,..., Hn of E, if Hi explains E better than any of the other hypotheses, infer that Hi is closer to the truth than any of the other hypotheses. Clearly, ABD3 requires an account of closeness to the truth, but many such accounts are on offer today (see, e.g., Niiniluoto 1998). One noteworthy feature of the congruous versions of abduction considered here is that they do not rely on the assumption of an implausible privilege on the reasoner's part that, we saw, ABD1 implicitly relies on. Another is that if one can be certain that, however many candidate explanations for the data one may have missed, none equals the best of those one has thought of, then the congruous versions license exactly the same inference as ABD1 does (supposing that one would not be certain that no potential explanation is as good as the best explanation one has thought of if the latter is not even satisfactory or sufficiently good). As mentioned, there is widespread agreement that people frequently rely on abductive reasoning. Which of the above rules exactly is it that people rely on? Or might it be still some further rule that they rely on? Or might they in some contexts rely on one version, and in others on another (Douven 2017, forthcoming)? Philosophical argumentation is unable to answer these questions. In recent years, experimental psychologists have started paying attention to the role humans give to explanatory considerations in reasoning. For instance, Tania Lombrozo and Nicholas Gwynne (2014) report experiments showing that how a property of a given class of things is explained to us--whether mechanistically, by reference to parts and processes, or functionally, by reference to functions and purposes--matters to how likely we are to generalise that property to other classes of things (see also Sloman 1994 and Williams and Lombrozo 2010). And Igor Douven and Jonah Schupbach (2015a), (2015b) present experimental evidence to the effect that people's probability updates tend to be influenced by explanatory considerations in ways that makes them deviate from strictly Bayesian updates (see below). Douven (2016b) shows that, in the aforementioned experiments, participants who gave more weight to explanatory considerations tended to be more accurate, as determined in terms of a standard scoring rule. (See Lombrozo 2012 and 2016 for useful overviews of recent experimental work relevant to explanation and inference.) Douven and Patricia Mirabile (2018) found some evidence indicating that people rely on something like ABD2, at least in some contexts, but for the most part, empirical work on the above-mentioned questions is lacking. With respect to the normative question of which of the previously stated rules we ought to rely on (if we ought to rely on any form of abduction), where philosophical argumentation should be able to help, the situation is hardly any better. In view of the argument of the bad lot, ABD1 does not look very good. Other arguments against abduction are claimed to be independent of the exact explication of the rule; below, these arguments will be found wanting. On the other hand, arguments that have been given in favor of abduction--some of which will also be discussed below--do not discern between specific versions. So, supposing people do indeed commonly rely on abduction, it must be considered an open question as to which version(s) of abduction they rely on. Equally, supposing it is rational for people to rely on abduction, it must be considered an open question as to which version, or perhaps versions, of abduction they ought to, or are at least permitted to, rely on. ## 3. The Status of Abduction Even if it is true that we routinely rely on abductive reasoning, it may still be asked whether this practice is rational. For instance, experimental studies have shown that when people are able to think of an explanation for some possible event, they tend to overestimate the likelihood that this event will actually occur. (See Koehler 1991, for a survey of some of these studies; see also Brem and Rips 2000.) More telling still, Lombrozo (2007) shows that, in some situations, people tend to grossly overrate the probability of simpler explanations compared to more complicated ones. Although these studies are not directly concerned with abduction in any of the forms discussed so far, they nevertheless suggest that taking into account explanatory considerations in one's reasoning may not always be for the better. (It is to be noted that Lombrozo's experiments are directly concerned with some proposals that have been made for explicating abduction in a Bayesian framework; see Section 4.) However, the most pertinent remarks about the normative status of abduction are so far to be found in the philosophical literature. This section discusses the main criticisms that have been levelled against abduction, as well as the strongest arguments that have been given in its defense. ### 3.1 Criticisms We have already encountered the so-called argument of the bad lot, which, we saw, is valid as a criticism of ABD1 but powerless against various (what we called) congruous rules of abduction. We here consider two objections that are meant to be more general. The first even purports to challenge the core idea underlying abduction; the second is not quite as general, but it is still meant to undermine a broad class of candidate explications of abduction. Both objections are due to Bas van Fraassen. The first objection has as a premise that it is part of the meaning of "explanation" that if one theory is more explanatory than another, the former must be more informative than the latter (see, e.g., van Fraassen 1983, Sect. 2). The alleged problem then is that it is "an elementary logical point that a more informative theory cannot be more likely to be true [and thus] attempts to describe inductive or evidential support through features that require information (such as 'Inference to the Best Explanation') must either contradict themselves or equivocate" (van Fraassen 1989, 192). The elementary logical point is supposed to be "most [obvious] ... in the paradigm case in which one theory is an extension of another: clearly the extension has more ways of being false" (van Fraassen 1985, 280). It is important to note, however, that in any other kind of case than the "paradigm" one, the putative elementary point is not obvious at all. For instance, it is entirely unclear in what sense Special Relativity Theory "has more ways of being false" than Lorentz's version of the aether theory, given that they make the same predictions. And yet the former is generally regarded as being superior, qua explanation, to the latter. (If van Fraassen were to object that the former is not really more informative than the latter, or at any rate not more informative in the appropriate sense--whatever that is--then we should certainly refuse to grant the premise that in order to be more explanatory a theory must be more informative.) The second objection, proffered in van Fraassen 1989 (Ch. 6), is levelled at probabilistic versions of abduction. The objection is that such rules must either amount to Bayes' rule, and thus be redundant, or be at variance with it but then, on the grounds of Lewis' dynamic Dutch book argument (as reported in Teller 1973), be probabilistically incoherent, meaning that they may lead one to assess as fair a number of bets which together ensure a financial loss, come what may; and, van Fraassen argues, it would be irrational to follow a rule that has this feature. However, this objection fares no better than the first. For one thing, as Patrick Maher (1992) and Brian Skyrms (1993) have pointed out, a loss in one respect may be outweighed by a benefit in another. It might be, for instance, that some probabilistic version of abduction does much better, at least in our world, than Bayes' rule, in that, on average, it approaches the truth faster in the sense that it is faster in assigning a high probability (understood as probability above a certain threshold value) to the true hypothesis (see Douven 2013, 2020, and Douven and Wenmackers 2017; see Climenhaga 2017 for discussion). If it does, then following that rule instead of Bayes' rule may have advantages which perhaps are not so readily expressed in terms of money yet which should arguably be taken into account when deciding which rule to go by. It is, in short, not so clear whether following a probabilistically incoherent rule must be irrational. For another thing, Douven (1999) argues that the question of whether a probabilistic rule is coherent is not one that can be settled independently of considering which other epistemic and decision-theoretic rules are deployed along with it; coherence should be understood as a property of packages of both epistemic and decision-theoretic rules, not of epistemic rules (such as probabilistic rules for belief change) in isolation. In the same paper, a coherent package of rules is described which includes a probabilistic version of abduction. (See Kvanvig 1994, Harman 1997, Leplin 1997, Niiniluoto 1999, and Okasha 2000, for different responses to van Fraassen's critique of probabilistic versions of abduction.) ### 3.2 Defenses Hardly anyone nowadays would want to subscribe to a conception of truth that posits a necessary connection between explanatory force and truth--for instance, because it stipulates explanatory superiority to be necessary for truth. As a result, a priori defenses of abduction seem out of the question. Indeed, all defenses that have been given so far are of an empirical nature in that they appeal to data that supposedly support the claim that (in some form) abduction is a reliable rule of inference. The best-known argument of this sort was developed by Richard Boyd in the 1980s (see Boyd 1981, 1984, 1985). It starts by underlining the theory-dependency of scientific methodology, which comprises methods for designing experiments, for assessing data, for choosing between rival hypotheses, and so on. For instance, in considering possible confounding factors from which an experimental setup has to be shielded, scientists draw heavily on already accepted theories. The argument next calls attention to the apparent reliability of this methodology, which, after all, has yielded, and continues to yield, impressively accurate theories. In particular, by relying on this methodology, scientists have for some time now been able to find ever more instrumentally adequate theories. Boyd then argues that the reliability of scientific methodology is best explained by assuming that the theories on which it relies are at least approximately true. From this and from the fact that these theories were mostly arrived at by abductive reasoning, he concludes that abduction must be a reliable rule of inference. Critics have accused this argument of being circular. Specifically, it has been said that the argument rests on a premise--that scientific methodology is informed by approximately true background theories--which in turn rests on an inference to the best explanation for its plausibility. And the reliability of this type of inference is precisely what is at stake. (See, for instance, Laudan 1981 and Fine 1984.) To this, Stathis Psillos (1999, Ch. 4) has responded by invoking a distinction credited to Richard Braithwaite, to wit, the distinction between premise-circularity and rule-circularity. An argument is premise-circular if its conclusion is amongst its premises. A rule-circular argument, by contrast, is an argument of which the conclusion asserts something about an inferential rule that is used in the very same argument. As Psillos urges, Boyd's argument is rule-circular, but not premise-circular, and rule-circular arguments, Psillos contends, need not be viciously circular (even though a premise-circular argument is always viciously circular). To be more precise, in his view, an argument for the reliability of a given rule R that essentially relies on R as an inferential principle is not vicious, provided that the use of R does not guarantee a positive conclusion about R's reliability. Psillos claims that in Boyd's argument, this proviso is met. For while Boyd concludes that the background theories on which scientific methodology relies are approximately true on the basis of an abductive step, the use of abduction itself does not guarantee the truth of his conclusion. After all, granting the use of abduction does nothing to ensure that the best explanation of the success of scientific methodology is the approximate truth of the relevant background theories. Thus, Psillos concludes, Boyd's argument still stands. Even if the use