We motivate and introduce a new method of abduction, Matrix Abduction, and apply it to modelling the use of non-deductive inferences in the Talmud such as Analogy and the rule of Argumentum A Fortiori. Given a matrix with entries in {0, 1}, we allow for one or more blank squares in the matrix, say a i , j =?. The method allows us to decide whether to declare a i , j = 0 or a i , j = 1 (...) or a i , j =? undecided. This algorithmic method is then applied to modelling several legal and practical reasoning situations including the Talmudic rule of Kal-Vachomer. We add an Appendix showing that this new rule of Matrix Abduction, arising from the Talmud, can also be applied to the analysis of paradoxes in voting and judgement aggregation. In fact we have here a general method for executing non-deductive inferences. (shrink)

Chalmers and Jackson (2001) offer an epistemic interpretation of the two-dimensional semantic framework advanced by Kaplan (1979, 1989), Stalnaker (1978), and others. Epistemic two-dimensional semantics (E2D) aims to re-forge the link between necessity and a priority seemingly broken by Kripke (1972/1980). On the E2D strategy, a priori knowledge of certain semantic intensions provides a route to a priori knowledge of a wide range of modal truths---nice outcome, if we can get it. E2D faces the serious challenge, however, that we typically (...) don't have even in-principle a priori access to the intensions at issue (Byrne and Pryor 2006, Melnyk 2001; see also Wilson 1982). As we substantiate, the "access-based challenge" to Chalmers and Jackson's version of E2D is successful; but the problem here isn't for E2D per se, but rather to E2D interpreted as appealing to a conceiving-based epistemology of intensions. Here we develop a version of E2D appealing to abduction rather than conceivability. We argue that abduction gives rise to beliefs that are reasonably taken to be a priori; and we show that E2D when combined with an abductive epistemology of intensions---that is, abductive two-dimensionalism---can successfully respond to the access-based challenge. We finish up with a case study, involving zombies and the mind-body problem, illustrating how the two versions of E2D may differ in application. (shrink)

The usual, comparative, conception of Inference to the Best Explanation (IBE) takes it to be ampliative. In this paper I propose a conception of IBE (‘Holmesian inference’) that takes it to be a species of eliminative induction and hence not ampliative. This avoids several problems for comparative IBE (e.g. how could it be reliable enough to generate knowledge?). My account of Holmesian inference raises the suspicion that it could never be applied, on the grounds that scientific hypotheses are inevitably underdetermined (...) by the evidence (i.e. are inevitably ampliative). I argue that this concern may be resisted by acknowledging, as Timothy Williamson has shown, that all knowledge is evidence. This suggests an approach to resisting scepticism different from those (e.g. the reliabilist approach) that embrace fallibilism. (shrink)

While “All events have a cause” is a synthetic statement making a factual claim about the world, “All effects have a cause” is analytic. When we take an event as an effect, no inference is required to deduce that it has a cause since this is what it means to be an effect. Some examples often given in the literature as examples of abduction work in the same way through semantic facts that follow from the way our beliefs represent those (...) effects; from this we may deduce not only that it has a cause, but what that cause is. (shrink)

When the indispensability argument for mathematical entities (IA) is spelled out, it would appear confirmational holism is needed for the argument to work. It has been argued that confirmational holism is a dispensable premise in the argument if a construal of naturalism, according to which it is denied that we can take different epistemic attitudes towards different parts of our scientific theories, is adopted. I argue that the suggested variety of naturalism will only appeal to a limited number of philosophers. (...) I then suggest that if we allow for some degree of separation between different component parts of theories, IA can be formulated as an argument aimed at more than a limited number of philosophers, but in implementing this strategy the notion of indispensability needs spelling out. The best way of spelling out indispensability is in terms of theory contribution, but doing so requires adopting inference to the best explanation (IBE). IBE is however sufficient for establishing the conclusion that IA is supposed to establish. Thus, IA is a redundant argument. (shrink)

We investigate the logical and conceptual connections between abductive reasoning construed as a process of belief change, on the one hand, and truth approximation, construed as increasing (estimated) verisimilitude, on the other. We introduce the notion of ‘(verisimilitude-guided) abductive belief change’ and discuss under what conditions abductively changing our theories or beliefs does lead them closer to the truth, and hence tracks truth approximation conceived as the main aim of inquiry. The consequences of our analysis for some recent discussions concerning (...) belief revision aiming at truth approximation and inference to the best explanation are also highlighted. (shrink)

