How can we determine the adequacy of a probabilistic coherence measure? A widely accepted approach to this question besides formulating adequacy constraints is to employ paradigmatic test cases consisting of a scenario providing a joint probability distribution over some specified set of propositions coupled with a normative coherence assessment for this set. However, despite the popularity of the test case approach, a systematic evaluation of the proposed test cases is still missing. This paper’s aim is to change this. Using a (...) custom written computer program for the necessary probabilistic calculations a large number of coherence measures in an extensive collection of test cases is examined. The result is a detailed overview of the test case performance of any probabilistic coherence measures proposed so far. It turns out that none of the popular coherence measures such as Shogenji’s, Glass’ and Olsson’s, Fitelson’s or Douven and Meijs’ but two rather unnoticed measures perform best. This, however, does not mean that the other measures can be rejected straightforwardly. Instead, the results presented here are to be understood as a contribution among others to the project of finding adequate probabilistic coherence measures. (shrink)

Coherence is the property of propositions hanging or fitting together. Intuitively, adding a proposition to a set of propositions should be compatible with either increasing or decreasing the set’s degree of coherence. In this paper we show that probabilistic coherence measures based on relative overlap are in conflict with this intuitive verdict. More precisely, we prove that according to the naive overlap measure it is impossible to increase a set’s degree of coherence by adding propositions and that according to the (...) refined overlap measure no set’s degree of coherence exceeds the degree of coherence of its maximally coherent subset. We also show that this result carries over to all other subset-sensitive refinements of the naive overlap measure. As both results stand in sharp contrast to elementary coherence intuitions, we conclude that extant relative overlap measures of coherence are inadequate. (shrink)

Over the years several non-equivalent probabilistic measures of coherence have been discussed in the philosophical literature. In this paper we examine these measures with respect to their empirical adequacy. Using test cases from the coherence literature as vignettes for psychological experiments we investigate whether the measures can predict the subjective coherence assessments of the participants. It turns out that the participants’ coherence assessments are best described by Roche’s coherence measure based on Douven and Meijs’ average mutual support approach and the (...) conditional probability. (shrink)

Jennifer Lackey has recently presented a new and lucid analysis of the notion ofjustified group belief, i.e. a set of individually necessary and jointly sufficient conditions for a group to justifiedly believe some proposition. In this paper, however, I argue that theanalysansshe proposes is too narrow: one of the conditions she takes to be necessary for justified group belief is not necessary. To substantiate this claim, I present a potential counterexample to Lackey's analysis where a group knows and thus justifiedly (...) believes some proposition but there is no single group member who actually believes that proposition. I close by defending the example against the objection that the group in question does notknowbut is at mostin a positionto know the target proposition. (shrink)

Relative overlap measures of coherence have recently been shown to have two devastating properties: according to the plain relative overlap measure, the degree of coherence of any set of propositions cannot be increased by adding further propositions, and according to the refined relative overlap measure, no set can be more coherent than its most coherent two-element subset. This result has been taken to rule out relative overlap as a foundation for a probabilistic explication of coherence. The present paper shows that (...) this view is premature: we propose a relative overlap measure that does not fall victim to the two properties. The guiding idea is to employ a well-established recipe for the construction of coherence measures and to adapt it to the idea of relative overlap. We show that this new measure keeps up with, or even outperforms, former overlap measures in a set of desiderata for coherence measures and a collection of popular test cases. This result re-establishes relative overlap as a candidate for a proper formalization of coherence. (shrink)

Coherence is a property of propositions hanging together or dovetailing with each other. About two decades ago, formal epistemologists started to engage in the project of explicating the seemingly elusive concept of coherence by means of probability theory. Since then, a plethora of coherence measures have been discussed in the literature. In this paper, we propose a general framework for coherence measures that encompasses the different frameworks of deviation measures, overlap measures and mutual support measures of coherence. Above that we (...) show that some of the new measures that can be obtained outperform existing coherence measures in important respects. (shrink)

Tomoji Shogenji is generally assumed to be the first author to have presented a probabilistic measure of coherence. Interestingly, Rudolf Carnap in his Logical Foundations of Probability discussed a function that is based on the very same idea, namely his well-known relevance measure. This function is largely neglected in the coherence literature because it has been proposed as a measure of evidential support and still is widely conceived as such. The aim of this paper is therefore to investigate Carnap’s measure (...) regarding its plausibility as a candidate for a probabilistic measure of coherence by comparing it to Shogenji’s. It turns out that both measures satisfy and violate the same adequacy constraints, despite not being ordinally equivalent exhibit a strong correlation with each other in a Monte Carlo simulation and perform similarly in a series of test cases for probabilistic coherence measures. (shrink)

According to Goldman and Olsson's so‐called conditional probability solution to the extra‐value‐of‐knowledge problem, knowledge is more valuable than mere true belief because having the former makes the acquisition of further similar true beliefs in the future more likely than having the latter does. Unfortunately, however, several philosophers have rejected the comparative probability claim Goldman and Olsson's solution is based on. In this paper, I present a new argument in defence of this claim. More precisely, I point out a highly plausible (...) necessary and sufficient condition for the latter and argue for its truth by bringing together confirmation‐theoretic and reliabilist considerations. I also explain where a number of objections against Goldman and Olsson's probabilistic claim seem to go wrong. (shrink)

Mark Siebel has presented a compelling argument against Branden Fitelson’s probabilistic measure of coherence. The present paper shows how Siebel’s argument can be strengthened and thereby extended to an argument against a huge class of coherence measures from the literature including William Roche’s average mutual firmness account, which has not been challenged up to now.