of abduction in Boyd's argument might have led to the conclusion that abduction is not reliable, one may still have worries about the argument's being rule-circular. For suppose that some scientific community relied not on abduction but on a rule that we may dub "Inference to the Worst Explanation" (IWE), a rule that sanctions inferring to the worst explanation of the available data. We may safely assume that the use of this rule mostly would lead to the adoption of very unsuccessful theories. Nevertheless, the said community might justify its use of IWE by dint of the following reasoning: "Scientific theories tend to be hugely unsuccessful. These theories were arrived at by application of IWE. That IWE is a reliable rule of inference--that is, a rule of inference mostly leading from true premises to true conclusions--is surely the worst explanation of the fact that our theories are so unsuccessful. Hence, by application of IWE, we may conclude that IWE is a reliable rule of inference." While this would be an utterly absurd conclusion, the argument leading up to it cannot be convicted of being viciously circular anymore than Boyd's argument for the reliability of abduction can (if Psillos is right). It would appear, then, that there must be something else amiss with rule-circularity. It is fair to note that for Psillos, the fact that a rule-circular argument does not guarantee a positive conclusion about the rule at issue is not sufficient for such an argument to be valid. A further necessary condition is "that one should not have reason to doubt the reliability of the rule--that there is nothing currently available which can make one distrust the rule" (Psillos 1999, 85). And there is plenty of reason to doubt the reliability of IWE; in fact, the above argument supposes that it is unreliable. Two questions arise, however. First, why should we accept the additional condition? Second, do we really have no reason to doubt the reliability of abduction? Certainly some of the abductive inferences we make lead us to accept falsehoods. How many falsehoods may we accept on the basis of abduction before we can legitimately begin to distrust this rule? No clear answers have been given to these questions. Be this as it may, even if rule-circularity is neither vicious nor otherwise problematic, one may still wonder how Boyd's argument is to convert a critic of abduction, given that it relies on abduction. But Psillos makes it clear that the point of philosophical argumentation is not always, and in any case need not be, to convince an opponent of one's position. Sometimes the point is, more modestly, to assure or reassure oneself that the position one endorses, or is tempted to endorse, is correct. In the case at hand, we need not think of Boyd's argument as an attempt to convince the opponent of abduction of its reliability. Rather, it may be thought of as justifying the rule from within the perspective of someone who is already sympathetic towards abduction; see Psillos 1999 (89). There have also been attempts to argue for abduction in a more straightforward fashion, to wit, via enumerative induction. The common idea of these attempts is that every newly recorded successful application of abduction--like the discovery of Neptune, whose existence had been postulated on explanatory grounds (see Section 1.2)--adds further support to the hypothesis that abduction is a reliable rule of inference, in the way in which every newly observed black raven adds some support to the hypothesis that all ravens are black. Because it does not involve abductive reasoning, this type of argument is more likely to also appeal to disbelievers in abduction. See Harre 1986, 1988, Bird 1998 (160), Kitcher 2001, and Douven 2002 for suggestions along these lines. ## 4. Abduction versus Bayesian Confirmation Theory In the past decade, Bayesian confirmation theory has firmly established itself as the dominant view on confirmation; currently one cannot very well discuss a confirmation-theoretic issue without making clear whether, and if so why, one's position on that issue deviates from standard Bayesian thinking. Abduction, in whichever version, assigns a confirmation-theoretic role to explanation: explanatory considerations contribute to making some hypotheses more credible, and others less so. By contrast, Bayesian confirmation theory makes no reference at all to the concept of explanation. Does this imply that abduction is at loggerheads with the prevailing doctrine in confirmation theory? Several authors have recently argued that not only is abduction compatible with Bayesianism, it is a much-needed supplement to it. The so far fullest defense of this view has been given by Lipton (2004, Ch. 7); as he puts it, Bayesians should also be "explanationists" (his name for the advocates of abduction). (For other defenses, see Okasha 2000, McGrew 2003, Weisberg 2009, and Poston 2014, Ch. 7; for discussion, see Roche and Sober 2013, 2014, and McCain and Poston 2014.) This requires some clarification. For what could it mean for a Bayesian to be an explanationist? In order to apply Bayes' rule and determine the probability for H after learning E, the Bayesian agent will have to determine the probability of H conditional on E. For that, he needs to assign unconditional probabilities to H and E as well as a probability to E given H; the former two are mostly called "prior probabilities" (or just "priors") of, respectively, H and E, the latter the "likelihood" of H on E. (This is the official Bayesian story. Not all of those who sympathize with Bayesianism adhere to that story. For instance, according to some it is more reasonable to think that conditional probabilities are basic and that we derive unconditional probabilities from them; see Hajek 2003, and references therein.) How is the Bayesian to determine these values? As is well known, probability theory gives us more probabilities once we have some; it does not give us probabilities from scratch. Of course, when H implies E or the negation of E, or when H is a statistical hypothesis that bestows a certain chance on E, then the likelihood follows "analytically." (This claim assumes some version of Lewis' (1980) Principal Principle, and it is controversial whether or not this principle is analytic; hence the scare quotes.) But this is not always the case, and even if it were, there would still be the question of how to determine the priors. This is where, according to Lipton, abduction comes in. In his proposal, Bayesians ought to determine their prior probabilities and, if applicable, likelihoods on the basis of explanatory considerations. Exactly how are explanatory considerations to guide one's choice of priors? The answer to this question is not as simple as one might at first think. Suppose you are considering what priors to assign to a collection of rival hypotheses and you wish to follow Lipton's suggestion. How are you to do this? An obvious--though still somewhat vague--answer may seem to go like this: Whatever exact priors you are going to assign, you should assign a higher one to the hypothesis that explains the available data best than to any of its rivals (provided there is a best explanation). Note, though, that your neighbor, who is a Bayesian but thinks confirmation has nothing to do with explanation, may well assign a prior to the best explanation that is even higher than the one you assign to that hypothesis. In fact, his priors for best explanations may even be consistently higher than yours, not because in his view explanation is somehow related to confirmation--it is not, he thinks--but, well, just because. In this context, "just because" is a perfectly legitimate reason, because any reason for fixing one's priors counts as legitimate by Bayesian standards. According to mainstream Bayesian epistemology, priors (and sometimes likelihoods) are up for grabs, meaning that one assignment of priors is as good as another, provided both are coherent (that is, they obey the axioms of probability theory). Lipton's recommendation to the Bayesian to be an explanationist is meant to be entirely general. But what should your neighbor do differently if he wants to follow the recommendation? Should he give the same prior to any best explanation that you, his explanationist neighbor, give to it, that is, lower his priors for best explanations? Or rather should he give even higher priors to best explanations than those he already gives? Perhaps Lipton's proposal is not intended to address those who already assign highest priors to best explanations, even if they do so on grounds that have nothing to do with explanation. The idea might be that, as long as one does assign highest priors to those hypotheses, everything is fine, or at least finer than if one does not do so, regardless of one's reasons for assigning those priors. The answer to the question of how explanatory considerations are to guide one's choice of priors would then presumably be that one ought to assign a higher prior to the best explanation than to its rivals, if this is not what one already does. If it is, one should just keep doing what one is doing. (As an aside, it should be noticed that, according to standard Bayesian usage, the term "priors" does not necessarily refer to the degrees of belief a person assigns before the receipt of any data. If there are already data in, then, clearly, one may assign higher priors to hypotheses that best explain the then-available data. However, one can sensibly speak of "best explanations" even before any data are known. For example, one hypothesis may be judged to be a better explanation than any of its rivals because the former requires less complicated mathematics, or because it is stated in terms of familiar concepts only, which is not true of the others. More generally, such judgments may be based on what Kosso (1992, 30) calls internal features of hypotheses or theories, that is, features that "can be evaluated without having to observe the world.") A more interesting answer to the above question of how explanation is to guide one's choice of priors has been given by Jonathan Weisberg (2009). We said that mainstream Bayesians regard one assignment of prior probabilities as being as good as any other. So-called objective Bayesians do not do so, however. These Bayesians think priors must obey principles beyond the probability axioms in order to be admissible. Objective Bayesians are divided among themselves over exactly which further principles are to be obeyed, but at least for a while they agreed that the Principle of Indifference is among them. Roughly stated, this principle counsels that, absent a reason to the contrary, we give equal priors to competing hypotheses. As is well known, however, in its original form the Principle of Indifference may lead to inconsistent assignments of probabilities and so can hardly be advertised as a principle of rationality. The problem is that there are typically various ways to partition logical space that appear plausible given the problem at hand, and that not all of them lead to the same prior probability assignment, even assuming the Principle of Indifference. Weisberg's proposal amounts to the claim that explanatory considerations may favor some of those partitions over others. Perhaps we will not always end up with a unique partition to which the Principle of Indifference is to be applied, but it would already be progress if we ended up with only a handful of partitions. For we could then still arrive in a motivated way at our prior probabilities, by proceeding in two steps, namely, by first applying the Principle of Indifference to the partitions separately, thereby possibly obtaining different assignments of priors, and by then taking a weighted average of the thus obtained priors, where the weights, too, are to depend on explanatory considerations. The result would again be a probability function--the uniquely correct prior probability function, according to Weisberg. The proposal is intriguing as far as it goes but, as Weisberg admits, in its current form, it does not go very far. For one thing, it is unclear how exactly explanatory considerations are to determine the weights required for the second step of the proposal. For another, it may be idle to hope that taking explanatory considerations into account will in general leave us with a manageable set of partitions, or that, even if it does, this will not be due merely to the fact that we are overlooking a great many prima facie plausible ways of partitioning logical space to begin with. (The latter point echoes the argument of the bad lot, of course.) Another suggestion