Some Closure Properties of Finite Definitions

There is no known syntactic characterization of the class of finite definitions in terms of a set of basic definitions and a set of basic operators under which the class is closed. Furthermore, it is known that the basic propositional operators do not preserve finiteness. In this paper I survey these problems and explore operators that do preserve finiteness. I also show that every definition that uses only unary predicate symbols and equality is bound to be finite.     

Are There Any Rules?

The ``model of rules' that Ronald Dworkin attacks is an absurdmodel of law, if rules are taken to be standards that have nounspecified counterinstances, and whose application isalways uncontroversial. Dworkin gives good reason to thinkthat there are no such standards or virtually none in (e.g.)English law. But the model of rules is not misconceived, asDworkin claims. Rather, it needs a better understanding of the idea of a rule. I argue that the view that the law of a community is a system of rules needs to meet an importantchallenge that Dworkin has raised for jurisprudence: to accountfor the fact that legal rights and duties are frequentlycontroversial. I give an account of social rules thatexplains why controversy over their application in particularcases is common, and can be deep. So controversy gives noreason to reject the model of rules.     

Biased judgments of the effects of speed change on travel time,fuel consumption and braking: Individual differences in the use of simplifying rules producing the same biases

The main purpose of this study was to identify different cognitive rules that lead to a particular judgment bias. To fulfill this purpose, a new method Spectral analysis was introduced and applied. Participants judged time saved by driving faster, fuel saved by replacing a car and braking capacity at different speeds. These problems invite the time saving bias (e.g., time saved from speed increases at higher speeds overestimated), the miles per gallon, MPG illusion (misjudgment of fuel saved by replacing a car) and the braking capacity bias (overestimation of braking capacity after speed increase). The average results replicated the biases. Spectral analysis of individual participants and problems showed that a speed difference rule explained about half of the time saving judgments and about three fourth of the MPG judgments. A difference between speeds rule described about one third of the biased braking judgments and a ratio/proportion rule about one fifth of the time saving and MPG judgments. All rules give biased judgments in all three domains. The paper ends with a discussion of hierarchies of cognitive rules, applications of the results, and how to mitigate or avoid the biases and the risks associated with the biases.     

Two approaches to the formalisation of defeasible deontic reasoning

This paper compares two ways of formalising defeasible deontic reasoning, both based on the view that the issues of conflicting obligations and moral dilemmas should be dealt with from the perspective of nonmonotonic reasoning. The first way is developing a special nonmonotonic logic for deontic statements. This method turns out to have some limitations, for which reason another approach is recommended, viz. combining an already existing nonmonotonic logic with a deontic logic. As an example of this method the language of Reiter's default logic is extended to include modal expressions, after which the argumentation framework in default logic of [20, 22] is used to give a plausible logical analysis of moral dilemmas and prima facie obligations.An earlier version of this article was written while the author was working at the Department of Computing, Imperial College London, supported by ESRC/MRC/SERC Joint Council Initiative Project G9212036. Work on the present version was supported by a research fellowship of the Royal Netherlands Academy of Arts and Sciences, and by Esprit WG 8319 Modelage. I thank one of the referees for his interesting comments. Also, many thanks are due to Marek Sergot for valuable discussions on the topic of this paper.     

Valuational semantics of rule derivability

If a certain semantic relation (which we call local consequence) is allowed to guide expectations about which rules are derivable from other rules, these expectations will not always be fulfilled, as we illustrate. An alternative semantic criterion (based on a relation we call global consequence), suggested by work of J.W. Garson, turns out to provide a much better — indeed a perfectly accurate — guide to derivability.     

The disputation — a special type of cooperative argumentative dialogue

This article consists of three parts, two introductory, in which the limits and the methods of analysis of dialogues are expounded, and the major part, in which the main features of a philosophical theory of disputation are outlined.

Peering into the opaque mind

Abstract

Carolyn Saarni’s pioneering research showed that young children learn how to hide their feelings—to conceal disappointment with a smile or to conceal amusement with a neutral expression. By 6 years of age, children understand the implications of such concealment. They can distinguish between: (i) an individual’s true but hidden emotion; (ii) the emotion that the individual overtly expresses; and (iii) the emotion that other people might mistakenly attribute to the individual. Effectively, young children grasp that the mind is opaque. Its contents can remain hidden from others. We examine two issues raised by this important conceptual insight. First, we ask how it emerges in young children—what experiences lead them to acknowledge the mind’s opacity? Second, in light of Saarni’s emphasis on the impact of cultural beliefs and practices, we discuss anthropological evidence that in certain cultures the mind’s opacity is regarded as a social desideratum so that enquiries into, or speculations about, a person’s private mental states are regarded as inappropriate. We consider the understanding of hidden emotion that children will acquire if they grow up in such a culture. We propose—paradoxically—that they will readily differentiate between what is actually felt and what is overtly expressed. We conclude by reviewing recent cross-cultural evidence lending initial support to that prediction.     

The Revival of Rejective Negation

Whether assent (acceptance) and dissent (rejection) are thought of as speech acts or as propositional attitudes, the leading idea of rejectivism is that a grasp of the distinction between them is prior to our understanding of negation as a sentence operator, this operator then being explicable as applying to A to yield something assent to which is tantamount to dissent from A. Widely thought to have been refuted by an argument of Frege"s, rejectivism has undergone something of a revival in recent years, especially in writings by Huw Price and Timothy Smiley. While agreeing that Frege"s argument does not refute the position, we shall air some philosophical qualms about it in Section 5, after a thorough examination of the formal issues in Sections 1–4. This discussion draws on – and seeks to draw attention to – some pertinent work of Kent Bendall in the 1970s.     

A New Representation Theorem for Contranegative Deontic Logic

The logic of an ought operator O is contranegative with respect to an underlying preference relation if it satisfies the property Op & (¬p)(¬q) Oq. Here the condition that is interpolative ((p (pq) q) (q (pq) p)) is shown to be necessary and sufficient for all -contranegative preference relations to satisfy the plausible deontic postulates agglomeration (Op & OqO(p&q)) and disjunctive division (O(p&q) Op Oq).