Changing weather conditions and barometer changes usually coincide. Accordingly, the propositions that my barometer falls and that the weather conditions deteriorate are quite coherent—especially under the assumption that there is a drop in atmospheric pressure. Nevertheless, scenarios like these involving common causes turn out to be highly problematic for a prominent class of probabilistic coherence measures, namely, those explicating coherence based on the idea of relevance-sensitivity. In this article, we show that none of these measures accords with the intuition that (...) in the light of a common cause, two propositions referring to the cause’s effects should turn out to be coherent. This result casts doubts on the view that these measures can be considered proper explications of the concept of coherence. 1Introduction2Relevance-Sensitive Coherence Measures3Common Causes, Screening-off, and Coherence4Discussion 4.1Multiple explications of coherence4.2Conditionalization versus set expansion5Conclusion. (shrink)

The probabilistic support relation is known to violate transitivity. But over the years, philosophers have identified various conditions under which it does not, most notably screening-off and weak screening-off. In this short discussion note, I wish to highlight another condition that, unfortunately, is often neglected in the literature. This condition is due to Mary Hesse who recognized its transitivity-ensuring property long before other conditions entered the stage. I show that her condition is logically independent of screening-off and weak screening-off, but (...) that, just like the two aforementioned, it entails the recently proposed very weak screening-off condition due to Jeanne Peijnenburg and David Atkinson. (shrink)

This paper presents a symmetry condition for probabilistic measures of confirmation which is weaker than commutativity symmetry, disconfirmation commutativity symmetry but also antisymmetry. It is based on the idea that for any value a probabilistic measure of confirmation can assign there is a corresponding case where degrees of confirmation are symmetric. It is shown that a number of prominent confirmation measures such as Carnap’s difference function, Rescher’s measure of confirmation, Gaifman’s confirmation rate and Mortimer’s inverted difference function do not satisfy (...) this condition and instead exhibit a previously unnoticed and rather puzzling behavior in certain cases of disconfirmation. This behavior also carries over to probabilistic measures of information change, causal strength, explanatory power and coherence. (shrink)

Francesco Praolini has recently put pressure on the view that justified believability is closed under conjunction introduction. Based on what he calls ‘the hybrid paradox,’ he argues that accepting the principle of conjunction closure for justified believability, quite surprisingly, entails that one must also accept the principle of factivity for justified believability, i.e. that there are no propositions that are justifiably believable and false at the same time. But proponents of conjunction closure can do without factivity, as I argue in (...) this short note. A less demanding principle is available. (shrink)

Thomas Kroedel has recently proposed an interesting Pareto-style condition on permissible belief. Despite the condition’s initial plausibility, this paper aims at providing a counterexample to it. The example is based on the view that a proper condition on permissible belief should not give permission to believe a proposition that undermines one’s belief system or whose epistemic standing decreases in the light of one’s de facto beliefs.

Thomas Kroedel has recently proposed an interesting Pareto-style condition on permissible belief. Despite the condition’s initial plausibility, this paper aims at providing a counterexample to it. The example is based on the view that a proper condition on permissible belief should not give permission to believe a proposition that undermines one’s belief system or whose epistemic standing decreases in the light of one’s de facto beliefs.

Ein prominenter Einwand gegen Kohärenztheorien der Rechtfertigung lautet, dass der zugrunde liegende Begriff der Kohärenz vage ist. In diesem Buch geben wir einen Überblick über die neuere Forschung im Bereich probabilistischer Kohärenzmaße, die den Begriff der Kohärenz mit Hilfe der Wahrscheinlichkeitstheorie zu präzisieren versuchen. Im ersten Teil des Buches werden sämtliche Kohärenzmaße sowie ihre jeweiligen Vor- und Nachteile vorgestellt. Dabei werden sowohl Adäquatheitsbedingungen als auch Testfälle für Kohärenzmaße berücksichtigt. Im zweiten Teil stehen dann mögliche Anwendungen von Kohärenzmaßen im Bereich der (...) Kohärenztheorie der Rechtfertigung im Mittelpunkt. Insbesondere die Frage nach der Wahrheits- und Verlässlichkeitsförderlichkeit werden mit Bezug auf die vorgestellten Maße diskutiert. Zudem wird der Zusammenhang zwischen Kohärenz und Konsistenz eingehend beleuchtet. Der letzte Teil des Buches widmet sich dann den Problemen und Einwänden sowohl gegen einzelne Klassen von Maßen als auch gegen das Projekt der probabilistischen Kohärenzmaße insgesamt. Hier werden unter anderem das Problem der Individuierung von Überzeugungen sowie der Zusammenhang zwischen dem Begriff der Kohärenz und dem der Erkärung betrachtet. (shrink)