about the connection between abduction and Bayesian reasoning--to be found in Okasha 2000, McGrew 2003, Lipton 2004 (Ch. 7), and Dellsen 2018--is that the explanatory considerations may serve as a heuristic to determine, even if only roughly, priors and likelihoods in cases in which we would otherwise be clueless and could do no better than guessing. This suggestion is sensitive to the well-recognized fact that we are not always able to assign a prior to every hypothesis of interest, or to say how probable a given piece of evidence is conditional on a given hypothesis. Consideration of that hypothesis' explanatory power might then help us to figure out, if perhaps only within certain bounds, what prior to assign to it, or what likelihood to assign to it on the given evidence. Bayesians, especially the more modest ones, might want to retort that the Bayesian procedure is to be followed if, and only if, either (a) priors and likelihoods can be determined with some precision and objectivity, or (b) likelihoods can be determined with some precision and priors can be expected to "wash out" as more and more evidence accumulates, or (c) priors and likelihoods can both be expected to wash out. In the remaining cases--they might say--we should simply refrain from applying Bayesian reasoning. A fortiori, then, there is no need for an abduction-enhanced Bayesianism in these cases. And some incontrovertible mathematical results indicate that, in the cases that fall under (a), (b), or (c), our probabilities will converge to the truth anyhow. Consequently, in those cases there is no need for the kind of abductive heuristics that the above-mentioned authors suggest, either. (Weisberg 2009, Sect. 3.2, raises similar concerns.) Psillos (2000) proposes yet another way in which abduction might supplement Bayesian confirmation theory, one that is very much in the spirit of Peirce's conception of abduction. The idea is that abduction may assist us in selecting plausible candidates for testing, where the actual testing then is to follow Bayesian lines. However, Psillos concedes (2004) that this proposal assigns a role to abduction that will strike committed explanationists as being too limited. Finally, a possibility that has so far not been considered in the literature is that abduction and Bayesianism do not so much work in tandem--as they do on the above proposals--as operate in different modes of reasoning; the Bayesian and the explanationist are characters that feature in different plays, so to speak. It is widely accepted that sometimes we speak and think about our beliefs in a categorical manner, while at other times we speak and think about them in a graded way. It is far from clear how these different ways of speaking and thinking about beliefs--the epistemology of belief and the epistemology of degrees of belief, to use Richard Foley's (1992) terminology--are related to one another. In fact, it is an open question whether there is any straightforward connection between the two, or even whether there is a connection at all. Be that as it may, given that the distinction is undeniable, it is a plausible suggestion that, just as there are different ways of talking and thinking about beliefs, there are different ways of talking and thinking about the revision of beliefs. In particular, abduction could well have its home in the epistemology of belief, and be called upon whenever we reason about our beliefs in a categorical mode, while at the same time Bayes' rule could have its home in the epistemology of degrees of belief. Hard-nosed Bayesians may insist that whatever reasoning goes on in the categorical mode must eventually be justifiable in Bayesian terms, but this presupposes the existence of bridge principles connecting the epistemology of belief with the epistemology of degrees of belief--and, as mentioned, whether such principles exist is presently unclear.
abelard	## 1. Life and Works ### 1.1 Life Abelard's life is relatively well-known. In addition to events chronicled in the public record, his inner life is revealed in his autobiographical letter Historia calamitatum ["The Story of My Troubles"] and in his famous correspondence with Heloise. Abelard was born into the lesser nobility around 1079 in Le Pallet, a small town in Brittany near Nantes. He received early training in letters, and took to his studies with enthusiasm; his later writings show familiarity with Cicero, Horace, Juvenal, Ovid, Lucan, Seneca, and Vergil. Abelard eventually renounced his inheritance, including its attendant knighthood, to pursue philosophy. He did so by travelling to study with well-known philosophers, most notably Roscelin and William of Champeaux. During the first years of the twelfth century, Abelard felt confident enough to set himself up as a lecturer, first at Melun and then at Corbeil, competing mainly with William of Champeaux (Paris) for students and reputation. The strain proved too much--Abelard's health failed, and he returned to Brittany for several years. Abelard returned to Paris sometime between 1108 and 1113 with his health restored and his ambition intact. He attended William of Champeaux's lectures, and entered into debate with William over the problem of universals. According to Abelard's report, he bested his teacher in debate, and gained his reputation as a dialectician of note, teaching at several schools. Around 1113 Abelard decided to study theology; he sought out the most eminent teacher of theology of his day, Anselm of Laon (not to be confused with Anselm of Canterbury), and became his student. It was not a good choice: Anselm's traditional methods did not appeal to Abelard, and, after some back-and-forth, Abelard returned to Paris to continue on his own. It would be the last time he studied with anyone. Upon returning to Paris, Abelard became scholar-in-residence at Notre Dame, a position he held until his romantic entanglement with Heloise led to his castration, at which point he entered the Benedictine monastery of Saint Denis and Heloise entered the convent of Argenteuil. After his recovery, Abelard resumed teaching at a nearby priory, primarily on theology and in particular on the Trinity. His method of philosophical analysis was seen as a direct challenge to more traditional approaches, and a synod, convened in Soissons to examine Abelard's writings, condemned them and required Abelard to make a public avowal of faith, an experience he found humiliating; shortly afterwards he was allowed to settle in a wild and uninhabited section of land, to devote himself to contemplation. It was not to be. Abelard says that poverty forced him to resume teaching. He and the students who flocked to him in droves constructed an oratory named the Paraclete, where he continued to write, teach, and research. This idyll came to an end around 1126, when Abelard accepted an invitation to become abbot of the monastery of Saint Gildas de Rhuys in Brittany; shortly afterwards he handed over the Paraclete to Heloise and the other nuns, whose convent had been expropriated. Abelard found the monks of Saint Gildas difficult and obstructive--even dangerous--and he claims that there were several attempts on his life while in residence. During this period he wrote the Historia calamitatum and corresponded with Heloise. By the mid-1130s Abelard was given permission to return to Paris (retaining his rank as abbot) and to teach in the schools on the Mont Ste.-Genevieve. It was during this time that his theological treatises were brought to the attention of Bernard of Clairvaux, who objected to some of Abelard's conclusions as well as to his approach to matters of faith. After some inconclusive attempts to resolve their differences, Abelard asked the archbishop of Sens to arrange a public dispute between himself and Bernard on 3 June 1140, to settle their disagreements. Bernard initially refused the invitation on the grounds that one should not debate matters of faith, but then accepted it and, unknown to Abelard, arranged to convene another commission of enquiry to review Abelard's works on suspicion of heresy. When Abelard discovered that there was no debate but instead a kangaroo court, he refused to take part, announcing his intention to appeal to the Pope directly. He walked out of the proceedings and began travelling to Rome. The Council condemned nineteen propositions it claimed to find in his works and adjourned. Bernard launched a successful campaign petitioning the Papal Court before Abelard was out of France; a letter from the Pope upholding the decision of the Council of Soissons reached Abelard while he was at Cluny; Abelard was ordered to silence. By all accounts Abelard complied immediately, even meeting peacefully with Bernard in reconciliation. Peter the Venerable, the abbot of Cluny, wrote to the Pope about these matters, and the Pope lifted Abelard's sentence. Abelard remained under the protection of Peter the Venerable first at Cluny, then at St. Marcel, as his health gradually deteriorated. Abelard died on 21 April 1142. His body was interred at the Paraclete, and today is (with Heloise) in Pere Lachaise cemetery in Paris. Abelard's students were active as kings, philosophers, poets, politicians, theologians, and monks; they include three popes and several heads of state. Explicit references to Abelard's thinking in the later Middle Ages are few, likely because of the cloud cast by the verdict of the Council of Soissons, but it is clear that he had a seminal influence on twelfth-century philosophy and perhaps on later fourteenth-century speculation as well. ### 1.2 Works The dates of composition and even the number of Abelard's writings remain largely obscure and a matter of controversy among scholars. One reason for this is that Abelard constantly revised and rewrote, so that several distinct versions of a given work might be in circulation; another reason is that several of his writings might represent 'teaching notes' constantly evolving in courses and seminars. Hence it is not clear that 'date of composition' is a well-defined notion when applied to the body of Abelard's work that we now possess. Apart from Abelard's correspondence, which can be dated with relative precision, Abelard's extant work falls into three categories. The first category consists of Abelard's works on dialectic--works concerned with logic, philosophy of language, metaphysics, and philosophy of mind. His two masterworks are: * Logica 'ingredientibus', "Logic" (starting with the words 'To those beginning...'). * Dialectica, "Dialectic." Both of these works follow the pattern of the logica vetus, the "old logic" inherited from antiquity: Porphyry's introduction to Aristotle, the Isagoge; Aristotle's Categories and On Interpretation; Boethius's Introduction to the Categorical Syllogism, Categorical Syllogisms, Hypothetical Syllogisms, On Topical Difference, and On Division. Abelard's works cover the material presented in the old logic, though they do so in different ways. His Logica 'ingredientibus' is a close textual commentary on the old logic, though only some of it survives, namely the commentaries on the Isagoge, the Categories, On Interpretation, and On Topical Differences; his Dialectica is an independent treatise on dialectic that treats the same material thematically, though neither the beginning (covering the Isagoge and the start of the Categories) nor the ending (on division and definition) have been preserved. In addition, there are four lesser works on dialectic: * Introductiones parvulorum, "Introductory Logic." * Logica 'nostrorum petitioni sociorum', "Logic" (starting with the words 'At the request of our friends...'). * Tractatus de intellectibus, "A Treatise on Understandings." * Sententiae secundum Magistrum Petrum, "Master Peter's Views." The first of these is a series of elementary commentaries on the old logic (though again not completely preserved); their simple level has led some scholars to think they must come from early in Abelard's career, others to deny that they are Abelard's work at all. Second, the Logica 'nostrorum petitioni sociorum' is something of a work-in-progress: it assumes knowledge of Abelard's earlier Logica 'ingredientibus' and discusses advanced points not dealt with there, but for long stretches it is also a straightforward paraphrase of or commentary on Porphyry's Isagoge; it has textual parallels with some of Abelard's other works and shows some knowledge of theology. The third work deals with concepts, or 'understandings', from both the point of view of logic (roughly as providing the meanings of terms) and from the point of view of the philosophy of mind (as vehicles