Defences of inference to the best explanation (IBE) frequently associate IBE with scientific realism, the idea that it is reasonable to believe our best scientific theories. I argue that this linkage is unfortunate. IBE does not warrant belief, since the fact that a theory is the best available explanation does not show it to be (even probably) true. What IBE does warrant is acceptance: taking a proposition as a premise in theoretical and/or practical reasoning. We ought to accept our best (...) scientific theories since they are the theories that are most likely to lead to the goal of science, which is that of knowledge. In support of this claim I invoke Bill Lycan's Panglossian reflections regarding Mother Nature.1. (shrink)

After a brief comparison of Aliseda’s account with different approaches to abductive reasoning, I relate abduction, as studied by Aliseda, to idealization, a notion which also occupies a very important role in scientific change, as well as to different ways of dealing with the growth of scientific knowledge understood as a particular kind of non-monotonic process. A particularly interesting kind of abductive reasoning could be that of finding an appropriate concretization case for a theory, originally revealed as extraordinarily success-ful but (...) later discovered to be strictly false or only approximately or ideally true. I try to show this with the example of the Kepler-Newton relation. At the end of the paper, I give criteria in order to construe abduc-tive explanations in correspondence with a reasonable account of empirical progress. (shrink)

Traditionally, the cognitive values have been thought to be a collective pool of considerations in science that frequently trade against each other. I argue here that a finer grained account of the value of cognitive values can help reduce such tensions. I separate the values into three groups, minimal epistemic criteria, pragmatic considerations, and genuine epistemic assurance, based in part on the distinction between values that describe theories per se and values that describe theory-evidence relationships. This allows us to clarify (...) why these values are central to science and what role they should play, while reducing the tensions among them. (shrink)

Weighing complex sets of evidence (i.e., from multiple disciplines and often divergent in implications) is increasingly central to properly informed decision-making. Determining “where the weight of evidence lies” is essential both for making maximal use of available evidence and figuring out what to make of such evidence. Weighing evidence in this sense requires an approach that can handle a wide range of evidential sources (completeness), that can combine the evidence with rigor, and that can do so in a way other (...) experts can assess and critique (transparency). But the democratic context in need of weight-of-evidence analysis also places additional constraints on the process, including communicability of the process to the general public, the need for an approach that can be used across a broad range of contexts (scope), and timeliness of process (practicality). I will compare qualitative and quantitative approaches with respect to both traditional epistemic criteria and criteria that arise from the democratic context, and argue that a qualitative explanatory approach can best meet the criteria and elucidate how to utilize the other approaches. This should not be surprising, as the approach I argue for is the one that most closely tracks general scientific reasoning. (shrink)

Van Fraassen (1989) argues that Inference to the Best Explanation is incoherent in the sense that adopting it as a rule for belief change will make one susceptible to a dynamic Dutch book. The present paper argues against this. A strategy is described that allows us to infer to the best explanation free of charge.

The advent of formal definitions of the simplicity of a theory has important implications for model selection. But what is the best way to define simplicity? Forster and Sober ([1994]) advocate the use of Akaike's Information Criterion (AIC), a non-Bayesian formalisation of the notion of simplicity. This forms an important part of their wider attack on Bayesianism in the philosophy of science. We defend a Bayesian alternative: the simplicity of a theory is to be characterised in terms of Wallace's Minimum (...) Message Length (MML). We show that AIC is inadequate for many statistical problems where MML performs well. Whereas MML is always defined, AIC can be undefined. Whereas MML is not known ever to be statistically inconsistent, AIC can be. Even when defined and consistent, AIC performs worse than MML on small sample sizes. MML is statistically invariant under 1-to-1 re-parametrisation, thus avoiding a common criticism of Bayesian approaches. We also show that MML provides answers to many of Forster's objections to Bayesianism. Hence an important part of the attack on Bayesianism fails. (shrink)

In this paper I argue that Norton's case against Brown's rationalism about thought experiments suffers from serious shortcomings, which relate to the nature of induction.

