Stig Pedersen

hiS volume in the Synthese Library Series is the result of a conference T held at the University of Roskilde, Denmark, October 31st-November 1st, 1997. The aim was to provide a forum within which philosophers, math ematicians, logicians and historians of mathematics could exchange ideas pertaining to the historical and philosophical development of proof theory. Hence the conference was called Proof Theory: History and Philosophical Significance. To quote from the conference abstract: Proof theory was developed as part of Hilberts Programme. According to Hilberts Programme one could provide mathematics with a firm and se cure foundation by formalizing all of mathematics and subsequently prove consistency of these formal systems by finitistic means. Hence proof theory was developed as a formal tool through which this goal should be fulfilled. It is well known that Hilbert's Programme in its original form was unfeasible mainly due to Gtldel's incompleteness theorems. Additionally it proved impossible to formalize all of mathematics and impossible to even prove the consistency of relatively simple formalized fragments of mathematics by finitistic methods. In spite of these problems, Gentzen showed that by extending Hilbert's proof theory it would be possible to prove the consistency of interesting formal systems, perhaps not by finitis tic methods but still by methods of minimal strength. This generalization of Hilbert's original programme has fueled modern proof theory which is a rich part of mathematical logic with many significant implications for the philosophy of mathematics.

One of the cornerstones of modern medicine is the search for what causes diseases to develop. A conception of multifactorial disease causes has emerged over the years. Theories of disease causation, however, have not quite been developed in accordance with this view. It is the purpose of this paper to provide a fundamental explication of aspects of causation relevant for discussing causes of disease.The first part of the analysis will discuss discrimination between singular and general causality. Singular causality, as in the specific patient, is a relation between a concrete sequence of causally linked events. General causation, e.g. as in disease etiology, means various categories of causal relations between event types. The paper introduces the concept of a reference case serving as a source for causal inference, reaching beyond the concept of general causality.

'Possible worlds' have been one of the true conundrum notions in philosophy. On the hand possible worlds have proved very useful in philosophical logic for obtaining significant formal results with sunbstantial philosophical import. Yet on the other they have generated much noise and commotion in especially metaphysics and epistemology. From a logical point of view they are useful tools or conceptual constructions, from a philosophical point of view troublesome entitites generating endless discussions.

Engineering science is a scientific discipline that from the point of view of epistemology and the philosophy of science has been somewhat neglected. When engineering science was under philosophical scrutiny it often just involved the question of whether engineering is a spin-off of pure and applied science and their methods. We, however, hold that engineering is a science governed by its own epistemology, methodology and ontology. This point is systematically argued by comparing the different sciences with respect to a particular set of characterization criteria

The aim of this thematically unified anthology is to track the history of epistemic logic, to consider some important applications of these logics of knowledge and belief in a variety of fields, and finally to discuss future directions of research with particular emphasis on 'active agenthood' and multi-modal systems. It is accessible to researchers and graduate students in philosophy, computer science, game theory, economics and related disciplines utilizing the means and methods of epistemic logic.