So far, color-naming studies have relied on a rather limited set of color stimuli. Most importantly, stimuli have been largely limited to highly saturated colors. Because of this, little is known about how people categorize less saturated colors and, more generally, about the structure of color categories as they extend across all dimensions of color space. This article presents the results from a large Internet-based color-naming study that involved color stimuli ranging across all available chroma levels in Munsell space. These (...) results help answer such questions as how English speakers name a more complex color set, whether English speakers use so-called basic color terms (BCTs) more frequently for more saturated colors, how they use non-BCTs in comparison with BCTs, whether non-BCTs are highly consensual in less saturated parts of the solid, how deep inside color space basic color categories extend, or how they behave on the chroma dimension. (shrink)

Conceptual spaces have become an increasingly popular modeling tool in cognitive psychology. The core idea of the conceptual spaces approach is that concepts can be represented as regions in similarity spaces. While it is generally acknowledged that not every region in such a space represents a natural concept, it is still an open question what distinguishes those regions that represent natural concepts from those that do not. The central claim of this paper is that natural concepts are represented by the (...) cells of an optimally designed similarity space. (shrink)

A number of authors have recently put forward arguments pro or contra various rules for scoring probability estimates. In doing so, they have skipped over a potentially important consideration in making such assessments, to wit, that the hypotheses whose probabilities are estimated can approximate the truth to different degrees. Once this is recognized, it becomes apparent that the question of how to assess probability estimates depends heavily on context.

According to the Lockean thesis, a proposition is believed just in case it is highly probable. While this thesis enjoys strong intuitive support, it is known to conflict with seemingly plausible logical constraints on our beliefs. One way out of this conflict is to make probability 1 a requirement for belief, but most have rejected this option for entailing what they see as an untenable skepticism. Recently, two new solutions to the conflict have been proposed that are alleged to be (...) non-skeptical. We compare these proposals with each other and with the Lockean thesis, in particular with regard to the question of how much we gain by adopting any one of them instead of the probability 1 requirement, that is, of how likely it is that one believes more than the things one is fully certain of. (shrink)

In this paper I discuss the rule of inference proposed by Kuipers under the name of Inference to the Best Theory. In particular, I argue that the rule needs to be strengthened if it is to serve realist purposes. I further describe a method for testing, and perhaps eventually justifying, a suitably strengthened version of it.

One of the many notable virtues of Igor Douven's The Art of Abduction is that it is open access. Since a well-written chapter-by-chapter overview of the book is.

Igor Douven establishes several new intransitivity results concerning evidential support. I add to Douven’s very instructive discussion by establishing two further intransitivity results and a transitivity result.

Assertions are the centre of gravity in social epistemology. They are the vehicles we use to exchange information within scientific groups and society as a whole. It is therefore essential to determine under which conditions we are permitted to make an assertion. In this paper we argue and provide empirical evidence for the view that the norm of assertion is justified belief: truth or even knowledge are not required. Our results challenge the knowledge account advocated by, e.g. Williamson (1996), in (...) general, and more specifically, put into question several studies conducted by Turri (2013, 2016) that support a knowledge norm of assertion. Instead, the justified belief account championed by, e.g. Douven (2006), seems to prevail. (shrink)

In a series of papers over the past twenty years, and in a new book, Igor Douven has argued that Bayesians are too quick to reject versions of inference to the best explanation that cannot be accommodated within their framework. In this paper, I survey their worries and attempt to answer them using a series of pragmatic and purely epistemic arguments that I take to show that Bayes’ Rule really is the only rational way to respond to your evidence.

