Diversity of evidence is widely claimed to be crucial for evidence amalgamation to have distinctive epistemic merits. Bayesian epistemologists capture this idea in the variety-of-evidence thesis: ceteris paribus, the strength of confirmation of a hypothesis by an evidential set increases with the diversity of the evidential elements in that set. Yet, formal exploration of this thesis has shown that it fails to be generally true. This article demonstrates that the thesis fails in even more circumstances than recent results would lead (...) us to expect. Most importantly, it can fail whatever the chance that the evidential sources are unreliable. Our results hold for two types of degrees of variety: reliability independence and testable aspect independence. We conclude that the variety-of-evidence thesis can, at best, be interpreted as an exception-prone rule of thumb. (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)

Some authors claim that minimal models have limited epistemic value (Fumagalli, 2016; Grüne-Yanoff, 2009a). Others defend the epistemic benefits of modelling by invoking the role of robustness analysis for hypothesis confirmation (see, e.g., Levins, 1966; Kuorikoski et al., 2010) but such arguments find much resistance (see, e.g., Odenbaugh & Alexandrova, 2011). In this paper, we offer a Bayesian rationalization and defence of the view that robustness analysis can play a confirmatory role, and thereby shed light on the potential of minimal (...) models for hypothesis confirmation. We illustrate our argument by reference to a case study from macroeconomics. At the same time, we also show that there are cases in which robustness analysis is detrimental to confirmation. We characterize these cases and link them to recent investigations on evidential variety (Landes, 2020b, 2021; Osimani and Landes, forthcoming). We conclude that robustness analysis over minimal models can confirm, but its confirmatory value depends on concrete circumstances. (shrink)

APA PsycNET abstract: This is the first volume of a two-volume work on Probability and Induction. Because the writer holds that probability logic is identical with inductive logic, this work is devoted to philosophical problems concerning the nature of probability and inductive reasoning. The author rejects a statistical frequency basis for probability in favor of a logical relation between two statements or propositions. Probability "is the degree of confirmation of a hypothesis (or conclusion) on the basis of some given evidence (...) (or premises)." Furthermore, all principles and theorems of inductive logic are analytic, and the entire system is to be constructed by means of symbolic logic and semantic methods. This means that the author confines himself to the formalistic procedures of word and symbol systems. The resulting sentence or language structures are presumed to separate off logic from all subjectivist or psychological elements. Despite the abstractionism, the claim is made that if an inductive probability system of logic can be constructed it will have its practical application in mathematical statistics, and in various sciences. 16-page bibliography. (PsycINFO Database Record (c) 2016 APA, all rights reserved). (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)

How we can reliably draw inferences from data, evidence and/or experience has been and continues to be a pressing question in everyday life, the sciences, politics and a number of branches in philosophy (traditional epistemology, social epistemology, formal epistemology, logic and philosophy of the sciences). In a world in which we can now longer fully rely on our experiences, interlocutors, measurement instruments, data collection and storage systems and even news outlets to draw reliable inferences, the issue becomes even more pressing. (...) While we were working on this question using a formal epistemology approach Landes and Osimani (2020); De Pretis et al. (2019); Osimani and Landes (2020); Osimani (2020), we realised that the width of current active interests in the notion of reliability was much broader than we initially thought. Given the breadth of approaches and angles present in philosophy (even in this journal Schubert 2012; Avigad 2021; Claveau and Grenier 2019; Kummerfeld and Danks 2014; Landes 2021; Trpin et al. 2021; Schippers 2014; Schindler 2011; Kelly et al. 2016; Mayo-Wilson 2014; Olsson and Schubert 2007; Pittard 2017), we thought that it would be beneficial to provide a forum for an open exchange of ideas, in which philosophers working in different paradigms could come together. Our call for expression of interest received a great variety of promised manuscripts, the variety is reflected in the published papers. They range from fields far away from our own interests such as quantum probabilities de Ronde et al. (2021), evolvable software systems Primiero et al. (2021), to topics closer to our own research in the philosophy of medicine Lalumera et al. (2020), psychology Dutilh et al. (2021), traditional epistemology Dunn (2021); Tolly (2021) to finally close shared interests in formal epistemology Romero and Sprenger (2021) even within our own department Merdes et al. (2021). Our job is now to reliably inform you about all the contributions in the papers in this special issue. Unfortunately, that task is beyond our capabilities. What we can and instead do is to summarise the contributed papers to inform your reliable inference to read them all in great detail. (shrink)

