basic objectives of dialogue logic in historical perspective

The extensive research in logic conducted by using concepts and methods of game theory as documented in this collection of papers, allows to see dialogue logic in a number of new perspectives. This situation may gain further clarity by looking back to the inception of dialogue logic in the late fifties and early sixties.     

In the shadow of giants: The work of mario pieri in the foundations of mathematics

A discussion is given of the research in the foundations of mathematics of Mario Pieri (1860-1913) and how it compares with the works of Christian von Staudt (1798-1867), Giuseppe Peano (1858-1932), David Hubert (1862-1943), and Alfred Tarski (1902-1983). The author demonstrates that the acceptance of Pieri’s results was overshadowed by the research of these four scholars, and argues that Pieri’s work merits a more significant place in the history of mathematics than it currently enjoys     

Hilbert and the internal logic of mathematics

Hilbert's programme is shown to have been inspired in part by what we can call Kronecker's programme in the foundations of an arithmetic theory of algebraic quantities.While finitism stays within the bounds of intuitive finite arithmetic, metamathematics goes beyond in the hope of recovering classical logic. The leap into the transfinite proved to be hazardous, not only from the perspective of Gödel's results, but also from a Kroneckerian point of view.Hilbert's rare admission of a Kroneckerian influence does not constitute the basis of such a reconstruction; it is rather Kronecker's mathematical practice which is seen as a forerunner of Hilbert's endeavour in the foundations of mathematics.I am indebted to an anonymous referee for many helpful critical remarks.     

Philosophical reflections on the foundations of mathematics

This article was written jointly by a philosopher and a mathematician. It has two aims: to acquaint mathematicians with some of the philosophical questions at the foundations of their subject and to familiarize philosophers with some of the answers to these questions which have recently been obtained by mathematicians. In particular, we argue that, if these recent findings are borne in mind, four different basic philosophical positions, logicism, formalism, platonism and intuitionism, if stated with some moderation, are in fact reconcilable, although with some reservations in the case of logicism, provided one adopts a nominalistic interpretation of Plato's ideal objects. This eclectic view has been asserted by Lambek and Scott (LS 1986) on fairly technical grounds, but the present argument is meant to be accessible to a wider audience and to provide some new insights.     

The historical foundations of the research-practice distinction in bioethics

The distinction between clinical research and clinical practice directs how we partition medicine and biomedical science. Reasons for a sharp distinction date historically to the work of the National Commission for the Protection of Human Subjects of Biomedical and Behavioral Research, especially to its analysis of the “boundaries” between research and practice in the Belmont Report (1978). Belmont presents a segregation model of the research-practice distinction, according to which research and practice form conceptually exclusive sets of activities and interventions. This model is still the standard in federal regulations today. However, the Commission’s deliberations and conclusions about the boundaries are more complicated, nuanced, and instructive than has generally been appreciated. The National Commission did not conclude that practice needs no oversight comparable to the regulation of research. It debated the matter and inclined to the view that the oversight of practice needed to be upgraded, though the Commission stopped short of proposing new regulations for its oversight, largely for prudential political reasons.     

Category theory and the foundations of mathematics: Philosophical excavations

The aim of this paper is to clarify the role of category theory in the foundations of mathematics. There is a good deal of confusion surrounding this issue. A standard philosophical strategy in the face of a situation of this kind is to draw various distinctions and in this way show that the confusion rests on divergent conceptions of what the foundations of mathematics ought to be. This is the strategy adopted in the present paper. It is divided into 5 sections. We first show that already in the set theoretical framework, there are different dimensions to the expression foundations of. We then explore these dimensions more thoroughly. After a very short discussion of the links between these dimensions, we move to some of the arguments presented for and against category theory in the foundational landscape. We end up on a more speculative note by examining the relationships between category theory and set theory.Various versions of this paper have been read by many people, many of whom have made crucial comments. Needless to say, I am entirely responsible for the claims made in this paper. I would particularly like to thank, in alphabetical order, Mario Bunge, Marta Bunge, Michael Hallett, Andrew Irvine, Saunders Mac Lane, Collin McLarty, Peneloppe Maddy and Mihaly Makkai. Part of the work was done while the author was a visiting fellow at REHSEIS in Paris and at the Center for Philosophy of Science in Pittsburgh. I would like to thank everyone for his or her help and support. I gratefully acknowledge the financial support received from the SSHRC of Canada while this work was done.     

Probability, logic and the cognitive foundations of rational belief

Since Pascal introduced the idea of mathematical probability in the 17th century discussions of uncertainty and “rational” belief have been dogged by philosophical and technical disputes. Furthermore, the last quarter century has seen an explosion of new questions and ideas, stimulated by developments in the computer and cognitive sciences. Competing ideas about probability are often driven by different intuitions about the nature of belief that arise from the needs of different domains (e.g., economics, management theory, engineering, medicine, the life sciences etc). Taking medicine as our focus we develop three lines of argument (historical, practical and cognitive) that suggest that traditional views of probability cannot accommodate all the competing demands and diverse constraints that arise in complex real-world domains. A model of uncertain reasoning based on a form of logical argumentation appears to unify many diverse ideas. The model has precursors in informal discussions of argumentation due to Toulmin, and the notion of logical probability advocated by Keynes, but recent developments in artificial intelligence and cognitive science suggest ways of resolving epistemological and technical issues that they could not address.