In this paper art history and visual studies, the disciplines that study visual culture, are presented as a field whose conjectural paradigm can be used to understand the epistemic problems associated with abduction. In order to do so, significant statements, concepts and arguments from the work of several specialists in this field have been highlighted. Their analysis shows the fruitfulness and potential for understanding the study of visual culture as a field that is interwoven with the assumptions of abductive cognition.

In this paper, we present a goal-directed proof procedure for abductive reasoning. This procedure will be compared with Aliseda’s approach based on semantic tableaux. We begin with some comments on Aliseda’s algorithms for computing conjunctive abductions and show that they do not entirely live up to their aims. Next we give a concise account of goal-directed proofs and we show that abductive explanations are a natural spin-off of these proofs. Finally, we show that the goal-directed procedure solves the problems we (...) encountered in Aliseda’s algorithms. (shrink)

The purpose of this paper is to argue that abductive reasoning is part of a cognitive process of interpreting something as being something. The paper holds two fundamental claims. First, it proposes a definition of interpretation as a type of cognitive event. Second, it is argued that in some cases the activity of interpreting is a process to search for plausible assumptions for consistent explanatory hypotheses formation. As a result of these two theses, it is concluded that logic of interpretation (...) could enrich and extend the study of so-called reproduction or hypothesis generation. The treatment given here to abduction is contrasted and integrated into the history of studies on logical pattern of abduction and its applications. (shrink)

Reasoning es una obra monumental de más de mil páginas editada en estrecha colaboración por el filósofo Jonathan E. Adler y el psicólogo Lance J. Rips para esclarecer el intrincado campo de investigación relacionado con los fundamentos de la inferencia y, en general, del razonamiento humano. En la actualidad, en pocos casos va unido el trabajo de compilar y editar textos científicos con el afán enciclopédico: un proyecto editorial que sobrepasa con razón los objetivos de la mayor parte de los (...) libros editados para la recopilación de artículos en torno a un mismo tema de investigación. Reasoning supone un empeño de características enciclopédicas: ha conseguido convertirse en una referencia obligada desde que saliera a la luz en 2008 para ofrecer al lector especialista artículos científicos de las más reputadas y consolidadas voces en aquellos campos de conocimiento presentes ya en los proyectos enciclopédicos europeos del siglo de las luces, a saber: el significado del racionalismo, los límites imputables a la naturaleza del conocimiento humano, las paradojas presentes en la inducción, etc. (shrink)

Las definiciones de argumentación son tan variadas como las distintas posiciones existentes en torno a la pregunta de qué hacemos exactamente cuando argumentamos y cuándo estamos, de hecho, argumentando. Incluso el mismo autor puede ofrecer más de una definición de lo que entiende por argumentación; en parte, porque el problema de la argumentación no se circunscribe a un solo ámbito, ni del conocimiento ni de la vida práctica.

In this paper art history and visual studies, the disciplines that study visual culture, are presented as a field whose conjectural paradigm can be used to understand the epistemic problems associated with abduction. In order to do so, significant statements, concepts and arguments from the work of several specialists in this field have been highlighted. Their analysis shows the fruitfulness and potential for understanding the study of visual culture as a field that is interwoven with the assumptions of abductive cognition.

There are various ``classical'' arguments against abduction as a logic of discovery,especially that (1) abduction is too weak a mode of inference to be of any use, and (2) in basic formulation of abduction the hypothesisis already presupposed to be known, so it is not the way hypotheses are discovered in the first place. In this paper I argue, by bringing forth the idea of strategies,that these counter-arguments are weaker than may appear. The concept of strategies suggests, inter alia, that (...) many inferential moves are taken into account at the same time. This is especially important in abductive reasoning, which is basically a very weak mode of inference. The importance of strategic thinking can already be seen in Charles S.Peirce's early treatments of the topic, and N.R.Hanson's later writings on abduction although they did not use the concept of``strategies.'' On the whole, I am arguing that the focus should be more on methodological processes, and not only on validity considerations, which have dominated the discussion about abduction. (shrink)

This book highlights some of the conceptual problems that still need to be solved and points out a number of fresh philosophical ideas to explore.

