Testimonial evidence that is particularly helpful to confirmation combines agreement on some content with variation of detail. I examine the phenomenon of “undesigned coincidences” from a probabilistic point of view to explain how varied reports, including those that dovetail in detail, assist confirmation of an hypothesis. The formal analysis uses recent work in probability theory surrounding the concepts of dependence, independence, and varied evidence. I also discuss the connection between these types of report connections and an hypothesis about the reliability (...) of the sources involved. (shrink)

The Variety of Evidence Thesis (VET) says that (ceteris paribus) the more diverse (or varied) of two bodies of evidence is the more confirmatory of a hypothesis H. Two recent types of Bayesian explication of VET account for the intuitive force of VET by defining variety as some function of the probabilities of the propositions which collectively constitute a body of evidence. I show that these two accounts of VET are not tracking a meaningful property of bodies of evidence, but (...) rather are tracking artifacts of how those bodies of evidence are described. According to each account, whether a body of evidence is more varied than another depends on how the bodies are split into parts. Furthermore, for each type of account there exists a way to redescribe the total evidence such that any two totalities are equally varied. ‡I would like to thank Elliott Sober for comments on multiple drafts of this paper, and Malcolm Forster, John Koolage, and Joel Velasco for comments on a verbal delivery. †To contact the author, please write to: Department of Philosophy, University of Wisconsin-Madison, 5185 Helen C. White Hall, 600 North Park Street, Madison, WI 53706; e-mail: [email protected]. (shrink)

Our epistemic access to the past is infamously patchy: historical information degrades and disappears and bygone eras are often beyond the reach of repeatable experiments. However, historical scientists have been remarkably successful at uncovering and explaining the past. I argue that part of this success is explained by the exploitation of dependencies between historical events, entities, and processes. For instance, if sauropod dinosaurs were hot blooded, they must have been gluttons; the high-energy demands of endothermy restrict sauropod grazing strategies. Understanding (...) such dependencies extends our reach into the past in spite of incomplete data. In addition, this serves as a counterexample to two accounts of method in the historical sciences. By one, historical science proceeds by identifying ‘smoking guns’: traces that discriminate between live hypotheses. By the other, historical hypotheses are supported by consilience: the convergence of independent lines of evidence. However, testing for ‘coherency’ between past hypotheses also plays a critical role in historical confirmation. Just as historical scientists exploit dependencies between past entities and present entities to infer what the past was like, they also exploit dependencies between past entities themselves. I do not suggest that archetypical historical science proceeds in this manner. Rather, the lesson I draw is that historical methodology cannot be characterized as archetypically relying on one method or another. Historical science is at base opportunistic, and is resistant to unitary analyses. 1 Introduction2 Snowballs and Explosions: The Basic Idea3 Were Sauropods Endothermic?4 Dependent Entities and Interdependent Explanations5 Smoking Guns and Consilience. (shrink)

Complaints are common about the arbitrary and conservative bias of special-majority rules. Such complaints, however, apply to asymmetrical versions of those rules alone. Symmetrical special-majority rules remedy that defect, albeit at the cost of often rendering no determinate verdict. Here what is formally at stake, both procedurally and epistemically, is explored in the choice between those two forms of special-majority rule and simple-majority rule; and practical ways are suggested of resolving matters left open by symmetrical special-majority rules – such as (...) ‘judicial extrapolation’ or ‘subsidiarity’ in a federal system. (shrink)

Crupi et al. (2008) offer a confirmation-theoretic, Bayesian account of the conjunction fallacy—an error in reasoning that occurs when subjects judge that Pr( h 1 & h 2 | e ) > Pr( h 1 | e ). They introduce three formal conditions that are satisfied by classical conjunction fallacy cases, and they show that these same conditions imply that h 1 & h 2 is confirmed by e to a greater extent than is h 1 alone. Consequently, they suggest (...) that people are tracking this confirmation relation when they commit conjunction fallacies. I offer three experiments testing the merits of Crupi et al.’s account specifically and confirmation-theoretic accounts of the conjunction fallacy more generally. The results of Experiment 1 show that, although Crupi et al.’s conditions do seem to be causally linked to the conjunction fallacy, they are not necessary for it; there exist cases that do not meet their three conditions in which subjects still tend to commit the fallacy. The results of Experiments 2 and 3 show that Crupi et al.’s conditions, and those offered by other confirmation-theoretic accounts of the fallacy, are not sufficient for the fallacy either; there exist cases that meet all three of CFT’s conditions in which subjects do not tend to commit the fallacy. Additionally, these latter experiments show that such confirmation-theoretic conditions are at best only weakly causally relevant to the presence of the conjunction fallacy. Given these findings, CFT’s account specifically, and any general confirmation-theoretic account more broadly, falls short of offering a satisfying explanation of the presence of the conjunction fallacy. (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)

In this article, I present a serious problem for confirmation measure Z.

This essay addresses the methodology of philosophy of science and illustrates how formal and empirical methods can be fruitfully combined. Special emphasis is given to the application of experimental methods to confirmation theory and to recent work on the conjunction fallacy, a key topic in the rationality debate arising from research in cognitive psychology. Several other issue can be studied in this way. In the concluding section, a brief outline is provided of three further examples.

What sort of evidence can confer the strongest support to a hypothesis? A natural answer is that the evidence entails the hypothesis. Roush (Tracking Truth: Knowledge, Evidence, and Science, Clarendon Press, Oxford, 2005) claims that the likelihood ratio measure of degree of incremental support can deliver this intuitively natural result, and regards it as unifying “[the] account of induction and deduction in the only way that makes sense” (p. 163). In this paper, we highlight a difficulty in the treatment of (...) this case, and question the great significance that is attached to this measure and its alleged capacity to accommodate the logicality requirement. We contrast the likelihood ratio measure with other measures (such as the Kemeny–Oppenheim measure and the difference measure), and argue that problems still emerge in light of tensions with plausible requirements for confirmation measures more generally. (shrink)

I propose a measure of dependence that relates a set of items of evidence to an hypothesis H and to H's negation. I dub this measure relative consilience and propose a method for using it as a correction factor for dependence among items of evidence. Using RC, I examine collusion and testimonial independence, the value of diverse evidence, and the strengthening of otherwise weak or non-existent cases. RC provides a valuable tool for formal epistemologists interested in analyzing cumulative case arguments.