Shahid Rahman

Logic, epistemology, and the unity of science

I. Some Programmatic Comments. 1. Logic, Epistemology and the Unity of Science: An Encyclopedic Project in the Spirit of Neurath and Diderot Shahid Rahman and John Symons. 2. An International Encyclopedia of the Unified Sciences translated by John Symons and Ramon Alvarado) Otto Neurath. II. Game Theory and Independence Friendly Logic as a Unifying Framework. 3. Towards a Unity of the Human Behavioral Sciences Herbert Gintis. 4. Some Coloured Remarks on the Foundations of Mathematics in the 20th Century Gerhard Heinzmann. 5. Logical Versus Nonlogical Concepts: An Untenable Dualism? Jaakko Hintikka. 6. Semantic Games in Logic and Epistemology Ahti-Veikko Pietarinen. 7. IF Logic, Game-Theoretical Semantics and New Prospects for Philosophy of Science Ahti-Veikko Pietarinen and Gabriel Sandu. III. Unity and Plurality in Science and in Logic. 8. Concepts Structured through Reduction: A Structuralist Resource Illuminates the Consolidation-Long-Term Potentiation (LTP) Link John Bickle. 9. The Unity of Science and the Unity of Being: A Sketch of a Formal Approach C. Ulises Moulines. 10. Logical Pluralism and the Preservation of Warrant Greg Restall. 11. In Defence of the Dog: Response to Restall Stephen Read. 12. Normic Laws, Non-monotonic Reasoning, and the Unity of Science Gerhard Schurz. 13. The Puzzling Role of Philosophy in Life Sciences: Bases for a Joint Program for Philosophy and History of Science Juan Manuel Torres. 14. The Creative Growth of Mathematics Jean Paul Van Bendegem. 15. Quantum Logic and the Unity of Science John Woods and Kent Peacock. IV. The Logic of the Knowledge-Seeking Activities. 16. Belief Contraction, Anti-formulae and Resource Overdraft: Part II Deletion in Resource Unbounded Logics Dov Gabbay, Odinaldo Rodrigues and John Woods. 17. Reasoning about Knowledge in Linear Logic: Modalities and Complexity Mathieu Marion and Mehrnouche Sadrzadeh. 18. A Solution to Fitchs Paradox of Knowability Helge Ruckert. 19. Theories of Knowledge and Ignorance Wiebe van der Hoek, Jan Jaspars and Elias Thijsse. 20. Action-Theoretic Aspects of Theory Choice Heinrich Wansing. 21. Some Computational Constraints in Epistemic Logic Timothy Williamson. IV. Contributions from Non-Classical Logics. 22. The Need for Adaptive Logics in Epistemology Diderik Batens. 23. Logics for Qualitative Reasoning Paulo Veloso and Walter Carnielli. 24. Logic of Dynamics and Dynamics of Logic: Some Paradigm Examples Bob Coecke, David J. Moore and Sonja Smets. 25. Complementarity and Paraconsistency Newton C. A. Da Costa and Decio Krause. 26. Law, Logic, Rhetoric: a Procedural Model of Legal Argumentation Arno Lodder. 27. Essentialist Metaphysics in a Scientific Framework Ulrich Nortmann. Index.

On how to be a dialogician

We will take as one of the main issues of this paper the challenge which the dialogical approaches offer to the relation of semantics and pragmatics concerning the concept of proof (strategy) and proposition (game). While our aim here will be to present the main technical and philosophical features of what can be seen as the dialogical approach to logic, illustrated through both very well known and new dialogics, we would also like to delineate the common pragmatic attitude which constitutes the cohesive force within the dialogical universe.

Dialogical connexive logic

Many of the discussions about conditionals can best be put as follows:can those conditionals that involve an entailment relation be formulatedwithin a formal system? The reasons for the failure of the classical approachto entailment have usually been that they ignore the meaning connectionbetween antecedent and consequent in a valid entailment. One of the firsttheories in the history of logic about meaning connection resulted from thestoic discussions on tightening the relation between the If- and the Then-parts of conditionals, which in this context was called συναρτησις(connection). This theory gave a justification for the validity of what we todayexpress through the formulae ¬(a → ¬ a) and ¬(¬ a → a). Hugh MacColl and, more recently, Storrs McCall (from 1877 to 1906 and from1963 to 1975 respectively) searched for a formal system in which the validity ofthese formulae could be expressed. Unfortunately neither of the resulting systems is very satisfactory. In this paper we introduce dialogical games with the help of a new connexive If-Then (“→”), the structural rules of which allow the Proponent to develop (formal) winning strategies not only for the above-mentioned connexive theses but also for (a → b) → ¬(a → ¬ b) and (a → b) → ¬(¬ a → b). Further on, we developthe corresponding tableau systems and conclude with some remarks on possibleperspectives and consequences of the dialogical approach to connexivity including the loss of uniform substitution leading to a new concept of logical form.