Methodological naturalism states (roughly speaking) that only science can be a route to knowledge. This purported piece of knowledge looks self-condemning, however; after all, it was formulated in the armchair, and not in the laboratory. I argue that on a popular (if largely unarticulated) construal of naturalism as inference to the best explanation, methodological naturalism escapes this charge of internal incoherence, and in fact is self-endorsing rather than self-condemning.

The simplicity of a theory seems closely related to how well the theory summarizes individual data points. Think, for example, of classic curve-fitting. It is easy to get perfect data-fit with a ‘‘theory’’ that simply lists each point of data, but such a theory is maximally unsimple (for the data-fit). The simple theory suggests instead that there is one underlying curve that summarizes this data, and we usually prefer such a theory even at some expense in data-fit. In general, it (...) seems, theorizing involves looking for regularities or patterns in our experience, and such regularities are interesting to us because they summarize how our experience goes. We could list all the ravens we’ve encountered, and their colors, or we could summarize.. (shrink)

After a brief comparison of Aliseda’s account with different approaches to abductive reasoning, I relate abduction, as studied by Aliseda, to idealization, a notion which also occupies a very important role in scientific change, as well as to different ways of dealing with the growth of scientific knowledge understood as a particular kind of non-monotonic process. A particularly interesting kind of abductive reasoning could be that of finding an appropriate concretization case for a theory, originally revealed as extraordinarily success-ful but (...) later discovered to be strictly false or only approximately or ideally true. I try to show this with the example of the Kepler-Newton relation. At the end of the paper, I give criteria in order to construe abduc-tive explanations in correspondence with a reasonable account of empirical progress. (shrink)

We initially characterize what we’ll call existence problems as problems where there is evidence that a putative entity exists and this evidence is not easily dismissed; however, the evidence is not adequate to justify the claim that the entity exists, and in particular the entity hasn’t been detected. The putative entity is elusive. We then offer a strategy for determining whether an existence problem is philosophical or scientific. According to this strategy (1) existence problems are characterized in terms of causal (...) roles, and (2) these problems are categorized as scientific or philosophical on the basis of the epistemic context of putative realizers. We argue that the first step of the strategy is necessary to avoid begging the question with regard to categorization of existence problems, and the second step categorizes existence problems on the basis of a distinction between two ways in which an entity can be elusive. This distinction between kinds of elusiveness takes as background a standard account of inference to the best explanation. Applying this strategy, we argue that the existence of a multiverse is a scientific problem. (shrink)

In this paper, I argue that van Fraassen’s “bad lot objection” against Inference to the Best Explanation [IBE] severely misses its mark. First, I show that the objection holds no special relevance to IBE; if the bad lot objection poses a serious problem for IBE, then it poses a serious problem for any inference form whatever. Second, I argue that, thankfully, it does not pose a serious threat to any inference form. Rather, the objection misguidedly blames a form of inference (...) for not achieving what it never set out to achieve in the first place. (shrink)

Human reasoning often involves explanation. In everyday affairs, people reason to hypotheses based on the explanatory power these hypotheses afford; I might, for example, surmise that my toddler has been playing in my office because I judge that this hypothesis delivers a good explanation of the disarranged state of the books on my shelves. But such explanatory reasoning also has relevance far beyond the commonplace. Indeed, explanatory reasoning plays an important role in such varied fields as the sciences, philosophy, theology, (...) medicine, forensics, and law. -/- This dissertation provides an extended study into the logic of explanatory reasoning via two general questions. First, I approach the question of what exactly we have in mind when we make judgments pertaining to the explanatory power that a hypothesis has over some evidence. This question is important to this study because these are the sorts of judgments that we constantly rely on when we use explanations to reason about the world. Ultimately, I introduce and defend an explication of the concept of explanatory power in the form of a probabilistic measure. This formal explication allows us to articulate precisely some of the various ways in which we might reason explanatorily. -/- The second question this dissertation examines is whether explanatory reasoning constitutes an epistemically respectable means of gaining knowledge. I defend the following ideas: The probability theory can be used to describe the logic of explanatory reasoning, the normative standard to which such reasoning attains. Explanatory judgments, on the other hand, constitute heuristics that allow us to approximate reasoning in accordance with this logical standard while staying within our human bounds. The most well known model of explanatory reasoning, Inference to the Best Explanation, describes a cogent, nondeductive inference form. And reasoning by Inference to the Best Explanation approximates reasoning directly via the probability theory in the real world. Finally, I respond to some possible objections to my work, and then to some more general, classic criticisms of Inference to the Best Explanation. In the end, this dissertation puts forward a clearer articulation and novel defense of explanatory reasoning. (shrink)