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)

It is surely obvious that medicine, like any other rational activity, must be based on evidence. The interest is in the details: how exactly are the general principles of the logic of evidence to be applied in medicine? Focussing on the development, and current claims of the ‘Evidence-Based Medicine’ movement, this article raises a number of difficulties with the rationales that have been supplied in particular for the ‘evidence hierarchy’ and for the very special role within that hierarchy of randomized (...) controlled trials (and meta-analyses of the results of randomized controlled trials). The point is not at all to question the application of a scientific approach to evidence in medicine, but, on the contrary, to indicate a number of areas where philosophers of science can contribute to a proper implementation of exactly that scientific-evidential approach. (shrink)

Amalgamating evidence from heterogeneous sources and across levels of inquiry is becoming increasingly important in many pure and applied sciences. This special issue provides a forum for researchers from diverse scientific and philosophical perspectives to discuss evidence amalgamation, its methodologies, its history, its pitfalls, and its potential. We situate the contributions therein within six themes from the broad literature on this subject: the variety-of-evidence thesis, the philosophy of meta-analysis, the role of robustness/sensitivity analysis for evidence amalgamation, its bearing on questions (...) of extrapolation and external validity of experiments, its connection with theory development, and its interface with causal inference, especially regarding causal theories of cancer. (shrink)

Varied evidence confirms more strongly than less varied evidence, ceteris paribus. This epistemological Variety of Evidence Thesis enjoys widespread intuitive support. We put forward a novel explication of one notion of varied evidence and the Variety of Evidence Thesis within Bayesian models of scientific inference by appealing to measures of entropy. Our explication of the Variety of Evidence Thesis holds in many of our models which also pronounce on disconfirmatory and discordant evidence. We argue that our models pronounce rightly. Against (...) a backdrop of failures of the Variety of Evidence Thesis, the intuitive case for the Variety of Evidence Thesis emerges strengthened. Our models do however not support the general case for the thesis since our explication of it fails to hold in certain cases. The parameter space of this failure is explored and an explanation for the failure is offered. (shrink)

Varied evidence for a hypothesis confirms it more strongly than less varied evidence, ceteris paribus. This epistemological Variety of Evidence Thesis enjoys long-standing widespread intuitive support. Recent literature has raised serious doubts that the correlational approach of explicating the thesis can vindicate it. By contrast, the eliminative approach due to Horwich vindicates the Variety of Evidence Thesis but only within a relatively narrow domain. I investigate the prospects of extending the eliminative approach to a larger domain by considering a larger (...) class of sensible explications of evidential variety. For a large subclass class of such explications I show how to construct cases in which the less diverse body of evidence for a hypothesis confirms more strongly. I hence argue that these prospects are dire since the eliminative approach widely fails to vindicate the thesis. (shrink)

Recent work in social epistemology has shown that, in certain situations, less communication leads to better outcomes for epistemic groups. In this paper, we show that, ceteris paribus, a Bayesian agent may believe less strongly that a single agent is biased than that an entire group of independent agents is biased. We explain this initially surprising result and show that it is in fact a consequence one may conceive on the basis of commonsense reasoning.

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)

Social scientists use many different methods, and there are often substantial disagreements about which method is appropriate for a given research question. In response to this uncertainty about the relative merits of different methods, W. E. B. Du Bois advocated for and applied “methodological triangulation”. This is to use multiple methods simultaneously in the belief that, where one is uncertain about the reliability of any given method, if multiple methods yield the same answer that answer is confirmed more strongly than (...) it could have been by any single method. Against this, methodological purists believe that one should choose a single appropriate method and stick with it. Using tools from voting theory, we show Du Boisian methodological triangulation to be more likely to yield the correct answer than purism, assuming the scientist is subject to some degree of diffidence about the relative merits of the various methods. This holds even when in fact only one of the methods is appropriate for the given research question. (shrink)

Wayne (1995) critiques the Bayesian explication of the confirmational significance of evidential diversity (CSED) offered by Horwich (1982). Presently, I argue that Wayne’s reconstruction of Horwich’s account of CSED is uncharitable. As a result, Wayne’s criticisms ultimately present no real problem for Horwich. I try to provide a more faithful and charitable rendition of Horwich’s account of CSED. Unfortunately, even when Horwich’s approach is charitably reconstructed, it is still not completely satisfying.