for mental content). The last work may be no more than a report of some of Abelard's lectures, and is concerned with logical and metaphysical puzzles about wholes and parts. The second category consists of Abelard's works on ethics: * Ethica seu Scito teipsum, "Ethics, or, Know Yourself." * Collationes, "Conversations" a.k.a. Dialogus inter Philosophum, Iudaeum, et Christianum, "The Dialogue of a Philosopher with a Jew and a Christian". The Ethics offers an analysis of moral worth and the degree of praise or blame that should attach to agents and their actions; it breaks off at the beginning of the second book. The Conversations is a pair of debates (among characters who appear to Abelard in a dream) over the nature of happiness and the supreme good: the Philosopher, who claims to follow only natural reason, first debates with the Jew, who follows the Old Law; the Philosopher then debates the Christian, who defends Christian ethics from a philosophical point of view. Abelard also wrote a slight work of practical advice for his son: * Carmen ad Astralabium, "Poem for Astralabe." Moral advice and edifying sentiments are found in this series of distichs. The third category consists of Abelard's works of philosophical theology. His three main works are devoted to a philosophical analysis of the Trinity, the several versions representing successive stages of his thought and his attempts at orthodoxy (each rewritten several times): * Theologia 'summi boni'. "Theology" (that begins with the words 'The highest good...'). * Theologia christiana, "Christian Theology." * Theologia 'scholarium', "Theology" (that begins with the words 'In the schools...'). The first version of the Theology seems to have been the work condemned at the Council of Soisssons, the last the work condemned at the Council of Sens. In addition to these three works, in which problems in philosophical theology are treated thematically, Abelard also wrote several commentaries: * Expositio orationis dominicae, "Analysis of the Lord's Prayer." * Expositio symboli Apostolorum, "Analysis of the Apostle's Creed." * Expositio fidei in symbolum Athanasii, "Analysis of Faith in the Athanasian Creed." * Hexaemeron, "Commentary on Genesis 1-2:25." * Commentaria in Epistolam Pauli ad Romanos, "Commentary on St. Paul's Letter to the Romans." The first three commentaries are brief, but Abelard's discussions of the first verses of Genesis and of Paul's letter are extensive and detailed (the latter also relevant to Abelard's ethical theory). Abelard also took up questions about faith and reason in a short work: * Soliloquium, "Soliloquy." This brief inner dialogue, modelled on Augustine's Soliloquies, has "Peter" talking things over with "Abelard." Theological questions of a more practical nature were raised by Heloise in a series of questions she asked on her behalf and on behalf of the nuns of the Paraclete: * Problemata Heloissae cum Petri Abaelardi solutionibus, "Heloise's Problem-List (with Abelard's Solutions)." Practical issues are also addressed in Abelard's sermons, hymns, and lamentations (planctus). Finally, Abelard composed an extremely influential theological work that contains no theoretical speculation at all: * Sic et non, "For and Against." Abelard assembles a series of 158 questions, each of which is furnished with patristic citations that imply a positive answer (sic) to the question and other patristic citations implying a negative answer (non). Abelard does not attempt to harmonize these apparently inconsistent remarks, but in his preface he lays down rules for proper hermeneutic investigation: look for ambiguity, check the surrounding context, draw relevant distinctions, and the like. Abelard's students and disciples also record many of his views, though this material has yet to be explored carefully. There are references in Abelard's extant works to other works we do not have: Grammatica, "Grammar"; Rhetorica, "Rhetoric"; a commentary on Ezekiel written at the beginning of his studies in theology; and others. It is possible some of these works may yet be found. ## 2. Metaphysics Abelard's metaphysics is the first great example of nominalism in the Western tradition. While his view that universals are mere words (nomina) justifies the label, nominalism--or, better, irrealism--is the hallmark of Abelard's entire metaphysics. He is an irrealist not only about universals, but also about propositions, events, times other than the present, natural kinds, relations, wholes, absolute space, hylomorphic composites, and the like. Instead, Abelard holds that the concrete individual, in all its richness and variety, is more than enough to populate the world. Abelard preferred reductive, atomist, and material explanations whenever possible; he devoted a great deal of effort to pouring cold water on the metaphysical excesses of his predecessors and contemporaries. Abelard defends his thesis that universals are nothing but words by arguing that ontological realism about universals is incoherent. More exactly, he holds that there cannot be any real object in the world satisfying Boethius's criteria for the universal, namely something present as a whole in many at once so as to constitute their substance (i.e. to make the individual in which it is present what it is). Hence, Abelard concludes, universality is not an ontological feature of the world but a semantic feature of language. Suppose universals were things in the world, so that one and the same item is completely present in both Socrates and an ass at the same time, making each to be wholly an animal. Abelard points out that then the same thing, animal, will be simultaneously rational (due to its role in constituting the species human being) and irrational (due to its role in constituting the species ass). But then contraries are simultaneously present in the same thing as a whole, which is impossible. To the rejoinder that rationality and irrationality are not actually present in the same thing, Abelard offers a twofold reply. First, he rejects the claim that they are present only potentially. Each species is actually informed by a contrary, and the genus is actually present in each as a whole; hence it is actually informed by one contrary in one species and by the other in the other; since it is wholly one and the same in each, it is therefore actually informed by contraries, and the contradiction results. Second, Abelard undertakes to establish that contraries will be present not merely in the genus but even in the selfsame individual. For Socrates is (an) animal, and so is Brunellus the Ass; but by transitivity--since each is wholly and completely animal--Socrates is Brunellus, and hence both rational and irrational. Put a different way, each is essentially an animal, and furthermore essentially rational and essentially irrational. If we object to this last piece of reasoning, on the grounds that individuals are unique in virtue of their non-essential features, Abelard replies that this view "makes accidents prior to substance." That is, the objection claims that individual things are individual in virtue of features that contingently characterize them, which confuses things with their features. Prospects are no better for realism if the universal is identified not with a single thing but with a collection of things. Abelard points out that collections are posterior to their parts, and, furthermore, the collection is not shared among its parts in the way a universal is said to be common to many. Nor does it help to try to identify the universal with the individual in some fashion, for example in claiming that Socrates qua human is taken as the universal human being; Abelard argues that if the universal really is the individual, then we are stuck with the consequence that either individuals such as Socrates are common to many, or there are as many universals as there are individuals, each of which is absurd. Abelard concludes that universality is merely linguistic, not a feature of the world. More precisely, Abelard holds that common nouns (such as 'animal'), verbs, and negative names (such as 'not-Socrates') are correctly predicable of many, and so count as universals. These terms are semantically general, in that their sense applies to more than one thing, but they do not thereby name some general thing; instead, they distributively refer to each of the individuals to which the term applies. For example, the term 'animal' has the sense living substance, which is inherently general, and it refers to each individual animal since each is a living substance--as Abelard puts it, since each has the status of being a living substance. But this is to leave the domain of metaphysics for semantics; see the discussion of Abelard's philosophy of language in Section 4. Abelard maintains that everything in the world apart from God and angels is either form, matter, or a composite of form and matter. The matter of something is that out of which it is made, whether it persists in the finished product (as bricks in a house) or is absorbed into it (as flour in bread). Ultimately, all material objects are composed of the four elements earth, air, fire, and water, but they do not retain their elemental forms in most combinations. In general, the form of a material object just is the configuration of its material parts: "We call the form strictly what comes from the composition of the parts." The form of a statue, for example, is its shape, which is no more than the arrangement of its matter--the curve of the nose, the size of the eyes, and so on. Forms are therefore supervenient on matter, and have no ontological standing independent of it. This is not to deny that forms exist, but to provide a particular explanation of what it is for a form to inhere in a given subject, namely for that subject to have its matter configured in a certain way. For example, the inherence of shape in the statue just is the way in which its bronze is arranged. Hence material things are identical with what they are made of--with one exception: human beings, whose forms are their immaterial (and immortal) souls. Strictly speaking, since human souls are capable of existence in separation form the body, they are not forms after all, though they act as substantial forms as long as they are joined to the body. Material composites of form and matter, humans excepted, are integral wholes made up of their discrete material parts as configured in a given way. Abelard countenances many types of integral wholes: collections, no matter how their members are selected; structured composites, whether naturally unified (such as Socrates and his limbs) or artificially unified (such as the walls, floor, and roof of a house); continuous quantities that are homogeneous material 'substances,' namely stuffs, such as water or gold; geometrical objects, such as lines, defined by the relative position of their parts; temporal wholes, such as a day and the hours that make it up. Most of these wholes are ontologically nothing beyond their material parts. Whether structured composites have any independent ontological standing depends on the status of their organizing forms. Abelard's theory of substantial integral wholes is not a pure mereology in the modern sense, since he holds that there are privileged divisions: just as a genus is properly divided into not just any species but its proximate species, so too the division of a whole must be into its principal parts. Intuitively, some wholes have a natural division that takes precedence over others; a sentence, for example, is divided into words, syllables, and letters, in precisely that order. According to Abelard, the principal parts of a whole are those whose conjunction immediately results in the complete whole. His intent seems to be that the nature of the composition (if any) that defines the integral whole also spells out its principal parts. A house consists of floor, walls, and roof put together in the right way. It is an open question whether each principal part (such as the wall) requires the existence of all of its subparts (every brick). The principal parts of a collection, for example, are just each of the members of the collection, whatever may be the case with any given member's subparts; the principal parts of an aggregation are the members located in proximity to one another. Individuals have natures, and in virtue of their natures they belong to determinate natural kinds. But an individual's nature is not something really shared with or common to other individuals; Abelard's refutation of realism has shown that this is impossible. Instead, Abelard takes a natural kind to be