In a recent article, Graham Oppy offers a lucid and intriguing examination of William Paley's design argument. Oppy sets two goals for his article. First, he sets out to challenge the "almost universal assumption" that Paley's argument is inductive by revealing it actually to be a deductive argument. Second, he attempts to expose Paley's argument as manifestly poor when interpreted in this way. I will argue that Oppy is unsuccessful in accomplishing his first goal, leaving his second goal quite irrelevant. (...) Contrary to Oppy's interpretation, Paley's argument is best interpreted as an inference to the best explanation. (shrink)

This article introduces and defends a probabilistic measure of the explanatory power that a particular explanans has over its explanandum. To this end, we propose several intuitive, formal conditions of adequacy for an account of explanatory power. Then, we show that these conditions are uniquely satisfied by one particular probabilistic function. We proceed to strengthen the case for this measure of explanatory power by proving several theorems, all of which show that this measure neatly corresponds to our explanatory intuitions. Finally, (...) we briefly describe some promising future projects inspired by our account. (shrink)

This book is a sustained defense of the compatibility of the presence of idealizations in the sciences and scientific realism. So, the book is essentially a detailed response to the infamous arguments raised by Nancy Cartwright to the effect that idealization and scientific realism are incompatible.

James McAllister’s 2003 article, “Algorithmic randomness in empirical data” claims that empirical data sets are algorithmically random, and hence incompressible. We show that this claim is mistaken. We present theoretical arguments and empirical evidence for compressibility, and discuss the matter in the framework of Minimum Message Length (MML) inference, which shows that the theory which best compresses the data is the one with highest posterior probability, and the best explanation of the data.

Abduction is a typical theme where logic and philosophy of science meet today: occasionally, with computer science as a go-between. This is just one instance of a broader study of ‘styles of reasoning’, dating back to Bolzano and Peirce. The resulting concern with ‘logical architecture’ moves us closer to cognitive science, and the dynamics of reasoning intertwined with learning and belief revision. The crucial process of self-correction involved here is usually triggered by others, and hence a shared target of logic (...) and philoso-phy of science should be the phenomenon of ‘intelligent interaction’ between rational agents. (shrink)

Inference to the Best Explanation (IBE) and Bayesianism are our two most prominent theories of scientific inference. Are they compatible? Van Fraassen famously argued that they are not, concluding that IBE must be wrong since Bayesianism is right. Writers since then, from both the Bayesian and explanationist camps, have usually considered van Fraassen's argument to be misguided, and have plumped for the view that Bayesianism and IBE are actually compatible. I argue that van Fraassen's argument is actually not so misguided, (...) and that it causes more trouble for compatibilists than is typically thought. Bayesianism in its dominant, subjectivist form, can only be made compatible with IBE if IBE is made subservient to conditionalization in a way that robs IBE of much of its substance and interest. If Bayesianism and IBE are to be fit together, I argue, a strongly objective Bayesianism is the preferred option. I go on to sketch this objectivist, IBE-based Bayesianism, and offer some preliminary suggestions for its development. (shrink)

Comparisons of rival explanations or theories often involve vague appeals to explanatory power. In this paper, we dissect this metaphor by distinguishing between different dimensions of the goodness of an explanation: non-sensitivity, cognitive salience, precision, factual accuracy and degree of integration. These dimensions are partially independent and often come into conflict. Our main contribution is to go beyond simple stipulation or description by explicating why these factors are taken to be explanatory virtues. We accomplish this by using the contrastive-counterfactual approach (...) to explanation and the view of understanding as an inferential ability. By combining these perspectives, we show how the explanatory power of an explanation in a given dimension can be assessed by showing the range of answers it provides to what-if-things-had-been-different questions and the theoretical and pragmatic importance of these questions. Our account also explains intuitions linking explanation to unification or to exhibition of a mechanism. (shrink)