A closer look at the probabilities of the notorious three prisoners.

The "problem of three prisoners", a counterintuitive teaser, is analyzed. It is representative of a class of probability puzzles where the correct solution depends on explication of underlying assumptions. Spontaneous beliefs concerning the problem and intuitive heuristics are reviewed. The psychological background of these beliefs is explored. Several attempts to find a simple criterion to predict whether and how the probability of the target event will change as a result of obtaining evidence are examined. However, despite the psychological appeal of these attempts, none proves to be valid in general. A necessary and sufficient condition for change in the probability of the target event, following observation of new data, is proposed. That criterion is an extension of the likelihood-ratio principle (which holds in the case of only two complementary alternatives) to any number of alternatives. Some didactic implications concerning the significance of the chance set-up and reliance on analogies are discussed.     

Explication of Inductive Probability

Inductive probability is the logical concept of probability in ordinary language. It is vague but it can be explicated by defining a clear and precise concept that can serve some of the same purposes. This paper presents a general method for doing such an explication and then a particular explication due to Carnap. Common criticisms of Carnap’s inductive logic are examined; it is shown that most of them are spurious and the others are not fundamental.     

Likelihoodism,Bayesianism, and relational confirmation

Likelihoodists and Bayesians seem to have a fundamental disagreement about the proper probabilistic explication of relational (or contrastive) conceptions of evidential support (or confirmation). In this paper, I will survey some recent arguments and results in this area, with an eye toward pinpointing the nexus of the dispute. This will lead, first, to an important shift in the way the debate has been couched, and, second, to an alternative explication of relational support, which is in some sense a “middle way” between Likelihoodism and Bayesianism. In the process, I will propose some new work for an old probability puzzle: the “Monty Hall” problem. Thanks to the participants of the Philosophy, Probability, and Modeling (PPM) Seminar at the University of Konstanz (especially Stephan Hartmann, Franz Huber, Wolfgang Spohn, and Teddy Seidenfeld), for a very fruitful discussion of an early draft of this paper in July, 2004. Since then, discussions and correspondences with Prasanta Bandyopadhyay, Luc Bovens, Alan Hájek, Jim Hawthorne, Jim Joyce, Jon Kvanvig (and other participants of his “Certain Doubts” blog, which had a thread on a previous draft of this paper), Patrick Maher, Sherri Roush, Richard Royall, Elliott Sober, Dan Steel, and an anonymous referee of Synthese has been very valuable.     

Bayesian probability

Bayesian decision theory is here construed as explicating a particular concept of rational choice and Bayesian probability is taken to be the concept of probability used in that theory. Bayesian probability is usually identified with the agent’s degrees of belief but that interpretation makes Bayesian decision theory a poor explication of the relevant concept of rational choice. A satisfactory conception of Bayesian decision theory is obtained by taking Bayesian probability to be an explicatum for inductive probability given the agent’s evidence.     

Conceptual Analysis and Analytical Definitions in Frege

Logical (or conceptual) analysis is in Frege primarily not an analysis of a concept but of its sense. Five Fregean philosophical principles are presented as constituting a framework for a theory of logical or conceptual analysis, which I call analytical explication. These principles, scattered and sometime latent in his writings are operative in Frege's critique of other views and in his constructive development of his own view. The proposed conception of analytical explication is partially rooted in Frege's notion of analytical definition. It may also be the basis of what is required of a reduction of one domain to another, if it is to have the philosophical significance many reductions allegedly have.     

Fallibilism and the value of knowledge

This paper defends the epistemological doctrine of fallibilism from recent objections. In “The Myth of Knowledge” Laurence BonJour argues that we should reject fallibilism for two main reasons: first, there is no adequate way to specify what level of justification is required for fallible knowledge; second, we cannot explain why any level of justification that is less than fully conclusive should have the significance that makes knowledge valuable. I will reply to these challenges in a way that allows me to make progress on a number of important issues in contemporary epistemology: epistemic value, the functional roles of knowledge attributions, experimental epistemology, skepticism, the Gettier problem, and the lottery paradox. My argument is motivated by appealing to various insights derived from the method of ‘practical explication’, particularly the idea that a central purpose of the concept of knowledge is to flag reliable informants. My conclusion is that various practical and theoretical considerations derived from the method of practical explication support the fallibilist conception of knowledge.     

