The English contribution to logic before Ockham

Summary The change of medieval philosophy, known to have taken place in the 14th century, is accompanied by a new and extensive application of terminist logic and by a growing importance of the university of Oxford. This essay asks the question whether this development can be explained as a development of a specific English tradition within medieval logic. In the first part of the paper it is briefly shown that a certain discontinuity can be observed in the most important continental intellectual centers; the sociological conditions which make possible such distinct local traditions within the general development of medieval scholasticism are considered shortly. The second and larger part of the paper is a census of the English contribution to logic before Ockham, ordered according to the various literary genres: Summulae, Syncategoremata/sophismata, Grammar, Commentaries on the Organon. This census tends to prove that terminist logic had a continuous tradition in Oxford, a fact which may account for the preponderance of Oxford logic in the early 14th century.A first draft of this paper was read by Norman Kretzmann and Eleonore Stump. I am very grateful to them for their valuable suggestions which have made substantial parts of the text more readable and less obscure. That it still remains very speculative and fragmentary could not be avoided even with their generous aid.     

No logic of cogency: Reply to Oakley

Despite the fact that the nature of the properties of causation is rarely discussed within the mental causation debate, the implicit assumption is that they are universals as opposed to tropes. However, in recent literature on the problem of mental causation, a new solution has emerged which aims to address the problem by appealing to tropes. It is argued that if the properties of causation are tropes rather than universals, then a psychophysical reductionism can be advanced which does not face the problem of multiple realizability. However, the 'trope solution' rests upon the assumption that one can combine a trope monism with a type dualism. I argue that such a combination cannot be allowed. Given a plausible interpretation of types within a trope ontology, trope monism in fact entails type monism. Consequently, if one identifies mental tropes with physical tropes, one must also identify mental and physical types and in doing so face a modified version of the multiple realizability argument.     

Quantum logic as a dynamic logic

We address the old question whether a logical understanding of Quantum Mechanics requires abandoning some of the principles of classical logic. Against Putnam and others (Among whom we may count or not E. W. Beth, depending on how we interpret some of his statements), our answer is a clear “no”. Philosophically, our argument is based on combining a formal semantic approach, in the spirit of E. W. Beth’s proposal of applying Tarski’s semantical methods to the analysis of physical theories, with an empirical–experimental approach to Logic, as advocated by both Beth and Putnam, but understood by us in the view of the operational- realistic tradition of Jauch and Piron, i.e. as an investigation of “the logic of yes–no experiments” (or “questions”). Technically, we use the recently-developed setting of Quantum Dynamic Logic (Baltag and Smets 2005, 2008) to make explicit the operational meaning of quantum-mechanical concepts in our formal semantics. Based on our recent results (Baltag and Smets 2005), we show that the correct interpretation of quantum-logical connectives is dynamical, rather than purely propositional. We conclude that there is no contradiction between classical logic and (our dynamic reinterpretation of) quantum logic. Moreover, we argue that the Dynamic-Logical perspective leads to a better and deeper understanding of the “non-classicality” of quantum behavior than any perspective based on static Propositional Logic.     

Discursive logic towards a logic of rational discourse

Both logic and philosophy of science investigate formal aspects of scientific discourse, i.e. properties of (non-monotonic) consequence operations for discursive logic. In the present paper we handle two of them: paraconsistency and enthymematycity.Supported by grants from the Alexander von Humboldt-Stiftung, form the Fulbright-Foundation and from the Center for Philosophy of Science at the University of Pittsburgh.Presented byJan Zygmunt     

Heterogeneous logic

This paper considers the question: what becomes of the notion of a logic as a way of codifying valid arguments when the customary assumption is dropped that the premisses and conclusions of these arguments are statements from some single language? An elegant treatment of the notion of a logic, when this assumption is in force, is that provided by Dana Scott's theory of consequence relations; this treatment is appropriately generalized in the present paper to the case where we do not make this assumption of linguistic homogeneity. Several applications of the resulting concept of a heterogeneous logic are suggested, but the main emphasis is on the formal development. One topic touched on is a certain contrast between the boolean and the intensional sentence-connectives in this more general setting.