a well-defined collection of things that have the same features, broadly speaking, that make them what they are. Why a given thing has some features rather than others is explained by how it got that way--the natural processes that created it result in its having the features it does, namely being the kind of thing it is; similar processes lead to similar results. On this reading, it is clear that natural kinds have no special status; they are no more than discrete integral wholes whose principle of membership is similarity, merely reflecting the fact that the world is divided into discrete similarity-classes of objects. Furthermore, such real relations of similarity are nothing themselves above and beyond the things that are similar. The division into natural kinds is, presumably, a 'shallow fact' about the world: matters could have been otherwise had God ordained them differently; fire might be cold, heavy bodies fall upwards, frogs reason. If these causal powers were different, then natural kinds might be different as well, or might not have been as sharply differentiated as they are now. Given how matters stand, natural kinds carve the world at its joints, but they are the joints chosen by God. ## 3. Logic Abelard was the greatest logician since Antiquity: he devised a purely truth-functional propositional logic, recognizing the distinction between force and content we associate with Frege, and worked out a complete theory of entailment as it functions in argument (which we now take as the theory of logical consequence). His logical system is flawed in its handling of topical inference, but that should not prevent our recognition of Abelard's achievements. Abelard observes that the same propositional content can be expressed with different force in different contexts: the content that Socrates is in the house is expressed in an assertion in 'Socrates is in the house'; in a question in 'Is Socrates in the house?'; in a wish in 'If only Socrates were in the house!' and so on. Hence Abelard can distinguish in particular the assertive force of a sentence from its propositional content, a distinction that allows him to point out that the component sentences in a conditional statement are not asserted, though they have the same content they do when asserted--'If Socrates is in the kitchen, then Socrates is in the house' does not assert that Socrates is in the kitchen or that he is in the house, nor do the antecedent or the consequent, although the same form of words could be used outside the scope of the conditional to make such assertions. Likewise, the distinction allows Abelard to define negation, and other propositional connectives, purely truth-functionally in terms of content, so that negation, for instance, is treated as follows: not-p is false/true if and only if p is true/false. The key to the theory of argument, for Abelard, is found in inferentia, best rendered as 'entailment', since Abelard requires the connection between the propositions involved to be both necessary and relevant. That is, the conclusion--more exactly, the sense of the final statement--is required by the sense of the preceding statement(s), so that it cannot be otherwise. Abelard often speaks of the sense of the final statement being "contained" in the sense of the preceding statement(s), much as we speak of the conclusion being contained in the premisses. An entailment is complete (perfecta) when it holds in virtue of the logical form (complexio) of the propositions involved. By this, Abelard tells us, he means that the entailment holds under any uniform substitution in its terms, the criterion now associated with Bolzano. The traditional four figures and moods of the categorical syllogism derived from Aristotle, and the doctrine of the hypothetical syllogism derived from Boethius, are all instances of complete entailments, or as we should say, valid inference. There is another way in which conclusions can be necessary and relevant to their premisses, yet not be formally valid (not be a complete entailment). The necessary connection among the propositions, and the link among their senses, might be a function of non-formal metaphysical truths holding in all possible worlds. For instance, human beings are a kind of animal, so the consequence 'If Socrates is a human being, Socrates is an animal' holds of necessity and the sense of the antecedent compels that of the consequent, but it is not formally valid under uniform substitution. Abelard takes such incomplete entailments to hold according to the theory of the topics (to be forms of so-called topical inference). The sample inference above is validated by the topic "from the species", a set of metaphysical relations one of which is expressible in the rule "Whatever the species is predicated of, so too is the genus" which grounds the inferential force of the entailment. Against Boethius, Abelard maintained that topical rules were only needed for incomplete entailment, and in particular are not required to validate the classical moods of the categorical and hypothetical syllogism mentioned in the preceding paragraph. Abelard spends a great deal of effort to explore the complexities of the theory of topical inference, especially charting the precise relations among conditional sentences, arguments, and what he calls "argumentation" (roughly what follows from conceded premisses). One of the surprising results of his investigation is that he denies that a correlate of the Deduction Theorem holds, maintaining that a valid argument need not correspond to an acceptable conditional sentence, nor conversely, since the requirements on arguments and conditionals differ. In the end, it seems that Abelard's principles of topical inference do not work, a fact that became evident with regard to the topic "from opposites": Abelard's principles lead to inconsistent results, a result noted by Alberic of Paris. This led to a crisis in the theory of inference in the twelfth century, since Abelard unsuccessfully tried to evade the difficulty. These debates seem to have taken place in the later part of the 1130s, as Abelard was about to become embroiled with Bernard of Clairvaux, and his attention was elsewhere. ## 4. Philosophy of Language Much of Abelard's philosophy of language is devoted to analyzing how a given expression or class of expressions function logically: what words are quantifiers, which imply negation, and the like, so that the logic described above may be applied. To do so, he relies on the traditional division, derived from Aristotle, that sees the main linguistic categories as name, verb, and their combination into the sentence. Abelard takes names to be conventionally significant simple words, usually without tense. So understood there are a wide variety of names: proper and common names; adjectives and adverbs; pronouns, whether personal, possessive, reflexive, or relative; conventional interjections such as 'Goodness!'; and, arguably, conjunctions and prepositions (despite lacking definite signification), along with participles and gerundives (which have tense). Abelard usually, though not always, treats compound names such as 'street-sweeper' reductively. Even so his list is not general enough to catalogue all referring expressions. In point of fact, much of Abelard's discussion of the semantics of names turns on a particular case that stands for the rest: common names. These are at the heart of the problem of universals, and they pose particular difficulties for semantics. When Abelard puts forward his claim that universality is only a linguistic phenomenon, so that universals are "nothing more than words," he raises the objection that unless common names are the names of common items, they will be meaningless, and so his view is no better than that of his teacher Roscelin (who held that universals were mere mouth noises). In reply Abelard clearly draws a distinction between two semantic properties names possess: reference (nominatio), a matter of what the term applies to; and sense (significatio), a matter of what hearing the term brings to mind, or more exactly the informational content (doctrina) of the concept the word is meant to give rise to, a causal notion. A few remarks about each are in order. Names, both proper and common, refer to things individually or severally. A name is linked with that of which it is the name as though there were someone who devised the name to label a given thing or kind of thing, a process known as "imposition" (modelled on Adam's naming the animals in Genesis 2:19), rather like baptism. This rational reconstruction of reference does not require the person imposing the name, the "impositor", to have anything more than an indefinite intention to pick out the thing or kind of thing, whatever its nature may be: > > The inventor [of names] intended to impose them according to some > natures or distinctive properties of things, even if he himself did > not know how to think correctly upon the nature or distinctive > property of a thing. > A name "has a definition in the nature of its imposition, even if we do not know what it is." Put in modern terms, Abelard holds a theory of direct reference, in which the extension of a term is not a function of its sense. We are often completely ignorant of the proper conceptual content that should be associated with a term that has been successfully imposed. A proper name--the name of a primary substance--signifies a concrete individual (hoc aliquid), picking out its bearer as personally distinct from all else. Therefore, proper names are semantically singular referring expressions, closely allied to indexicals, demonstratives, and singular descriptions (or descriptive terms). Common names, by contrast, are semantically allied with expressions that have what Abelard calls "plural signification". On the one hand, common names are like plural nouns; the common name 'man' is grammatically singular but operates like the plural term 'men'--each refers to every man, although the plural term signifies individuals as part of a collection, whereas the common name distributively refers to each individual. On the other hand, common names are like terms such as 'trio' or 'pair' in that they pick out a determinate plurality of individuals, but only on an occasion of use, since their extension is variable. Thus a common name distributively refers to concrete individuals, though not to them qua individuals. Instead, it severally picks out those individuals having a given nature: 'human being' refers to Socrates and to Plato, in virtue of each of them being human. This is not a shared feature of any sort; Socrates just is what he is, namely human, and likewise Plato is what he is, namely human too. Abelard states his deflationary position clearly in his Logica 'ingredientibus': > > Now it seems we should stay away from accepting the agreement among > things according to what is not any thing--it's as though > we were to unite in nothing things that now exist!