There is currently no viable alternative to the Bayesian analysis of scientific inference, yet the available versions of Bayesianism fail to do justice to several aspects of the testing and confirmation of scientific hypotheses. Bayes or Bust? provides the first balanced treatment of the complex set of issues involved in this nagging conundrum in the philosophy of science. Both Bayesians and anti-Bayesians will find a wealth of new insights on topics ranging from Bayes’s original paper to contemporary formal learning theory.In (...) a paper published posthumously in 1763, the Reverend Thomas Bayes made a seminal contribution to the understanding of "analogical or inductive reasoning." Building on his insights, modem Bayesians have developed an account of scientific inference that has attracted numerous champions as well as numerous detractors. Earman argues that Bayesianism provides the best hope for a comprehensive and unified account of scientific inference, yet the presently available versions of Bayesianisin fail to do justice to several aspects of the testing and confirming of scientific theories and hypotheses. By focusing on the need for a resolution to this impasse, Earman sharpens the issues on which a resolution turns. John Earman is Professor of History and Philosophy of Science at the University of Pittsburgh. (shrink)

There is currently no viable alternative to the Bayesian analysis of scientific inference, yet the available versions of Bayesianism fail to do justice to several aspects of the testing and confirmation of scientific hypotheses. Bayes or Bust? provides the first balanced treatment of the complex set of issues involved in this nagging conundrum in the philosophy of science. Both Bayesians and anti-Bayesians will find a wealth of new insights on topics ranging from Bayes's original paper to contemporary formal learning theory. (...) In a paper published posthumously in 1763, the Reverend Thomas Bayes made a seminal contribution to the understanding of "analogical or inductive reasoning." Building on his insights, modem Bayesians have developed an account of scientific inference that has attracted numerous champions as well as numerous detractors. Earman argues that Bayesianism provides the best hope for a comprehensive and unified account of scientific inference, yet the presently available versions of Bayesianisin fail to do justice to several aspects of the testing and confirming of scientific theories and hypotheses. By focusing on the need for a resolution to this impasse, Earman sharpens the issues on which a resolution turns. John Earman is Professor of History and Philosophy of Science at the University of Pittsburgh. (shrink)

Objective Bayesian epistemology invokes three norms: the strengths of our beliefs should be probabilities, they should be calibrated to our evidence of physical probabilities, and they should otherwise equivocate sufficiently between the basic propositions that we can express. The three norms are sometimes explicated by appealing to the maximum entropy principle, which says that a belief function should be a probability function, from all those that are calibrated to evidence, that has maximum entropy. However, the three norms of objective Bayesianism (...) are usually justified in different ways. In this paper we show that the three norms can all be subsumed under a single justification in terms of minimising worst-case expected loss. This, in turn, is equivalent to maximising a generalised notion of entropy. We suggest that requiring language invariance, in addition to minimising worst-case expected loss, motivates maximisation of standard entropy as opposed to maximisation of other instances of generalised entropy. Our argument also provides a qualified justification for updating degrees of belief by Bayesian conditionalisation. However, conditional probabilities play a less central part in the objective Bayesian account than they do under the subjective view of Bayesianism, leading to a reduced role for Bayes’ Theorem. (shrink)

In robustness analysis, hypotheses are supported to the extent that a result proves robust, and a result is robust to the extent that we detect it in diverse ways. But what precise sense of diversity is at work here? In this paper, I show that the formal explications of evidential diversity most often appealed to in work on robustness – which all draw in one way or another on probabilistic independence – fail to shed light on the notion of diversity (...) relevant to robustness analysis. I close by briefly outlining a promising alternative approach inspired by Horwich’s (1982) eliminative account of evidential diversity. (shrink)