Abstract. The aim of this paper is to present a topological method for constructing discretizations (tessellations) of conceptual spaces. The method works for a class of topological spaces that the Russian mathematician Pavel Alexandroff defined more than 80 years ago. Alexandroff spaces, as they are called today, have many interesting properties that distinguish them from other topological spaces. In particular, they exhibit a 1-1 correspondence between their specialization orders and their topological structures. Recently, a special type of Alexandroff spaces was (...) used by Ian Rumfitt to elucidate the logic of vague concepts in a new way. According to his approach, conceptual spaces such as the color spectrum give rise to classical systems of concepts that have the structure of atomic Boolean algebras. More precisely, concepts are represented as regular open regions of an underlying conceptual space endowed with a topological structure. Something is subsumed under a concept iff it is represented by an element of the conceptual space that is maximally close to the prototypical element p that defines that concept. This topological representation of concepts comes along with a representation of the familiar logical connectives of Aristotelian syllogistics in terms of natural settheoretical operations that characterize regular open interpretations of classical Boolean propositional logic. In the last 20 years, conceptual spaces have become a popular tool of dealing with a variety of problems in the fields of cognitive psychology, artificial intelligence, linguistics and philosophy, mainly due to the work of Peter Gärdenfors and his collaborators. By using prototypes and metrics of similarity spaces, one obtains geometrical discretizations of conceptual spaces by so-called Voronoi tessellations. These tessellations are extensionally equivalent to topological tessellations that can be constructed for Alexandroff spaces. Thereby, Rumfitt’s and Gärdenfors’s constructions turn out to be special cases of an approach that works for a more general class of spaces, namely, for weakly scattered Alexandroff spaces. This class of spaces provides a convenient framework for conceptual spaces as used in epistemology and related disciplines in general. Alexandroff spaces are useful for elucidating problems related to the logic of vague concepts, in particular they offer a solution of the Sorites paradox (Rumfitt). Further, they provide a semantics for the logic of clearness (Bobzien) that overcomes certain problems of the concept of higher2 order vagueness. Moreover, these spaces help find a natural place for classical syllogistics in the framework of conceptual spaces. The crucial role of order theory for Alexandroff spaces can be used to refine the all-or-nothing distinction between prototypical and nonprototypical stimuli in favor of a more fine-grained gradual distinction between more-orless prototypical elements of conceptual spaces. The greater conceptual flexibility of the topological approach helps avoid some inherent inadequacies of the geometrical approach, for instance, the so-called “thickness problem” (Douven et al.) and problems of selecting a unique metric for similarity spaces. Finally, it is shown that only the Alexandroff account can deal with an issue that is gaining more and more importance for the theory of conceptual spaces, namely, the role that digital conceptual spaces play in the area of artificial intelligence, computer science and related disciplines. Keywords: Conceptual Spaces, Polar Spaces, Alexandroff Spaces, Prototypes, Topological Tessellations, Voronoi Tessellations, Digital Topology. (shrink)

Is evidential support transitive? The answer is negative when evidential support is understood as confirmation so that X evidentially supports Y if and only if p(Y | X) > p(Y). I call evidential support so understood “support” (for short) and set out three alternative ways of understanding evidential support: support-t (support plus a sufficiently high probability), support-t* (support plus a substantial degree of support), and support-tt* (support plus both a sufficiently high probability and a substantial degree of support). I also (...) set out two screening-off conditions (under which support is transitive): SOC1 and SOC2. It has already been shown that support-t is non-transitive in the general case (where it is not required that SOC1 holds and it is not required that SOC2 holds), in the special case where SOC1 holds, and in the special case where SOC2 holds. I introduce two rather weak adequacy conditions on support measures and argue that on any support measure meeting those conditions it follows that neither support-t* nor support-tt* is transitive in the general case, in the special case where SOC1 holds, or in the special case where SOC2 holds. I then relate some of the results to Douven’s evidential support theory of conditionals along with a few rival theories. (shrink)

Many epistemologists have responded to the lottery paradox by proposing formal rules according to which high probability defeasibly warrants acceptance. Douven and Williamson present an ingenious argument purporting to show that such rules invariably trivialise, in that they reduce to the claim that a probability of 1 warrants acceptance. Douven and Williamson’s argument does, however, rest upon significant assumptions – amongst them a relatively strong structural assumption to the effect that the underlying probability space is both finite and (...) uniform. In this paper, I will show that something very like Douven and Williamson’s argument can in fact survive with much weaker structural assumptions – and, in particular, can apply to infinite probability spaces. (shrink)

I develop a probabilistic account of coherence, and argue that at least in certain respects it is preferable to (at least some of) the main extant probabilistic accounts of coherence: (i) Igor Douven and Wouter Meijs’s account, (ii) Branden Fitelson’s account, (iii) Erik Olsson’s account, and (iv) Tomoji Shogenji’s account. Further, I relate the account to an important, but little discussed, problem for standard varieties of coherentism, viz., the “Problem of Justified Inconsistent Beliefs.”.

