Recent years have been blessed with an abundance of logical systems, arising from a multitude of applications. A logic can be characterised in many different ways. Traditionally, a logic is presented via the following three components: 1. an intuitive non-formal motivation, perhaps tie it in to some application area 2. a semantical interpretation 3. a proof theoretical formulation. There are several types of proof theoretical methodologies, Hilbert style, Gentzen style, goal directed style, labelled deductive system style, and so on. The (...) tableau methodology, invented in the 1950s by Beth and Hintikka and later per fected by Smullyan and Fitting, is today one of the most popular, since it appears to bring together the proof-theoretical and the semantical approaches to the pre of a logical system and is also very intuitive. In many universities it is sentation the style first taught to students. Recently interest in tableaux has become more widespread and a community crystallised around the subject. An annual tableaux conference is being held and proceedings are published. The present volume is a Handbook a/Tableaux pre senting to the community a wide coverage of tableaux systems for a variety of logics. It is written by active members of the community and brings the reader up to frontline research. It will be of interest to any formal logician from any area. (shrink)

Free Public Reason examines the idea of public justification, stressing its importance but also questioning the coherence of the concept itself. Although public justification is employed in the work of theorists such as John Rawls, Jeremy Waldron, Thomas Nagel, and others, it has received little attention on its own as a philosophical concept. In this book Fred D'Agostino shows that the concept is composed of various values, interests, and notions of the good, and that no ranking of these is (...) possible. The notion of public justification itself is thus shown to be contestable. In demonstrating this, D'Agostino undermines many current political theories that rely on this concept. Having broken down the foundations of public justification, D'Agostino then offers an alternative model of how a workable consensus on its meaning might be reached through the interactions of a community of interpreters or delegates at a constitutional convention. (shrink)

INTRODUCTION The editors of this volume - Jarvie and D'Agostino - encountered John Watkins at such different times in his career that they have never ...

Discussion of the cognitive division of labor has usually made very little contact with relevant materials from other disciplines, including theoretical biology, management science, and design theory. This article draws on these materials to consider some unavoidable conundrums faced by any attempt to present a particular way of dividing tasks among a labor team as the uniquely rational way of doing this, given the interdependence of the underlying evaluative standards by which the products of a system of division of labor (...) will be judged. Divisions of labor will typically cut across these interdependencies in ways which leave the outcomes of a process of labor hostage to path dependencies and suboptimalities. Some attempts to avoid these results are shown to be unsuccessful. All these difficulties are compounded by the fact that, in many cases, the division of labor has to be constructed over a ground of values that is itself being constructed simultaneously with the products which they are invoked to assess. Key Words: risk spreading • interdependency • NK fitness landscapes • complexity • epistasis • Kuhn • modularity • path dependency. (shrink)

We show that Smullyan's analytic tableaux cannot p-simulate the truth-tables. We identify the cause of this computational breakdown and relate it to an underlying semantic difficulty which is common to the whole tradition originating in Gentzen's sequent calculus, namely the dissonance between cut-free proofs and the Principle of Bivalence. Finally we discuss some ways in which this principle can be built into a tableau-like method without affecting its analytic nature.

In our information societies, tasks and decisions are increasingly outsourced to automated systems, machines, and artificial agents that mediate human relationships, by taking decisions and acting on the basis of algorithms. This raises a critical issue: how are algorithmic procedures and applications to be appraised and governed? This question needs to be investigated, if one wishes to avoid the traps of ICTs ending up in isolating humans behind their screens and digital delegates, or harnessing them in a passive role, by (...) curtailing their freedom and autonomy. (shrink)

We discuss the interpolation property on some important families of non classical logics, such as intuitionistic, modal, fuzzy, and linear logics. A special paragraph is devoted to a generalization of the interpolation property, uniform interpolation.

Ian C. Jarvie developed the idea of situational logic in a subtle and effective way. He was also interested in, as well as a contributor to, the institution of academic publication. This chapter provides a situational analysis of an important recurrent pattern in academic publishing, namely, the concentration of work around particular topics, despite the fact that most such work will be unrewarded in the economy of esteem that is meant to be in play.

In this paper we provide a detailed proof-theoretical analysis of a natural deduction system for classical propositional logic that (i) represents classical proofs in a more natural way than standard Gentzen-style natural deduction, (ii) admits of a simple normalization procedure such that normal proofs enjoy the Weak Subformula Property, (iii) provides the means to prove a Non-contamination Property of normal proofs that is not satisfied by normal proofs in the Gentzen tradition and is useful for applications, especially in formal argumentation, (...) (iv) naturally leads to defining a notion of depth of a proof, to the effect that, for every fixed natural k, normal k-depth deducibility is a tractable problem and converges to classical deducibility as k tends to infinity. (shrink)

Is expertise in applied ethics compatible with individual autonomy and democratic self‐governance? This depends on whether a ‘tracking condition’ is satisfied for expert claims about issues in applied ethics. This condition requires that, when expert deliberations are properly conducted they ‘track’ the courses of reasoning that the experts’ clients would themselves have undertaken if they had (perhaps subject to certain conditions) considered the matters for themselves. Pluralism of the kind thematised by Isaiah Berlin and Stuart Hampshire suggests that the tracking (...) condition typically will not be satisfied and, hence, that whatever experts are praticising in applied ethics they are doing it contrary to democratic principles of autonomy and self‐government. The implications of this result are sketched and some standard objections briefly considered. (shrink)

