Inference to the Best Explanation Made Coherent

Theory and Decision, 2002

The justification of Bayes' rule by cognitive rationality principles is undertaken by extending the propositional axiom systems usually proposed in two contexts of belief change: revising and updating. Probabilistic belief change axioms are introduced, either by direct transcription of the set-theoretic ones, or in a stronger way but nevertheless in the spirit of the underlying propositional principles. Weak revising axioms are shown to be satisfied by a General Conditioning rule, extending Bayes' rule but also compatible with others, and weak updating axioms by a General Imaging rule, extending Lewis' rule. Strong axioms (equivalent to the Miller–Popper axiom system) are necessary to justify Bayes' rule in a revising context, and justify in fact an extended Bayes' rule which applies, even if the message has zero probability.

The Philosophical Quarterly, 2013

European Journal for Philosophy of Science

The Problem of Old Evidence (POE) states that Bayesian confirmation theory cannot explain why a theory H can be confirmed by a piece of evidence E already known. Different dimensions of POE have been highlighted. Here, I consider the dynamic and static dimension. In the former, we want to explain how the discovery that H accounts for E confirms H. In the latter, we want to understand why E is and will be a reason to prefer H over its competitors. The aim of the paper is twofold. Firstly, I stress that two recent solutions to the dynamic dimension, recently proposed by Eva and Hartmann, can be read in terms of Inference to the Best Explanation (IBE). On this basis, I gauge the weaknesses and strengths of the two models by showing that the two authors endorse a particular formulation of IBE, and that it is still unsure if it is the one descriptively used. Moreover, I contend that, while one condition of their first model is not expression of this formulation, the only condition of their second model is. Secondly, I focus on the static dimension of POE which, now, has to be expressed in IBE terms. To solve it, I rely on the counterfactual approach, and on a version of IBE in which explanatory considerations help to evaluate the terms in Bayes' theorem. However, it turns out that the problems of the counterfactual approach recur even when it is used to solve the static POE in IBE terms.

How do we reconcile the claim of Bayesianism to be a correct normative theory of scientific reasoning with the explanationists' claim that Inference to the Best Explanation provides a correct description of our inferential practices? I first develop Peter Lipton's approach to compatibilism and then argue that three challenges remain, focusing in particular on the idea that IBE can lead to knowledge. Answering those challenges requires renouncing standard Bayesianism's commitment to personalism, while also going beyond objective Bayesianism regarding the constraints on good priors. The result is a non-standard, super-objective Bayesianism that identifies probabilities with evaluations of plausibil-ity in the light of the evidence, conforming to Williamson's account of evidential probability.

We provide a novel Bayesian justification of inference to the best explanation (IBE). More specifically, we present conditions under which explanatory considerations can provide a significant confirmatory boost for hypotheses that provide the best explanation of the relevant evidence. Furthermore, we show that the proposed Bayesian model of IBE is able to deal naturally with the best known criticisms of IBE such as van Fraassen’s ‘bad lot’ argument.

Proceedings of the Ninth Conference on Uncertainty in …, 1993

In a probability-based reasoning system, Bayes' theorem and its variations are often used to revise the system's beliefs. However, if the explicit con ditions and the implicit conditions of probability assignments are properly distinguished, it follows that Bayes' theorem is not a generally applicable revision rule. Upon properly distinguishing be lief revision from belief updating, we see that Jeffrey's rule and its variations are not revision rules, either. Without these distinctions, the lim itation of the Bayesian approach is often ignored or underestimated. Revision, in its general form, cannot be done in the Bayesian approach, because a probability distribution function alone does not contain the information needed by the operation. 1. mE {0, 1 }, that is, the new evidence is binary-valued, so it can be simply written as A or-.A. 2. A E S, otherwise its probability is undefined. 3. Pc(A) > 0, otherwise it cannot be used as a denomi nator in Bayes' theorem. 3 EXPLICIT CONDITION VS. IMPLICIT CONDITION Why do we need a revision rule in a plausible reasoning system?

Theoria, 2008

Bayesianism and Inference to the best explanation (IBE) are two different models of inference. Recently there has been some debate about the possibility of "bayesianizing" IBE. Firstly I explore several alternatives to include explanatory considerations in Bayes's Theorem. Then I distinguish two different interpretations of prior probabilities: "IBE-Bayesianism" (IBE-Bay) and "frequentist-Bayesianism" (Freq-Bay). After detailing the content of the latter, I propose a rule for assessing the priors. I also argue that Freq-Bay: (i) endorses a role for explanatory value in the assessment of scientific hypotheses; (ii) avoids a purely subjectivist reading of prior probabilities; and (iii) fits better than IBE-Bayesianism with two basic facts about science, i.e., the prominent role played by empirical testing and the existence of many scientific theories in the past that failed to fulfil their promises and were subsequently abandoned.

Andrés Rivadulla: Éxito, razón y cambio en física, Madrid: Ed. Trotta, 2004

In these pages I offer my solution to the problem of inductive probability of theories. Against the existing expectations in certain areas of the current philosophy of science, I argue that Bayes’s Theorem does not constitute an appropriate tool to assess the probability of theories and that we would do well to banish the question about how likely a certain scientific theory is to be true, or to what extent one theory is more likely true than another. Although I agree with Popper that inductive probability is impossible, I disagree with him in the way Sir Karl presents his argument, as I have showed elsewhere, so my proof is completely different. The argument I present in this paper is based on applying Bayes’s Theorem to specific situations that show its inefficiency both in the case of whether a hypothesis becomes all the more likely true the greater the empirical evidence that supports it, as whether the probability calculus allows to identify a given hypothesis from a set of hypotheses incompatible with each other as the most likely true.

Synthese, 2007

The British Journal for the Philosophy of Science, 2021

When a proposition is established, it can be taken as evidence for other propositions. Can the Bayesian theory of rational belief and action provide an account of establishing? I argue that it can, but only if the Bayesian is willing to endorse objective constraints on both probabilities and utilities, and willing to deny that it is rationally permissible to defer wholesale to expert opinion. I develop a new account of deference that accommodates this latter requirement.