Online research in philosophy

This paper discusses the nature and the status of inference to the best explanation (IBE). We (1) outline the foundational role given IBE by its defenders and the arguments of critics who deny it any place at all; (2) argue that, on the two main conceptions of explanation, IBE cannot be a foundational inference rule; (3) sketch an account of IBE that makes it contextual and dependent on substantive empirical assumptions, much as simplicity seems to be; (4) show how that account avoids the critics' complaints and leaves IBE an important role; and (5) sketch how our account can clarify debates over IBE in arguments for scientific realism.

This paper evaluates four competing psychological explanations for why the jury in the O.J. Simpson murder trial reached the verdict they did: explanatory coherence, Bayesian probability theory, wishful thinking, and emotional coherence. It describes computational models that provide detailed simulations of juror reasoning for explanatory coherence, Bayesian networks, and emotional coherence, and argues that the latter account provides the most plausible explanation of the jury's decision.

A measure of coherence is said to be truth conducive if and only if a higher degree of coherence (as measured) results in a higher likelihood of truth. Recent impossibility results strongly indicate that there are no (non-trivial) probabilistic coherence measures that are truth conducive. Indeed, this holds even if truth conduciveness is understood in a weak ceteris paribus sense (Bovens & Hartmann, 2003, Bayesian epistemology. New York, Oxford: Oxford University Press; Olsson, 2005, Against coherence: Truth probability and justification. Oxford: Oxford University Press). This raises the problem of how coherence could nonetheless be an epistemically important property. Our proposal is that coherence may be linked in a certain way to reliability. We define a measure of coherence to be reliability conducive if and only if a higher degree of coherence (as measured) results in a higher probability that the information sources are reliable. Restricting ourselves to the most basic case, we investigate which coherence measures in the literature are reliability conducive. It turns out that, while a number of measures fail to be reliability conducive, except possibly in a trivial and uninteresting sense, Shogenji’s measure and several measures generated by Douven and Meijs’s recipe are notable exceptions to this rule.

Many philosophers of science have argued that a set of evidence that is "coherent" confirms a hypothesis which explains such coherence. In this paper, we examine the relationships between probabilistic models of all three of these concepts: coherence, confirmation, and explanation. For coherence, we consider Shogenji's measure of association (deviation from independence). For confirmation, we consider several measures in the literature, and for explanation, we turn to Causal Bayes Nets and resort to causal structure and its constraint on probability. All else equal, we show that focused correlation, which is the ratio of the coherence of evidence and the coherence of the evidence conditional on a hypothesis, tracks confirmation. We then show that the causal structure of the evidence and hypothesis can put strong constraints on how coherence in the evidence does or does not translate into confirmation of the hypothesis.

This paper aims to contribute to our understanding of the notion of coherence by explicating in probabilistic terms, step by step, what seem to be our most basic intuitions about that notion, to wit, that coherence is a matter of hanging or fitting together, and that coherence is a matter of degree. A qualitative theory of coherence will serve as a stepping stone to formulate a set of quantitative measures of coherence, each of which seems to capture well the aforementioned intuitions. Subsequently it will be argued that one of those measures does better than the others in light of some more specific intuitions about coherence. This measure will be defended against two seemingly obvious objections.

It is shown that the probabilistic theories of coherence proposed up to now produce a number of counter-intuitive results. The last section provides some reasons for believing that no probabilistic measure will ever be able to adequately capture coherence. First, there can be no function whose arguments are nothing but tuples of probabilities, and which assigns different values to pairs of propositions {A, B} and {A, C} if A implies both B and C, or their negations, and if P(B)=P(C). But such sets may indeed differ in their degree of coherence. Second, coherence is sensitive to explanatory relations between the propositions in question. Explanation, however, can hardly be captured solely in terms of probability.

It is well known that the process of scientific inquiry, according to Peirce, is drivenby three types of inference, namely abduction, deduction, and induction. What isbehind these labels is, however, not so clear. In particular, the common identificationof abduction with Inference to the Best Explanation (IBE) begs the question,since IBE appears to be covered by Peirce's concept of induction, not that of abduction.Consequently, abduction ought to be distinguished from IBE, at least on Peirce's account. The main aim of the paper, however, is to show that this distinction is most relevant with respect to current problems in philosophy of science and epistemology (like attempts to supply suitable notions of realism and truth as well as related concepts like coherence and unification). In particular, I also try to show that (and in what way) Peirce's inferential triad can function as a method that ensures both coherence and correspondence. It is in this respect that his careful distinction between abduction and induction (or IBE) ought to be heeded.

Two of the probabilistic measures of coherence discussed in this paper take probabilistic dependence into account and so depend on prior probabilities in a fundamental way. An example is given which suggests that this prior-dependence can lead to potential problems. Another coherence measure is shown to be independent of prior probabilities in a clearly defined sense and consequently is able to avoid such problems. The issue of prior-dependence is linked to the fact that the first two measures can be understood as measures of coherence as striking agreement, while the third measure represents coherence as agreement. Thus, prior (in)dependence can be used to distinguish different conceptions of coherence.

This article generalizes the explanationist account of inference to the best explanation (IBE). It draws a clear distinction between IBE and abduction and presents abduction as the first step of IBE. The second step amounts to the evaluation of explanatory power, which consist in the degree of explanatory virtues that a hypothesis exhibits. Moreover, even though coherence is the most often cited explanatory virtue, on pain of circularity, it should not be treated as one of the explanatory virtues. Rather, coherence should be equated with explanatory power and considered to be derivable from the other explanatory virtues: unification, explanatory depth and simplicity.

A measure of coherence is said to be reliability conducive if and only if a higher degree of coherence (as measured) among testimonies implies a higher probability that the witnesses are reliable. Recently, it has been proved that several coherence measures proposed in the literature are reliability conducive in scenarios of equivalent testimonies (Olsson and Schubert 2007; Schubert, to appear). My aim is to investigate which coherence measures turn out to be reliability conducive in the more general scenario where the testimonies do not have to be equivalent. It is shown that four measures are reliability conducive in the present scenario, all of which are ordinally equivalent to the Shogenji measure. I take that to be an argument for the Shogenji measure being a fruitful explication of coherence.