We have considered two strategies for using native utterances as evidence for assigning native beliefs. We have shown that each of these two strategies (literalism and symbolism) can avoid the logical difficulties mentioned in section 1 — so long, at least, as we employ an account of the logical form of belief sentences developed by Burdick. We have also considered the methodological principles which provide the basis for translational practice. Based on our consideration of these principles, we then argued that (...) we must prefer the literalist strategy for attributing beliefs. Only the literalist strategy enables us to provide a recursive account of the significance of native utterances, and only the literalist strategy enables us to maximize the truth of our claims about native beliefs. (shrink)

Kuhn’s “essential tension” between conservative and innovative imperatives in enquiry has an empirical analogue—between the potential benefits of collectivization of enquiry and the social dynamic impediments to effective sharing of information and insights in collective settings. A range of empirical materials from social psychology and organization theory are considered which bear on the issue of balancing these opposing forces and an institution is described in which they are balanced in a way which is appropriate for collective knowledge production.

In his renowned collection Philosophy as a Way of Life, Pierre Hadot suggests that the original trait of philosophy as a method by which one exercises themselves to achieve a new way of living and seeing the world fails with the rise of modernity. In that time, philosophy increasingly takes on a merely theoretical aspect, tending toward a system. However, Hadot himself glimpses at the dawn of modernity some instances of the original trait of philosophy still very much present, and (...) in his wake, Michel Foucault warns that between the late 16th and early 17th centuries the philosophical question of the reform of the mind attests to a still very close link between asceticism and truth. This book aims to develop just such an idea by thoroughly analyzing the most representative works of the reform of the mind in the early modern period: Francis Bacon's New Organon (1620), René Descartes' Discourse on the Method (1637), and Baruch Spinoza's Treatise on the Emendation of the Intellect (1677). From this analysis it will emerge that these modern works fully deserve to be counted among the tradition of philosophy as way of life. On closer inspection, the inquiries about method elaborated in these works are fully understandable only when read in the light of a broader and more complex philosophical need: to establish the spiritual conditions for accessing truth and aspiring to full self-realization. (shrink)

This book supports the idea that the ancient conception of philosophy as a way of life does not disappear in early modernity, but is transformed into a search for how to cure, guide, and free the human mind.

This book was published in 2003.This volume presents a detailed examination of incommensurability in the value-theoretical sense. Exploring how choosers deal with problems and constraints of choice, the author draws on work in cognitive psychology, in sociology, in jurisprudence, in economics, and in the theory of value to show how choosers learn to make trade-offs when there is potential incommensurability among the options they are considering. The analysis is also informed by recent work in the tradition of Michel Foucault. With (...) so many modern devices and ideals of government dependent on the comparability of options, this book is timely and can inform public debate about de-regulation, user-pays, accountability, and the substitution of market mechanisms for government regulation and supply. (shrink)

In this paper I discuss Kant’s philosophy of grammar in order to argue that: (a) the formal analysis of language implies that there is a structural correspondence between logical and grammatical form; (b) there is a distinction between the sense in which logic is formal and the sense in which grammar is formal; (c) universal grammar descends from the system of categorial functions that are investigated in the transcendental analytic; (d) transcendental grammar implies that the universal form of human language (...) has its ground in the universal structure of thought; (e) the concept of a grammatical norm is clarified once we combine the theory of universal grammar with how linguistic experience takes place. (shrink)

Deductive inference is usually regarded as being “tautological” or “analytical”: the information conveyed by the conclusion is contained in the information conveyed by the premises. This idea, however, clashes with the undecidability of first-order logic and with the (likely) intractability of Boolean logic. In this article, we address the problem both from the semantic and the proof-theoretical point of view. We propose a hierarchy of propositional logics that are all tractable (i.e. decidable in polynomial time), although by means of growing (...) computational resources, and converge towards classical propositional logic. The underlying claim is that this hierarchy can be used to represent increasing levels of “depth” or “informativeness” of Boolean reasoning. Special attention is paid to the most basic logic in this hierarchy, the pure “intelim logic”, which satisfies all the requirements of a natural deduction system (allowing both introduction and elimination rules for each logical operator) while admitting of a feasible (quadratic) decision procedure. We argue that this logic is “analytic” in a particularly strict sense, in that it rules out any use of “virtual information”, which is chiefly responsible for the combinatorial explosion of standard classical systems. As a result, analyticity and tractability are reconciled and growing degrees of computational complexity are associated with the depth at which the use of virtual information is allowed. (shrink)

Using only propositional connectives and the provability predicate of a Σ1-sound theory T containing Peano Arithmetic we define recursively enumerable relations that are complete for specific natural classes of relations, as the class of all r. e. relations, and the class of all strict partial orders. We apply these results to give representations of these classes in T by means of formulas.