--namely, when > we say that this [human] and that one agree in the human status, that > is to say: in that they are human. But we mean precisely that they are > human and don't differ in this regard--let me repeat: [they > don't differ] in that they are human, although we're not > appealing to any thing [in this explanation]. > Socrates and Plato are real; their agreement is real, too, but it isn't to be explained by appealing to any thing--their agreement just is their each being human. From a metaphysical point of view they have the same standing as human beings; this does not involve any metaphysically common shared ingredient, or indeed appeal to any ingredient at all. That is the sense in which there is a "common reason" for the imposition of a common name. For all that signification is posterior to reference, names do have signification as well. Abelard holds that the signification of a term is the informational content of the concept that is associated with the term upon hearing it, in the normal course of events. Since names are only conventionally significant, which concept is associated with a given name depends in part on the psychological conditioning of language-users, in virtue of which Abelard can treat signification as both a causal and a normative notion: the word 'rabbit' ought to cause native speakers of English to have the concept of a rabbit upon hearing it. Abelard is careful to insist that the signification is a matter of the informational content carried in the concept--mere psychological associations, even the mental images characteristic of a given concept, are not part of what the word means. Ideally, the concept will correspond to a real definition that latches onto the nature of the thing, the way 'rational mortal animal' is thought to be the real definition of 'human being', regardless of other associated features (even necessary features such as risibility) or fortuitous images (as any mental image of a human will be of someone with determinate features). Achieving such clarity in our concepts is, of course, an arduous business, and requires an understanding of how understanding itself works (see the discussion of Abelard's philosophy of mind in Section 5). Yet one point should be clear from the example. The significations of some names, such as those corresponding to natural-kind terms, are abstractions in the sense that they include only certain features of the things to which the term refers. They do not positively exclude all other features, though, and are capable of further determinate specification: 'rational mortal animal' as the content of the concept of 'human being' signifies all humans, whatever their further features may be--tall or short, fat or thin, male or female, and so on. What holds for the semantics of names applies for the most part to verbs. The feature that sets verbs apart from names, more so than tense or grammatical person, is that verbs have connective force (vis copulativa). This is a primitive and irreducible feature of verbs that can only be discharged when they are joined with names in the syntactically appropriate way, reminiscent of the 'unsaturatedness' of concepts in Frege. Sentences are made up of names and verbs in such a way that the meaning of the whole sentence is a function of the meaning of its parts. That is, Abelardian semantics is fundamentally compositional in nature. The details of how the composition works are complex. Abelard works directly with a natural language (Latin) that, for all its artificiality, is still a native second tongue. Hence there are many linguistic phenomena Abelard is compelled to analyze that would be simply disallowed in a more formal framework. For example, Abelard notes that most verbs can occur as predicates in two ways, namely as a finite verbal form or as a nominal form combined with an auxiliary copula, so that we may say either 'Socrates runs' or 'Socrates is running'; the same holds for transitive predication, for instance 'Socrates hits Plato' and 'Socrates is hitting Plato.' Abelard argues that in general the pure verbal version of predication is the fundamental form, which explains and clarifies the extended version; the latter is only strictly necessary where simple verbal forms are lacking. (The substantive verb 'is' requires special treatment.) Hence for Abelard the basic analysis of a predicative statement recognizes that two fundamentally different linguistic categories are joined together: the name n and the simple verbal function V( ), combined in the well-formed sentence V(n). Abelard argues that sentences (propositiones) must signify more than just the understandings of the constituent name and verb. First, a sentence such as 'Socrates runs' deals with Socrates and with running, not with anyone's understandings. We talk about the world, not merely someone's understanding of the world. Second, sentences like 'If something is human, it is an animal' are false if taken to be about understandings, for someone could entertain the concept human without entertaining the concept animal, and so the antecedent would obtain without the consequent. Third, understandings are evanescent particulars, mere mental tokenings of concepts. But at least some consequential sentences are necessary, and necessity can't be grounded on things that are transitory, and so not on understandings. Sentences must therefore signify something else in addition to understandings, something that can do what mere understandings cannot. Abelard describes this as signifying what the sentence says, calling what is said by the sentence its dictum (plural dicta). To the modern philosophical ear, Abelard's dicta might sound like propositions, abstract entities that are the timeless bearers of truth and falsity. But Abelard will have nothing to do with any such entities. He declares repeatedly and emphatically that despite being more than and different from the sentences that express them, dicta have no ontological standing whatsoever. In the short space of a single paragraph he says that they are "no real things at all" and twice calls them "absolutely nothing." They underwrite sentences, but they aren't real things. For although a sentence says something, there is not some thing that it says. The semantic job of sentences is to say something, which is not to be confused with naming or denoting some thing. It is instead a matter of proposing how things are, provided this is not given a realist reading. Likewise, the truth of true sentences is not a property inhering in some timeless entity, but no more than the assertion of what the sentence says--that is, Abelard adopts a deflationary account of truth. A sentence is true if things stand in the way it says, and things make sentences true or false in virtue of the way they are (as well as in virtue of what the sentences say), and nothing further is required. The sentence 'Socrates runs' is true because Socrates runs, which is all that can be said or needs to be said. ## 5. Philosophy of Mind Aristotelian philosophy of mind offers two analyses of intentionality: the conformality theory holds that we think of an object by having its very form in the mind, the resemblance theory that we do so by having a mental image in the mind that naturally resembles the object. Abelard rejects each of these theories and proposes instead an adverbial theory of thought, showing that neither mental images nor mental contents need be countenanced as ontologically independent of the mind. He gives a contextual explication of intentionality that relies on a linguistic account of mental representation, adopting a principle of compositionality for understandings. The first Aristotelian analysis takes understanding to be the mind's acquisition of the form of the object that is understood, without its matter. For an understanding to be about some thing--say, a cat--is for the form of the cat to be in the mind or intellective soul. The inherence of the form in matter makes the matter to be a thing of a certain kind, so that the inherence of the form cat in matter produces an actual cat, whereas the (immaterial) inherence of the form cat in the mind transforms the mind into an understanding of a cat: the mind becomes (formally) identical with its object. Since the 'aboutness' of understanding is analyzed as the commonness or identity of form in the understanding and the thing understood, we may call this approach the conformality theory of understanding. This theory captures the intuition that understanding somehow inherits or includes properties of what is understood, by reducing the intentionality of understanding to the objective identity of the form in the mind and the form in the world. The second Aristotelian analysis takes understanding to be the mind's possession of a concept that is a natural likeness of, or naturally similar to, that of which it is a concept. For an understanding to be about some thing, such as a cat, is for there to be an occurrent concept in the mind that is a natural likeness of a cat. The motivation for calling the likeness "natural" is to guarantee that the resemblance between the understanding and what is understood is objective, and that all persons have access to the same stock of concepts. (The conformality theory does this by postulating the objective existence of forms in things and by an identical process in all persons of assimilating or acquiring forms.) We may call this approach the resemblance theory of understanding: mental acts are classified according to the distinct degree and kind of resemblance they have to the things that are understood. The resemblance theory faces well-known problems in spelling out the content of resemblance or likeness. For example, a concept is clearly immaterial, and as such radically differs from any material object. Furthermore, there seems to be no formal characteristic of a mental act in virtue of which it can non-trivially be said to resemble anything else. To get around these difficulties, mediaeval philosophers, like the British Empiricists centuries later, appealed to a particular kind of resemblance, namely pictorial resemblance. A portrait of Socrates is about Socrates in virtue of visually resembling Socrates in the right ways. And just as there are pictorial images that are about their subjects, so too are there mental images that are about things. These mental images, whether they are concepts or are contained in concepts, explain the way in which a concept is 'about' an object. For an understanding to be about a cat is for it to be or contain a mental image of a cat. The phenomenon of mental 'aboutness' is explicated by the more familiar case of pictorial aboutness, itself reduced to a real relation of resemblance. Despite their common Aristotelian heritage, the conformality theory and the resemblance theory are not equivalent. The transformation of the mind through the inherence of a form is not necessarily the same as the mind's possession of a concept. Equally, natural likeness or resemblance need not be understood as identity of form; formal identity need not entail genuine resemblance, due to the different subjects in which the form is embodied. The standard way to reconcile the conformality theory and the resemblance theory is to take the mind's possession of a concept to be its ability to transform itself through the inherence of a form, construing formal identity as natural likeness, where having a form in the mind that is identical to the form of the object understood just is to have a mental image of that very object. Abelard argues against conformality as follows. Consider a tower, which is a material object with a certain length, depth, and height; assume that these features compose its form, much as the shape of a statue is its form. According to Aristotelian metaphysics, the inherence of a form in a subject makes the subject into something characterized by that form, as for instance whiteness inhering in Socrates makes him something white. The forms of the tower likewise make that in which they inhere to be tall, wide, massive--all physical properties. If these forms inhere in the mind, then, they should make the mind tall, wide, and massive, an absurd conclusion: the mind "cannot extend itself in length or width." Yet it is a cardinal thesis of the conformality theory that the mind has the identical form that is possessed by the external object, the tower, although the form of (say) length is by its very nature physical. Thus, Abelard concludes, conformality is incoherent. Abelard's main objection to the resemblance theory is that mental images qua images, like any sign, are inert: they require interpretation. A sign is just an object. It may be taken in a significative role, though it need not be. Abelard notes that this distinction holds equally for non-mental signs: we can treat a statue as a lump of bronze or as a likeness. Mental images are likewise inert. For a sign to function significatively, then, something more is required beyond its mere presence or existence. But the resemblance theory doesn't recognize the need to interpret the mental image as an image, and thereby mistakenly identifies understanding with the mere presence of a mental image in the mind. Abelard concludes that mental images have only an instrumental role in thought, describing them as "intermediary signs of things" (intersigna rerum). Intentionality derives instead from the act of attention (attentio) directed upon the mental image. Proof is found in the fact that that we can "vary the understanding" simply by attending to different features of the mental image: the selfsame image--say, a fig tree--can be used to think about this very fig tree, or trees in general, or plant life, or my lost love with whom I sat under it, or anything whatsoever. There is no intrinsic feature of the mental image in virtue of which it is about any given thing; if there were, Abelard notes, we could determine by inspection what a sign is about--but we can't. Mental images, therefore, can't explain the intentionality of understanding, because their role is merely instrumental. We think with them, and cannot avoid them; but they do not explain intentionality. Abelard draws the conclusion that intentionality is a primitive and irreducible feature of the mind, our acts of attending