Explication Defended

How can formal methods be applied to philosophical problems that involve informal concepts of ordinary language? Carnap answered this question by describing a methodology that he called “explication." Strawson objected that explication changes the subject and does not address the original philosophical problem; this paper shows that Carnap’s response to that objection was inadequate and offers a better response. More recent criticisms of explication by Boniolo and Eagle are shown to rest on misunderstandings of the nature of explication. It is concluded that explication is an appropriate methodology for formal philosophy.     

On the Quinean-analyticity of mathematical propositions

This paper investigates the relation between Carnap and Quine??s views on analyticity on the one hand, and their views on philosophical analysis or explication on the other. I argue that the stance each takes on what constitutes a successful explication largely dictates the view they take on analyticity. I show that although acknowledged by neither party (in fact Quine frequently expressed his agreement with Carnap on this subject) their views on explication are substantially different. I argue that this difference not only explains their differences on the question of analyticity, but points to a Quinean way to answer a challenge that Quine posed to Carnap. The answer to this challenge leads to a Quinean view of analyticity such that arithmetical truths are analytic, according to Quine??s own remarks, and set theory is at least defensibly analytic.     

The distribution postulate in Bohm's theory

On Bohm's formulation of quantum mechanics particles always have determinate positions and follow continuous trajectories. Bohm's theory, however, requires a postulate that says that particles are initially distributed in a special way: particles are randomly distributed so that the probability of their positions being represented by a point in any regionR in configuration space is equal to the square of the wave-function integrated overR. If the distribution postulate were false, then the theory would generally fail to make the right statistical predictions. Further, if it were false, then there would at least in principle be situations where a particle would approach an eigenstate of having one position but in fact always be somewhere very different. Indeed, we will see how this might happen even if the distribution postulate were true. This will help to show how loose the connection is between the wave-function and the positions of particles in Bohm's theory and what the precise role of the distribution postulate is. Finally, we will briefly consider two attempts to formulate a version of Bohm's theory without the distribution postulate.     

Unification: What is it,how do we Reach and why do we Want it?

This article has three aims. The first is to give a partial explication of the concept of unification. My explication will be partial because I confine myself to unification of particular events, because I do not consider events of a quantitative nature, and discuss only deductive cases. The second aim is to analyze how unification can be reached. My third aim is to show that unification is an intellectual benefit. Instead of being an intellectual benefit unification could be an intellectual harm, i.e., a state of mind we should try to avoid by all means. By calling unification an intellectual benefit, we claim that this form of understanding has an intrinsic value for us. I argue that unification really has this alleged intrinsic value. This revised version was published online in June 2006 with corrections to the Cover Date.     

The Burden of Criticism: Consequences of Taking a Critical Stance

Some critical reactions hardly give clues to the arguer as to how to respond to them convincingly. Other critical reactions convey some or even all of the considerations that make the critic critical of the arguer’s position and direct the arguer to defuse or to at least contend with them. First, an explication of the notion of a critical reaction will be provided, zooming in on the degree of “directiveness” that a critical reaction displays. Second, it will be examined whether there are normative requirements that enhance the directiveness of criticism. Does the opponent have in circumstances a dialectical obligation to provide clarifications, explanations, or even arguments? In this paper, it is hypothesized that the competitiveness inherent in critical discussion must be mitigated by making the opponent responsible for providing her counterconsiderations, if available, thus assisting the proponent in developing an argumentative strategy that defuses them.     

The degree of epistemic justification and the conjunction fallacy

This paper describes a formal measure of epistemic justification motivated by the dual goal of cognition, which is to increase true beliefs and reduce false beliefs. From this perspective the degree of epistemic justification should not be the conditional probability of the proposition given the evidence, as it is commonly thought. It should be determined instead by the combination of the conditional probability and the prior probability. This is also true of the degree of incremental confirmation, and I argue that any measure of epistemic justification is also a measure of incremental confirmation. However, the degree of epistemic justification must meet an additional condition, and all known measures of incremental confirmation fail to meet it. I describe this additional condition as well as a measure that meets it. The paper then applies the measure to the conjunction fallacy and proposes an explanation of the fallacy.     

Inductivism and falsificationism reconcilable

Summary Inductivism is understood as the explication of the degree of confirmation as conditional logical probability. Inductivism is not recommendable in the form of Carnap's -system, but tenable in the form of Bayesianism. Objections directed at it are either irrelevant or can be taken account of within Bayesianism.     

