The Leibnizian "Circle"

Paper by Fabrizio Mondador

INFORMATION-THEORETIC LOGIC

Information-theoretic approaches to formal logic analyse the "common intuitive" concept of propositional implication (or argumental validity) in terms of information content of propositions and sets of propositions: one given proposition implies a second if the former contains all of the information contained by the latter; an argument is valid if the conclusion contains no information beyond that of the premise-set. This paper locates information-theoretic approaches historically, philosophically and pragmatically. Advantages and disadvantages are identified by examining such approaches in themselves and by contrasting them with standard transformation-theoretic approaches. Transformation-theoretic approaches analyse validity (and thus implication) in terms of transformations that map one argument onto another: a given argument is valid if no transformation carries it onto an argument with all true premises and false conclusion. Model-theoretic, set-theoretic, and substitution-theoretic approaches, which dominate current literature, can be construed as transformation-theoretic, as can the so-called possible-worlds approaches. Ontic and epistemic presuppositions of both types of approaches are considered. Attention is given to the question of whether our historically cumulative experience applying logic is better explained from a purely information-theoretic perspective or from a purely transformation-theoretic perspective or whether apparent conflicts between the two types of approaches need to be reconciled in order to forge a new type of approach that recognizes their basic complementarity

Scientific change and the meanings of terms : an examination of P.K. Feyerabend's incommensurability theses

Feyerabend's incommensurability thesis concerning scientific change engenders a number of logical problems. While it is possible to examine Feyerabend's theory in relation to his historical arguments, the defects implicit in his arguments for the theory render more appropriate an analytical approach. These defects arise from the conjunction of presuppositions and theses that form the background to Feyerabend's claims for an incommensurability thesis. This background contains Feyerabend's criticisms of the traditional empiricism of the twentieth century and its reductionist account of scientific development, his objections to any attempt to rationalize science, his claim that there are fundamental conceptual and ontological changes in science, and his adoption of a meaning variance thesis which envisages wholesale changes in the meanings of all descriptive terms when one theory is replaced by another. While the criticism against traditional empiricism can be upheld, it does not necessitate the conclusion that alternative theories are incommensurable. Feyerabend's attack on Lakatos' rational Reconstructionism is not conclusive: he overlooks the possibility that there do exist standards of criticism, which can be termed "rational", operating within the sciences. The suggestion, supported by Hanson and Kuhn, that there are fundamental conceptual changes in science is open to criticism. The case against radical meaning variance is more complex as it requires the support of a theory of meaning. It is not clear that Feyerabend can, using Wharf's controversial ideas about language, provide a suitable theory of meaning to support his claims. A more satisfactory theory of meaning, based on views of Frege and Wittgenstein, while not denying some changes in the meanings of scientific terms, does not entail the consequence that there are necessarily radical changes in meaning from theory to theory. Although the objections to traditional empiricism are sound and a moderate thesis of meaning variance is acceptable, these do not give rise to the view that competing theories are incommensurable. Historical evidence shows the need to take into consideration the gradual, rather than revolutionary, nature of scientific development. This is compatible both with a moderate thesis of meaning variance and with a modification of the network model developed by Duhem, Quine and Hesse

Categoricity

After a short preface, the first of the three sections of this paper is devoted to historical and philosophic aspects of categoricity. The second section is a self-contained exposition, including detailed definitions, of a proof that every mathematical system whose domain is the closure of its set of distinguished individuals under its distinguished functions is categorically characterized by its induction principle together with its true atoms (atomic sentences and negations of atomic sentences). The third section deals with applications especially those involving the distinction between characterizing a system and axiomatizing the truths of a syste

On the foundations of legal reasoning in international law

Issues pertaining to the "foundations" of legal reasoning in international law break down into several discrete questions: what do statements about law mean; how do they get their meaning: to what do legal terms refer; in what does knowledge of law consist; how do we reason with legal concepts; what constitutes a criterion for argumentative success; how do bodies of legal concepts combine to form systems; is the conceptual organisation of different types of legal system, such as municipal law and international law, necessarily (or even factually) the same at some fundamental level?... This thesis is concerned with some measure with all of these questions, but the focus throughout is on those of the meaning of what we say about law, of legal knowledge, and of topological issues regarding legal systems (that is, how various types of legal system stand, conceptually, to one another). The thesis falls into two parts. The first, which is critical in nature, looks at some of the ways in which modern positivism has attempted to supply answers to these questions. It shall be argued that underlying those attempts is a particular view about the foundations of legal reasoning which has remained fairly constant in modern legal theory, not only among the positivists but also commonly among their sceptic rivals. Several difficulties with this view are raised and explored, all of which have contributed to the notion that international law is, when viewed through the spectacles of a municipal lawyer, at best a primitive system of law. The heart of Part I is a discussion of the character of legal knowledge. This takes place in the context of an account of the "Institutional Theory of Law" (ITL), as propounded by Neil MacCormick and Ota Weinberger. The argument that emerges is one broadly in favour of ITL, though critical of the methodological and philosophical assumptions on the basis of which the main edifice of the theory rests. It is submitted that such assumptions are the result of misplaced views about semantics and the nature of reference. Part I ends with the suggestion of an alternative, and hopefully more stable, strategy for generating the account of legal knowledge for which ITL strove. Part II comprises a positive thesis about the foundations of legal reasoning in international law, developed on the back of the strategy in Part I