to things. Different acts of attention are intrinsically different from one another; they are about what they are about in virtue of being the kind of attention they are. Hence Abelard adopts what is nowadays called an adverbial theory of thought. Given that intentionality is primitive, Abelard adopts a contextual approach to mental content: he embeds these irreducible acts of attention in a structure whose articulation helps define the character of its constituent elements. The structure Abelard offers is linguistic, a logic of mental acts: just as words can be said to express thoughts, so too we can use the articulated logic of language to give a theory of understanding. In short, Abelard gives something very like a linguistic account of mental representation or intentionality. To this end he embraces a principle of compositionality, holding that what an understanding is about is a function of what its constituent understandings are about. The unity of the understanding of a complex is a function of its logical simplicity, which is characterized by the presence of what Abelard calls "a single dominant conjunction" (the logical operator of greatest scope). Hence the understanding of a complex may be treated as a complex of distinct understandings, aggregated in the same thought, with its (logical) structure flowing from the 'dominant conjunction' over the other logical operations governing its constituent understandings. Abelard's acts of attention thus display the logical structure of the understanding they express, and thereby give the semantics of written or spoken language. Much of Abelard's writings on logic and dialectic are given over to working out the details as a scheme for explicating mental content. ## 6. Ethics Abelard takes the rational core of traditional Christian morality to be radically intentionalist, based on the following principle: the agent's intention alone determines the moral worth of an action. His main argument against the moral relevance of consequences turns on what contemporary philosophers often refer to as moral luck. Suppose two men each have the money and the intention to establish shelters for the poor, but one is robbed before he can act whereas the second is able to carry out his intention. According to Abelard, to think that there is a moral difference between them is to hold that "the richer men were the better they could become ... this is the height of insanity!" Deed-centred morality loses any kind of purchase on what might have been the case. Likewise, it cannot offer any ground for taking the epistemic status of the agent into account, although most people would admit that ignorance can morally exculpate an agent. Abelard makes the point with the following example: imagine the case of fraternal twins, brother and sister, who are separated at birth and each kept in complete ignorance of even the existence of the other; as adults they meet, fall in love, are legally married and have sexual intercourse. Technically this is incest, but Abelard finds no fault in either to lay blame. Abelard concludes that in themselves deeds are morally indifferent. The proper subject of moral evaluation is the agent, via his or her intentions. It might be objected that the performance or nonperformance of the deed could affect the agent's feelings, which in turn may affect his or her intentions, so that deeds thereby have moral relevance (at least indirectly). Abelard denies it: > > For example, if someone forces a monk to lie bound in chains between > two women, and by the softness of the bed and the touch of the women > beside him he is brought to pleasure (but not to consent), who may > presume to call this pleasure, which nature makes necessary, a fault? > We are so constructed that the feeling of pleasure is inevitable in certain situations: sexual intercourse, eating delicious food, and the like. If sexual pleasure in marriage is not sinful, then the pleasure itself, inside or outside of marriage, is not sinful; if it is sinful, then marriage cannot sanctify it--and if the conclusion were drawn that such acts should be performed wholly without pleasure, then Abelard declares they cannot be done at all, and it was unreasonable (of God) to permit them only in a way in which they cannot be performed. On the positive side, Abelard argues that unless intentions are the key ingredient in assessing moral value it is hard to see why coercion, in which one is forced to do something against his or her will, should exculpate the agent; likewise for ignorance--though Abelard points out that the important moral notion is not simply ignorance but strictly speaking negligence. Abelard takes an extreme case to make his point. He argues that the crucifiers of Christ were not evil in crucifying Jesus. (This example, and others like it, got Abelard into trouble with the authorities, and it isn't hard to see why.) Their ignorance of Christ's divine nature didn't by itself make them evil; neither did their acting on their (false and mistaken) beliefs, in crucifying Christ. Their non-negligent ignorance removes blame from their actions. Indeed, Abelard argues that they would have sinned had they thought crucifying Christ was required and did not crucify Christ: regardless of the facts of the case, failing to abide by one's conscience in moral action renders the agent blameworthy. There are two obvious objections to Abelard's intentionalism. First, how is it possible to commit evil voluntarily? Second, since intentions are not accessible to anyone other than the agent, doesn't Abelard's view entail that it is impossible to make ethical judgements? With regard to the first objection, Abelard has a twofold answer. First, it is clear that we often want to perform the deed and at the same time do not want to suffer the punishment. A man wants to have sexual intercourse with a woman, but not to commit adultery; he would prefer it if she were unmarried. Second, it is clear that we sometimes "want what we by no means want to want": our bodies react with pleasure and desire independently of our wills. If we act on such desires, then our action is done "of" will, as Abelard calls it, though not voluntarily. There is nothing evil in desire: there is only evil in acting on desire, and this is compatible with having contrary desires. With regard to the second objection, Abelard grants that other humans cannot know the agent's intentions--God, of course, does have access to internal mental states, and so there can be a Final Judgement. However, Abelard does not take ethical judgement to pose a problem. God is the only one with a right to pass judgement. Yet this fact doesn't prevent us from enforcing canons of human justice, because, Abelard holds, human justice has primarily an exemplary and deterrent function. In fact, Abelard argues, it can even be just to punish an agent we strongly believe had no evil intention. He cites two cases. First, a woman accidentally smothers her baby while trying to keep it warm at night, and is overcome with grief. Abelard maintains that we should punish her for the beneficial example her punishment may have on others: it may make other poor mothers more careful not to accidentally smother their babies while trying to keep them warm. Second, a judge may have excellent (but legally impermissible) evidence that a witness is perjuring himself; since he cannot show that the witness is lying, the judge is forced to rule on the basis of the witness's testimony that the accused, whom he believes to be innocent, is guilty. Human justice may with propriety ignore questions of intention. Since there is divine justice, ethical notions are not an idle wheel--nor should they be, even on Abelard's understanding of human justice, since they are the means by which we determine which intentions to promote or discourage when we punish people as examples or in order to deter others. There is a sense, then, in which the only certifiable sin is acting against one's conscience, unless one is morally negligent. Yet if we cannot look to the intrinsic value of the deeds or their consequences, how do we determine which acts are permissible or obligatory? Unless conscience has a reliable guide, Abelard's position seems to open the floodgates to well-meaning subjectivism. Abelard solves the problem by taking obedience to God's will--the hallmark of morally correct behaviour, and itself an instance of natural law--to be a matter of the agent's intention conforming to a purely formal criterion, namely the Golden Rule ("Do to others as you would be done to"). This criterion can be discovered by reason alone, without any special revelation or religious belief, and is sufficient to ensure the rightness of the agent's intention. But the resolution of this problem immediately leads to another problem. Even if we grant Abelard his naturalistic ethics, why should an agent care if his or her intentions conform to the Golden Rule? In short, even if Abelard were right about morality, why be moral? Abelard's answer is that our happiness--to which no one is indifferent--is linked to virtue, that is, to habitual morally correct behaviour. Indeed, Abelard's project in the Collationes is to argue that reason can prove that a merely naturalistic ethics is insufficient, and that an agent's happiness is necessarily bound up with accepting the principles of traditional Christian belief, including the belief in God and an Afterlife. In particular, he argues that the Afterlife is a condition to which we ought to aspire, that it is a moral improvement even on the life of virtue in this world, and that recognizing this is constitutive of wanting to do what God wants, that is, to live according to the Golden Rule, which guarantees as much as anything can (pending divine grace) our long-term postmortem happiness. The Philosopher first argues with the Jew, who espouses a 'strict observance' moral theory, namely obedience to the Mosaic Law. One of the arguments the Jew offers is the Slave's Wager (apparently the earliest-known version of Pascal's Wager). Imagine that a Slave is told one morning by someone he doesn't know whether to trust that his powerful and irritable Master, who is away for the day, has left instructions about what to do in his absence. The Slave can follow the instructions or not. He reasons that if the Master indeed left the instructions, then by following them he will be rewarded and by not following them he will be severely punished, whereas if the Master did not leave the instructions he would not be punished for following them, though he might be lightly punished for not following them. (This conforms to the standard payoff matrix for Pascal's Wager.) That is the position the Jew finds himself in: God has apparently demanded unconditional obedience to the Mosaic Law, the instructions left behind. The Philosopher argues that the Jew may have other choices of action and, in any event, that there are rational grounds for thinking that ethics is not a matter of action in conformity to law but a matter of the agent's intentions, as we have seen above. The Philosopher then argues with the Christian. He initially maintains that virtue entails happiness, and hence there is no need of an Afterlife since a virtuous person remains in the same condition whether dead or alive. The Christian, however, reasons that the Afterlife is better, since in addition to the benefits conferred by living virtuously, the agent's will is no longer impeded by circumstances. In the Afterlife we are no longer subject to the body, for instance, and hence are not bound by physical necessities such as food, shelter, clothing, and the like. The agent can therefore be as purely happy as life in accordance with virtue could permit, when no external circumstances could affect the agent's actions. The Philosopher grants that the Afterlife so understood is a clear improvement even on the virtuous life in this world, and joins with the Christian in a cooperative endeavour to define the nature of the virtues and the Supreme Good. Virtue is its own reward, and in the Afterlife nothing prevents us from rewarding ourselves with virtue to the fullest extent possible. ## 7. Theology Abelard held that reasoning has a limited role to play in matters of faith. That he gave reasoning a role at all brought him into conflict with those we might now call anti-dialecticians, including his fellow abbot Bernard of Clairvaux. That the role he gave it is limited brought him into conflict with those he called "pseudo-dialecticians," including his former teacher Roscelin. Bernard of Clairvaux and other anti-dialecticians seem to have thought that