Dummett's logic LC quantified, Q-LC, is shown to be characterized by the extended frame Q+, ,D, where Q+ is the set of non-negative rational numbers, is the numerical relation less or equal then and D is the domain function such that for all v, w Q+, Dv and if v w, then D v . D v D w . Moreover, simple completeness proofs of extensions of Q-LC are given.

The paper presents an epistemic logic with quantification over agents of knowledge and with a syntactical distinction between de re and de dicto occurrences of terms. Knowledge de dicto is characterized as ‘knowledge that’, and knowlegde de re as ‘knowledge of’. Transition semantics turns out to be an adequate tool to account for the distinctions introduced.

Predicate extensions of the intermediate logic of the weak excluded middle and of the modal logic S4.2 are introduced and investigated. In particular it is shown that some of them are characterized by subclasses of the class of directed frames with either constant or nested domains.

A general strategy for proving completeness theorems for quantified modal logics is provided. Starting from free quantified modal logic K, with or without identity, extensions obtained either by adding the principle of universal instantiation or the converse of the Barcan formula or the Barcan formula are considered and proved complete in a uniform way. Completeness theorems are also shown for systems with the extended Barcan rule as well as for some quantified extensions of the modal logic B. The incompleteness of (...) Q°.B + BF is also proved. (shrink)

The main aim of this paper is to introduce the logic QE-LC whose language contains the existence predicate E and which is characterized by the class of connected (Kripke) E-models with nested domains.

Theoretical approaches to public opinion are hard to find in the sociological literature, with the exception of the seminal work of Jürgen Habermas. One important alternative, although almost unknown in the English-speaking world, is offered in a few contributions by the systems theoretician Niklas Luhmann. Both critical theory and systems theory start from a historical analysis of the conditions that led to the rise of a public sphere and understand its function as the limitation and control of the arbitrariness of (...) power. Critical theory considers the public sphere as a social space where citizens can participate and discuss freely and without constraints. Thus, it legitimizes political power. Systems theory presents a completely different concept of the public sphere and conceives of it in terms of second-order observation. Through public opinion the modern political system observes itself and stimulates as well as limits its decision-making processes. This paper argues that both approaches share the idea that the political system, like every other social subsystem, must generate a system-specific uncertainty in order to limit its own arbitrariness and to be able to develop its decision-making potential. Both approaches locate this uncertainty in the sphere of public opinion. But they radically differ in the way they conceptualize public opinion’s effects on modern politics. Such differences between critical theory and systems theory are illustrated by an analysis of recent political events. (shrink)

The aim of this paper is to provide a decision procedure for Dummett's logic LC, such that with any given formula will be associated either a proof in a sequent calculus equivalent to LC or a finite linear Kripke countermodel.

We show how to use diagrams in order to obtain straightforward completeness theorems for extensions of K4.3 and a very simple and constructive proof of Bull's theorem: every normal extension of S4.3 has the finite model property.

Foundational questions in logic, mathematics, computer science and physics are constant sources of epistemological debate in contemporary philosophy. To what extent is the transfinite part of mathematics completely trustworthy? Why is there a general 'malaise' concerning the logical approach to the foundations of mathematics? What is the role of symmetry in physics? Is it possible to build a coherent worldview compatible with a macroobjectivistic position and based on the quantum picture of the world? What account can be given of opinion (...) change in the light of new evidence? These are some of the questions discussed in this volume, which collects 14 lectures on the foundations of science given at the School of Philosophy of Science, Trieste, October 1989. The volume will be of particular interest to any student or scholar engaged in interdisciplinary research into the foundations of science in the context of contemporary debates. (shrink)

The essays collected in this volume address such questions from different points of view and will interest students and scholars in several branches of scientific knowledge.

Education conceives itself as something that cannot end. Pedagogy talks of lifelong learning and teachers would never say that their work is finished just because students graduate. But edu...

Open peer commentary on the article “The Autopoiesis of Social Systems and its Criticisms” by Hugo Cadenas & Marcelo Arnold. Upshot: I discuss two aspects of Cadenas & Arnold’s target article. The first concerns some clarifications of the sociological importance of the concept of autopoiesis and the second the criticisms of this concept and its applications in the social sciences.

In this paper we present two calculi for intuitionistic logic. The first one, IG, is characterized by the fact that every proof-search terminates and termination is reached without jeopardizing the subformula property. As to the second one, SIC, proof-search terminates, the subformula property is preserved and moreover proof-search is performed without any recourse to metarules, in particular there is no need to back-track. As a consequence, proof-search in the calculus SIC is accomplished by a single tree as in classical logic.