Contributing to Discourse

For people to contribute to discourse, they must do more than utter the right sentence at the right time. The basic requirement is that they add to their common ground in an orderly way. To do this, we argue, they try to establish for each utterance the mutual belief that the addressees have understood what the speaker meant well enough for current purposes. This is accomplished by the collective actions of the current contributor and his or her partners, and these result in units of conversation called contributions. We present a model of contributions and show how it accounts for a variety of features of everyday conversations.     

A Representation Theorem for a Decision Theory With Conditionals

This paper investigates the role of conditionals in hypothetical reasoning and rational decision making. Its main result is a proof of a representation theorem for preferences defined on sets of sentences (and, in particular, conditional sentences), where an agent’s preference for one sentence over another is understood to be a preference for receiving the news conveyed by the former. The theorem shows that a rational preference ordering of conditional sentences determines probability and desirability representations of the agent’s degrees of belief and desire that satisfy, in the case of non-conditional sentences, the axioms of Jeffrey’s decision theory and, in the case of conditional sentences, Adams’ expression for the probabilities of conditionals. Furthermore, the probability representation is shown to be unique and the desirability representation unique up to positive linear transformation. This revised version was published online in June 2006 with corrections to the Cover Date.     

Transformations of the Concept of Reason

This outline of the transformations of the concept of reason is based on the idea that this can be presented/illustrated by means of a historical sketch of the criticism of reason, because all essential differentiations in that concept can be understood as consequences of critical arguments. In Kant's work, the Critique of Speculative Reason reaches its first conclusion; it was followed by a Critique of Critical Reason by Hegel and his followers, and Schopenhauer established a new type of critical argument: the Critique of Functional Reason which dominates the radical criticism of reason in our time. This radical criticism is the great challenge for the philosophy of reason today.     

Some cautions regarding statistical power in split-plot designs

We show that if overall sample size and effect size are held constant, the power of theF test for a one-way analysis of variance decreases dramatically as the number of groups increases. This reduction in power is even greater when the groups added to the design do not produce treatment effects. If a second independent variable is added to the design, either a split-plot or a completely randomized design may be employed. For the split-plot design, we show that the power of theF test on the betweengroups factor decreases as the correlation across the levels of the within-groups factor increases. The attenuation in between-groups power becomes more pronounced as the number of levels of the withingroups factor increases. Sample size and total cost calculations are required to determine whether the split-plot or completely randomized design is more efficient in a particular application. The outcome hinges on the cost of obtaining (or recruiting) a single subject relative to the cost of obtaining a single observation: We call this thesubject-to-observation cost (SOC) ratio. Split-plot designs are less costly than completely randomized designs only when the SOC ratio is high, the correlation across the levels of the within-groups factor is low, and the number of such levels is small.