the meaning of a proposition of the faith, to the extent that it can be grasped, is plain; beyond that plain meaning, there is nothing we can grasp at all, in which case reason is clearly no help. That is, the anti-dialecticians were semantic realists about the plain meaning of religious sentences. Hence their impatience with Abelard, who seemed not only bent on obfuscating the plain meaning of propositions of the faith, which is bad enough, but to do so by reasoning, which has no place either in grasping the plain meaning (since the very plainness of plain meaning consists in its being grasped immediately without reasoning) or in reaching some more profound understanding (since only the plain meaning is open to us at all). Abelard has no patience for the semantic realism that underlies the sophisticated anti-dialectical position. Rather than argue against it explicitly, he tries to undermine it. From his commentaries on scripture and dogma to his works of speculative theology, Abelard is first and foremost concerned to show how religious claims can be understood, and in particular how the application of dialectical methods can clarify and illuminate propositions of the faith. Furthermore, he rejects the claim that there is a plain meaning to be grasped. Outlining his method in the Prologue to his Sic et non, Abelard describes how he initially raises a question, e.g. whether priests are required to be celibate, and then arranges citations from scriptural and patristic authorities that at least seem to answer the question directly into positive and negative responses. (Abelard offers advice in the Prologue for resolving the apparent contradictions among the authorities using a variety of techniques: see whether the words are used in the same sense on both sides; draw relevant distinctions to resolve the issue; look at the context of the citation; make sure that an author is speaking in his own voice rather than merely reporting or paraphrasing someone else's position; and so on.) Now each authority Abelard cites seems to speak clearly and unambiguously either for a positive answer to a given question or for a negative one. If ever there were cases of plain meaning, Abelard seems to have found them in authorities, on opposing sides of controversial issues. His advice in the Prologue amounts to saying that sentences that seem to be perfect exemplars of plain meaning in fact have to be carefully scrutinized to see just what their meaning is. Yet that is just to say that they do not have plain meaning at all; we have to use reason to uncover their meaning. Hence the anti-dialecticians don't have a case. There is a far more serious threat to the proper use of reason in religion, Abelard thinks (Theologia christiana 3.20): > > Those who claim to be dialecticians are usually led more easily to > [heresy] the more they hold themselves to be well-equipped with > reasons, and, to that extent more secure, they presume to attack or > defend any position the more freely. Their arrogance is so great that > they think there isn't anything that can't be understood > and explained by their petty little lines of reasoning. Holding all > authorities in contempt, they glory in believing only > themselves--for those who accept only what their reason persuades > them of, surely answer to themselves alone, as if they had eyes that > were unacquainted with darkness. > Such pseudo-dialecticians take reason to be the final arbiter of all claims, including claims about matters of faith. More exactly, Abelard charges them with holding that (a) everything can be explained by human reason; (b) we should only accept what reason persuades us of; (c) appeals to authority have no rational persuasive force. Real dialecticians, he maintains, reject (a)-(c), recognizing that human reason has limits, and that some important truths may lie outside those limits but not beyond belief; which claims about matters of faith we should accept depends on both the epistemic reliability of their sources (the authorities) and their consonance with reason to the extent they can be investigated. Abelard's arguments for rejecting (a)-(c) are sophisticated and subtle. For the claim that reason may be fruitfully applied to a particular article of faith, Abelard offers a particular case study in his own writings. The bulk of Abelard's work on theology is devoted to his dialectical investigation of the Trinity. He elaborates an original theory of identity to address issues surrounding the Trinity, one that has wider applicability in metaphysics. The upshot of his enquiries is that belief in the Trinity is rationally justifiable since as far as reason can take us we find that the doctrine makes sense--at least, once the tools of dialectic have been properly employed. The traditional account of identity, derived from Boethius, holds that things may be either generically, specifically, or numerically the same or different. Abelard accepts this account but finds it not sufficiently fine-grained to deal with the Trinity. The core of his theory of identity, as presented in his Theologia christiana, consists in four additional modes of identity: (1) essential sameness and difference; (2) numerical sameness and difference, which Abelard ties closely to essential sameness and difference, allowing a more fine-grained distinction than Boethius could allow; (3) sameness and difference in definition; (4) sameness and difference in property (in proprietate). Roughly, Abelard's account of essential and numerical sameness is intended to improve upon the identity-conditions for things in the world given by the traditional account; his account of sameness in definition is meant to supply identity-conditions for the features of things; and his account of sameness in property opens up the possibility of there being different identity-conditions for a single thing having several distinct features. Abelard holds that two things are the same in essence when they are numerically the same concrete thing (essentia), and essentially different otherwise. The Morning Star is essentially the same as the Evening Star, for instance, since each is the selfsame planet Venus. Again, the formal elements that constitute a concrete thing are essentially the same as one another and essentially the same as the concrete thing of which they are the formal constituents: Socrates is his essence (Socrates is what it is to be Socrates). The corresponding general thesis does not hold for parts, however. Abelard maintains that the part is essentially different from the integral whole of which it is a part, reasoning that a given part is completely contained, along with other parts, in the whole, and so is less than the quantity of the whole. Numerical difference does not map precisely onto essential difference. The failure of numerical sameness may be due to one of two causes. First, objects are not numerically the same when one has a part that the other does not have, in which case the objects are essentially different as well. Second, objects are numerically different when neither has a part belonging to the other. Numerical difference thus entails the failure of numerical sameness, but not conversely: a part is not numerically the same as its whole, but it is not numerically different from its whole. Thus one thing is essentially different from another when either they have only a part in common, in which case they are not numerically the same; or they have no parts in common, in which case they are numerically different as well as not numerically the same. Since things may be neither numerically the same nor numerically different, the question "How many things are there?" is ill-formed as it stands and must be made more precise, a fact Abelard exploits in his discussion of the Trinity. Essential and numerical sameness and difference apply directly to things in the world; they are extensional forms of identity. By contrast, sameness and difference in definition is roughly analogous to modern theories of the identity of properties. Abelard holds that things are the same in definition when what it is to be one requires that it be the other, and conversely; otherwise they differ in definition. Finally, things are the same in property when they specify features that characterize one another. Abelard offers an example to clarify this notion. A cube of marble exemplifies both whiteness and hardness; what is white is essentially the same as what is hard, since they are numerically the same concrete thing, namely the marble cube; yet the whiteness and the hardness in the marble cube clearly differ in definition--but even so, what is white is characterized by hardness (the white thing is hard), and conversely what is hard is characterized by whiteness (the hard thing is white). The properties of whiteness and hardness are "mixed" since, despite their being different in definition, each applies to the selfsame concrete thing (namely the marble cube) as such and also as it is characterized by the other. The interesting case is where something has properties that "remain so completely unmixed" that the items they characterize are different in property. Consider a form-matter composite in relation to its matter. The matter out of which a form-matter composite is made is essentially the same as the composite, since each is the entire material composite itself. Yet despite their essential sameness, they are not identical; the matter is not the composite, nor conversely. The matter is not the composite, for the composite comes to be out of the matter, but the matter does not come to be out of itself. The composite is not the matter, since "nothing is in any way a constitutive part of or naturally prior to itself." Instead, the matter is prior to the composite since it has the property priority with respect to the composite, whereas the composite is posterior to its matter since it has the property posteriority with respect to its matter. Now despite being essentially the same, the matter is not characterized by posteriority, unlike the composite, and the composite is not characterized by priority, unlike the matter. Hence the matter and composite are different in property; the properties priority and posteriority are unmixed--they differ in property. Now for the payoff. Abelard deploys his theory of identity to shed light on the Trinity as follows. The three Persons are essentially the same as one another, since they are all the same concrete thing (namely God). They differ from one another in definition, since what it is to be the Father is not the same as what it is to be the Son or what it is to be the Holy Spirit. The three Persons are numerically different from one another, for otherwise they would not be three, but they are not numerically different from God: if they were there would be three gods, not one. Moreover, each Person has properties that uniquely apply to it--unbegotten to the Father, begotten to the Son, and proceeding to the Holy Spirit--as well as properties that are distinctive of it, such as power for the Father, wisdom for the Son, and goodness for the Holy Spirit. The unique properties are unmixed in Abelard's technical sense, for the Persons differ from one another in their unique properties, and such properties do not apply to God; the distinctive properties are mixed, though, in that God is characterized by each (the powerful God is the wise God is the good God). Further than that, Abelard holds, human reason cannot go; but reason validates the analysis (strictly speaking only a "likeness" or analogy) as far as it can go.
abhidharma	"## 1. Abhidharma: its origins and texts\n\n\n\nThe early history of Buddhism in India is remarkably(...TRUNCATED)
abilities	"## 1. A taxonomy\n\n\n\nWhat is an ability? On one reading, this question is a demand\nfor a *the(...TRUNCATED)
abner-burgos	"## 1. Life\n\n\n\nThere are not many sources on the life of Abner. The majority of the\nsources are(...TRUNCATED)
abrabanel	"## 1. Life and Works\n\n\n\n\nThere exists a large debate in the secondary literature concerning th(...TRUNCATED)
abstract-objects	"## 1. Introduction\n\n\n\nThe abstract/concrete distinction has a curious status in contemporary\np(...TRUNCATED)
essential-accidental	"## 1. The Modal Characterization of the Essential/Accidental Property Distinction\n\n\n\nAccording (...TRUNCATED)
action	"## 1. About the Question: What is an Action?\n\n\n\nThe central question in philosophy of action is(...TRUNCATED)
shared-agency	"## 1. The traditional ontological problem and the Intention Thesis\n\n\n\nAgency is sometimes exerc(...TRUNCATED)

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