Spiritual Experiences of Gay Men and Lesbians

The spiritual and religious lives of gay men and lesbians are often misunderstood by counselors who have too little information about this rich and diverse population. This article offers an explication of the challenges facing gay persons, a model that will be useful in counseling sessions, and a list of resources for further information.     

What is the probability of replicating a statistically significant effect?

If an initial experiment produces a statistically significant effect, what is the probability that this effect will be replicated in a follow-up experiment? I argue that this seemingly fundamental question can be interpreted in two very different ways and that its answer is, in practice, virtually unknowable under either interpretation. Although the data from an initial experiment can be used to estimate one type of replication probability, this estimate will rarely be precise enough to be of any use. The other type of replication probability is also unknowable, because it depends on unknown aspects of the research context. Thus, although it would be nice to know the probability of replicating a significant effect, researchers must accept the fact that they generally cannot determine this information, whichever type of replication probability they seek.     

Carnapian explications,experimental philosophy,and fruitful concepts

It seems natural to think that Carnapian explication and experimental philosophy can go hand in hand. But what exactly explicators can gain from the data provided by experimental philosophers remains controversial. According to an influential proposal by Shepherd and Justus, explicators should use experimental data in the process of ‘explication preparation’. Against this proposal, Mark Pinder has recently suggested that experimental data can directly assist an explicator’s search for fruitful replacements of the explicandum. In developing his argument, he also proposes a novel aspect of what makes a concept fruitful, namely, that it is taken up by the relevant community. In this paper, I defend explication preparation against Pinder’s objections and argue that his uptake proposal conflates theoretical and practical success conditions of explications. Furthermore, I argue that Pinder’s suggested experimental procedure needs substantial revision. I end by distinguishing two kinds of explication projects, and showing how experimental philosophy can contribute to each of them.     

How to Define a Number? A General Epistemological Account of Simon Stevin’s Art of Defining

This paper explores Simon Stevin’s l’Arithmétique of 1585, where we find a novel understanding of the concept of number. I will discuss the dynamics between his practice and philosophy of mathematics, and put it in the context of his general epistemological attitude. Subsequently, I will take a close look at his justificational concerns, and at how these are reflected in his inductive, a postiori and structuralist approach to investigating the numerical field. I will argue that Stevin’s renewed conceptualisation of the notion of number is a sort of “existential closure” of the numerical domain, founded upon the practice of his predecessors and contemporaries. Accordingly, I want to make clear that l’Aritmetique have to be read not as an ontological analysis or exploration of the numerical field, but as an explication of a mathematical ethos. In this sense, this article also intends to make a specific contribution to the broader issue of the “ethics of geometry.”     

Partition priming in judgment under uncertainty

We show that likelihood judgments are biased toward an ignorance-prior probability that assigns equal credence to each mutually exclusive event considered by the judge. The value of the ignorance prior depends crucially on how the set of possibilities (i.e., the state space) is subjectively partitioned by the judge. For instance, asking "what is the probability that Sunday will be hotter than any other day next week?" facilitates a two-fold case partition, [Sunday hotter, Sunday not hotter], thus priming an ignorance prior of 1/2. In contrast, asking "what is the probability that the hottest day of the week will be Sunday?" facilitates a seven-fold class partition, [Sunday hottest, Monday hottest, etc.], priming an ignorance prior of 1/7. In four studies, we observed systematic partition dependence: Judgments made by participants presented with either case or class formulations of the same query were biased toward the corresponding ignorance prior.     

Black Box Arguments

“Black box argument” is a metaphor for modular components of argumentative discussion that are, within a particular discussion, not open to expansion. In public policy debate such as the controversy over abstinence-only sex education, scientific conclusions enter the discourse as black boxes consisting of a result returned from an external and largely impenetrable process. In one way of looking at black box arguments, there is nothing fundamentally new for the argumentation theorist: A black box argument is very like any other appeal to authority, and what might be said about any particular form of black box will turn out to be a particularized version of what might be said about evaluating arguments based on authority. But in another way of looking at black box arguments, they are a constantly evolving technology for coming to conclusions and making these conclusions broadly acceptable. Black boxes are to argumentation what material inventions are to engineering and related sciences. They are anchored in and constrained by fundamental natural processes, but they are also new things that require theoretical explication and practical assessment.