Indicative conditionals and tendency causal claims are closely related (e.g., Frosch and Byrne, 2012), but despite these connections, they are usually studied separately. A unifying framework could consist in their dependence on probabilistic factors such as high conditional probability and statistical relevance (e.g., Adams, 1975; Eells, 1991; Douven, 2008, 2015). This paper presents a comparative empirical study on differences between judgments on tendency causal claims and indicative conditionals, how these judgments are driven by probabilistic factors, and how these factors (...) differ in their predictive power for both causal and conditional claims. (shrink)

Van Fraassen's Judy Benjamin problem asks how one ought to update one's credence in A upon receiving evidence of the sort ``A may or may not obtain, but B is k times likelier than C'', where {A,B,C} is a partition. Van Fraassen's solution, in the limiting case of increasing k, recommends a posterior converging to the probability of A conditional on A union B, where P is one's prior probability function. Grove and Halpern, and more recently Douven and Romeijn, (...) have argued that one ought to leave credence in A unchanged, i.e. fixed at P(A). We argue that while the former approach is superior, it brings about a Reflection violation due in part to neglect of a ``regression to the mean'' phenomenon, whereby when C is eliminated by random evidence that leaves A and B alive, the ratio P(A):P(B) ought to drift in the direction of 1:1. (shrink)

The Ramsey Test is considered to be the default test for the acceptability of indicative conditionals. I will argue that it is incompatible with some of the recent developments in conceptualizing conditionals, namely the growing empirical evidence for the _Relevance Hypothesis_. According to the hypothesis, one of the necessary conditions of acceptability for an indicative conditional is its antecedent being positively probabilistically relevant for the consequent. The source of the idea is _Evidential Support Theory_ presented in Douven (2008). I (...) will defend the hypothesis against alleged counterexamples, and show that it is supported by growing empirical evidence. Finally, I will present a version of the Ramsey test which incorporates the relevance condition and therefore is consistent with growing empirical evidence for the relevance hypothesis. (shrink)

Luck has become an increasingly important factor in epistemology during recent years as either a preventor of knowledge (Pritchard 2013) or even as one of the conditions of knowledge (Zagzebski 1994, Hetherington 2013), thus begging the question of its definition. Following the probabilistic and degree-minding "new paradigm psychology of reasoning" (Evans 2012, Elqayam & Over 2012, Pfeifer & Douven 2014) and renouncing the "old paradigm" of bivalence, the first main feature of this article lies in the introduction of "gradualism" (...) according to which vast parts of reality comes in degrees (=metaphysical or ontological gradualism) and, given that theoretical constructs are supposed to accurately correspond to reality, according to which gradualistic or degree-minding frameworks need to be established in all of philosophy or science (=theoretical gradualism). As the second and more central feature of this article, and building on gradualism and Riggs' (2007) pivotal idea that "luck comes in degrees", I will then develop my own gradualistic account of luck with two always necessary gradual conditions (low enough chance and high enough significance) and one sometimes necessary gradual condition (low enough control or high enough lack of control). During the presentation of this new account of luck, I will also deliver decisive arguments against prominent luck philosopher Duncan Pritchard's latest version of the modal account of luck (forthcoming) which contains major mistakes in respect to all three conditions of luck. (shrink)

A ‘lottery belief’ is a belief that a particular ticket has lost a large, fair lottery, based on nothing more than the odds against it winning. The lottery paradox brings out a tension between the idea that lottery beliefs are justified and the idea that that one can always justifiably believe the deductive consequences of things that one justifiably believes – what is sometimes called the principle of closure. Many philosophers have treated the lottery paradox as an argument against the (...) second idea – but I make a case here that it is the first idea that should be given up. As I shall show, there are a number of independent arguments for denying that lottery beliefs are justified. (shrink)