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

Aspects of the constructive omega rule within automated deduction

In general, cut elimination holds for arithmetical systems with the w -rule, but not for systems with ordinary induction. Hence in the latter, there is the problem of generalisation, since arbitrary formulae can be cut in. This makes automatic theorem -proving very difficult. An important technique for investigating derivability in formal systems of arithmetic has been to embed such systems into semi- formal systems with the w -rule. This thesis describes the implementation of such a system. Moreover, an important application is presented in the form of a new method of generalisation by means of "guiding proofs" in the stronger system, which sometimes succeeds in producing proofs in the original system when other methods fail

What structuralism could not be

Frege's arithmetical-platonism is glossed as the first step in developing the thesis; however, it remains silent on the subject of structures in mathematics: the obvious examples being groups and rings, lattices and topologies. The structuralist objects to this silence, also questioning the sufficiency of Fregean platonism is answering a number of problems: e.g. Benacerraf's Twin Puzzles of Epistemic and Referential Access. The development of structuralism as a philosophical position, based on the slogan 'All mathematics is structural' collapses: there is no single coherent account which remains faithful to the tenets of structuralism and solves the puzzles of platonism. This prompts the adoption of a more modest structuralism, the aim of which is not to solve the problems facing arithmetical-platonism, but merely to give an account of the 'obviously structural areas of mathematics'. Modest strucmralism should complement an account of mathematical systems; here, Frege's platonism fulfils that role, which then constrains and shapes the development of this modest structuralism. Three alternatives are considered; a substitutional account, an account based on a modification of Dummett's theory of thin reference and a modified from of in re structuralism. This split level analysis of mathematics leads to an investigation of the robustness of the truth predicate over the two classes of mathematical statement. Focussing on the framework set out in Wright's Truth and Objectivity, a third type of statement is identified in the literature: Hilbert's formal statements. The following thesis arises: formal statements concern no special subject matter, and are merely minimally truth apt; the statements of structural mathematics form a subdiscourse - identified by the similarity of the logical grammar - displaying cognitive command. Thirdly, the statements of mathematics which concern systems form a subdiscourse which has both cognitive command and width of cosmological role. The extensions of mathematical concepts are such that best practice on the part of mathematicians either tracks or determines that extension - at least in simple cases. Examining the notions of response dependence leads to considerations of indefinite extensibility and intuitionism. The conclusion drawn is that discourse about structures and mathematical systems are response dependent but that this does not give rise to any revisionary arguments contra intuitionism

Situation semantics and its foundations

The aim of this thesis is to examine several aspects of situation semantics and to evaluate the contribution which the theory makes to our understanding of language, in particular whether it brings us nearer to a solution of some traditional puzzles with attitude reports.The presentation is in three parts. The first part, comprising chapters one and two, consists of a general introduction to the issues involved and tackles the question of where situation semantics places the boundary between semantics and pragmatics. The second and main part, chapters three to six, is devoted to demonstrating the language- dependent status of abstract situations. The interpretations of expressions and the role of the setting in composition are analysed in chapter three. In chapter four I consider Russell's views on propositions and the Russellian semantics Richards has given. Chapter five examines in detail the suggestion of chapter three that the level of abstract situations is not independent of language, recasts situation semantics accordingly as an interpreted language, and lastly considers an extension of situation semantics to include molecular facts. In chapter six situation semantics is related to direct reference semantics. Finally, chapters seven and eight treat attitude reports, analysing firstly the ingredients of Barwise and Perry's approach to the semantics of the attitudes, and secondly setting out some traditional puzzles and considering how situation semantics deals with them.The goal throughout is to clarify and understand what the ideas and insights behind situation semantics are and to determine their importance for semantic theory

Cognition and Inquiry: The Pragmatics of Conditional Reasoning

This thesis reports the results of both normative and empirical investigations into human conditional reasoning, i.e. reasoning using if ... then and related constructions. Previous empirical investigations have concentrated on experimental paradigms like Wason's Selection Task, where subjects must assess evidence relevant to the truth or falsity of a conditional rule. Popperian falsification provided the normative theory by which to assess errorful behaviour on these tasks. However, it is doubtful whether this is an appropriate normative theory from which to derive a competence model of human reasoning abilities. The relationship between normative theory and competence model need not be direct, no more than the relationship between competence model and performance needs to be. However, research in this area has imported a theory directly into individual psychology from the philosophy of science. On the apparently orthodox assumption of directness, continued adherence to this import may stand in need of re-assessment in the light of the quite radical descriptive inadequacy of falsification as a model of rational scientific inquiry. However, this model also possesses the virtue of relating the interpretation of the rule directly to the normative task strategy. Hence, this thesis has two aims: first, to retain the virtue of a direct relation between normative task strategy and interpretation while simultaneously offering a competence model which is consistent with more recent and descriptively adequate accounts of the process of scientific inquiry. In Part I, this will involve introducing a semantic theory (situation semantics) and showing that the process of inquiry implicit in this semantic theory is consistent with recent normative conceptions in the philosophy of science. The second aim is to show that the competence model derived in Part I can provide a sound rational basis for subjects' observed patterns of reasoning in conditional reasoning tasks. In Part II, chapter 5, the data obtained from the Wason Selection Task using only affirmative rules is discussed and the behaviour observed rationally reconstructed in terms of the competence model of Part I. A central concept of that model is partial interpretation (motivated by concerns of context sensitivity). Prima facie evidence for partial interpretation is provided by the observation of defective truth tables. However, in conditional reasoning experiments using negated constituents, this evidence has been interpreted differently. A subsidiary aim of Part II (which will constitute the largest section of this thesis) therefore concerns the empirical demonstration of the consistency of this data with the competence model