Coherentism maintains that coherent beliefs are more likely to be true than incoherent beliefs, and that coherent evidence provides more confirmation of a hypothesis when the evidence is made coherent by the explanation provided by that hypothesis. Although probabilistic models of credence ought to be well-suited to justifying such claims, negative results from Bayesian epistemology have suggested otherwise. In this essay we argue that the connection between coherence and confirmation should be understood as a relation mediated by the causal relationships (...) among the evidence and a hypothesis, and we offer a framework for doing so by fitting together probabilistic models of coherence, confirmation, and causation. We show that the causal structure among the evidence and hypothesis is sometimes enough to determine whether the coherence of the evidence boosts confirmation of the hypothesis, makes no difference to it, or even reduces it. We also show that, ceteris paribus, it is not the coherence of the evidence that boosts confirmation, but rather the ratio of the coherence of the evidence to the coherence of the evidence conditional on a hypothesis. (shrink)

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. (shrink)

The book can also be used as an excellent text for graduate-level courses in AI, operations research, or applied probability.

Scientific reasoning is—and ought to be—conducted in accordance with the axioms of probability. This Bayesian view—so called because of the central role it accords to a theorem first proved by Thomas Bayes in the late eighteenth ...

Probabilistic models have much to offer to philosophy. We continually receive information from a variety of sources: from our senses, from witnesses, from scientific instruments. When considering whether we should believe this information, we assess whether the sources are independent, how reliable they are, and how plausible and coherent the information is. Bovens and Hartmann provide a systematic Bayesian account of these features of reasoning. Simple Bayesian Networks allow us to model alternative assumptions about the nature of the information sources. (...) Measurement of the coherence of information is a controversial matter: arguably, the more coherent a set of information is, the more confident we may be that its content is true, other things being equal. The authors offer a new treatment of coherence which respects this claim and shows its relevance to scientific theory choice. Bovens and Hartmann apply this methodology to a wide range of much discussed issues regarding evidence, testimony, scientific theories, and voting. Bayesian Epistemology is an essential tool for anyone working on probabilistic methods in philosophy, and has broad implications for many other disciplines. (shrink)

Robustness arguments hold that hypotheses are more likely to be true when they are confirmed by diverse kinds of evidence. Robustness arguments require the confirming evidence to be independent. We identify two kinds of independence appealed to in robustness arguments: ontic independence —when the multiple lines of evidence depend on different materials, assumptions, or theories—and probabilistic independence. Many assume that OI is sufficient for a robustness argument to be warranted. However, we argue that, as typically construed, OI is not a (...) sufficient independence condition for warranting robustness arguments. We show that OI evidence can collectively confirm a hypothesis to a lower degree than individual lines of evidence, contrary to the standard assumption undergirding usual robustness arguments. We employ Bayesian networks to represent the ideal empirical scenario for a robustness argument and a variety of ways in which empirical scenarios can fall short of this ideal. (shrink)

The variety-of-evidence thesis has been criticized by Bovens and Hartmann. This article points to two limitations of their Bayesian model: the conceptualization of unreliable evidential sources as randomizing and the restriction to comparing full independence to full dependence. It is shown that the variety-of-evidence thesis is rehabilitated when unreliable sources are reconceptualized as systematically biased. However, it turns out that allowing for degrees of independence leads to a qualification of the variety-of-evidence thesis: as Bovens and Hartmann claimed, more independence does (...) not always imply stronger confirmation. (shrink)

The article argues for the epistemic rationale of triangulation, namely, the use of multiple and independent sources of evidence. It claims that triangulation is to be understood as causal reasoning from data to phenomenon, and it rationalizes its epistemic value in terms of controlling for likely errors and biases of particular data-generating procedures. This perspective is employed to address objections against triangulation concerning the fallibility and scope of the inference, as well as problems of independence, incomparability, and discordance of evidence. (...) The debate on the existence of social preferences is used as an illustrative case. (shrink)

We appeal to the theory of Bayesian Networks to model different strategies for obtaining confirmation for a hypothesis from experimental test results provided by less than fully reliable instruments. In particular, we consider (i) repeated measurements of a single test consequence of the hypothesis, (ii) measurements of multiple test consequences of the hypothesis, (iii) theoretical support for the reliability of the instrument, and (iv) calibration procedures. We evaluate these strategies on their relative merits under idealized conditions and show some surprising (...) repercussions on the variety-of-evidence thesis and the Duhem-Quine thesis. (shrink)