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)

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)

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)

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)

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.

Despite Richard Dawkins’s recent claim that the standard philosophical problem of God’s existence is in fact a scientific problem, he suggests no strategy for determining whether an existence problem is scientific as opposed to philosophical. We offer such a strategy, the de-constitutionalizing strategy, according to which (1) existence problems are characterized in terms of causal roles, and (2) the categorization of these problems as philosophical or scientific is made in terms of the epistemic context of potential realizers. We’ll 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, in turn, is supported by a theoretical account of inference to the best explanation. We then apply this strategy to argue that the existence of God is currently a philosophical problem. We end with a further case intended to <span class='Hi'>test</span> the usefulness of the strategy: the categorization of the existence of a multiverse. (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)

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.

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)