From Games to Dialogues and Back

In this article two game-theoretically flavored approaches to logic are systematically compared: dialogical logic founded by Paul Lorenzen and Kuno Lorenz, and the game-theoretical semantics of Jaakko Hintikka. For classical proposi-tional logic and for classical first-order logic, an exact connection between ‘in-tuitionistic dialogues with hypotheses’ and semantic games is established. Various questions of a philosophical nature are also shown to arise as a result of the comparison, among them the relation between the model-theoretic and proof-theoretic approaches to the philosophy of logic and mathematics.

Context-Sensitivity in Jain Philosophy: A Dialogical Study of Siddharṣigaṇi’s Commentary on the Handbook of Logic

In classical India, Jain philosophers developed a theory of viewpoints (naya-vāda) according to which any statement is always performed within and dependent upon a given epistemic perspective or viewpoint. The Jainas furnished this epistemology with an (epistemic) theory of disputation that takes into account the viewpoint in which the main thesis has been stated. The main aim of our paper is to delve into the Jain notion of viewpoint-contextualisation and to develop the elements of a suitable logical system that should offer a reconstruction of the Jainas’ epistemic theory of disputation. A crucial step of our project is to approach the Jain theory of disputation with the help of a theory of meaning for logical constants based on argumentative practices called dialogical logic. Since in the dialogical framework the meaning of the logical constants is given by the norms or rules for their use in a debate, it provides a meaning theory closer to the Jain context-sensitive disputation theory than the main-stream formal model-theoretic semantics.

Constructive Type Theory and the Dialogical Approach to Meaning

. November 2013 Volume 8: Games, Game Theory and Game Semantics pages 1-72. DOI: . Also online in: www.thebalticyearbook.org

Hugh Maccoll and the birth of logical pluralism.

This chapter outlines the path that led MacColl from his notion of statement to his various proposals for innovating logic. MacColls philosophical ideas are based on a kind of instrumentalism, which is extended beyond both of the mainstream paradigms of formal logic; mathematics as logic (logicism) and logic as algebra. It is impossible to resist the temptation to compare MacColls contributions to science with his literary incursions. MacColl penned both one of the most conservative Victorian books on science fiction of his time and one of the most innovative proposals on logic of the 19 th century. MacColl gave preference to the propositional interpretation because of its generality and called it pure logic. The main connective in his pure logic is the conditional and accordingly his algebra contains a specific operator for this connective. Two main factors might have been determinant for the fact that his work fell into oblivion; one is related to technical issues, and the other to his philosophical position.

Hugh maccoll: eine bibliographische erschließung seiner hauptwerke und notizen zu ihrer rezeptionsgeschichte

The work of Hugh MacColl (1837–1909) suffered the same fate after his death as before it:despite being vaguely alluded to and in part even commended, on the whole it has remained an unknown quantity. Even worse, those of his ideas which have played a decisive role in the history of logic have been credited to his successors; this is especially the case with the definition of strict implication and the first formal development of formal modal logic. This paper takes an initial step towards a rectification of this unfortunate misrepresentation, presenting a bibliography of MacColl’s most significant publications with particular regard to their reception

Linking Game-Theoretical Approaches with Constructive Type Theory Dialogical Strategies, CTT demonstrations and the Axiom of Choice

This title links two of the most dominant research streams in philosophy of logic, namely game theory and proof theory. As the work’s subtitle expresses, the authors will build this link by means of the dialogical approach to logic. One important aspect of the present study is that the authors restrict themselves to the logically valid fragment of Constructive Type Theory (CTT). The reason is that, once that fragment is achieved the result can be extended to cover the whole CTT system. The first chapters in the brief offer overviews on the two frameworks discussed in the book with an emphasis on the dialogical framework. The third chapter demonstrates the left-to-right direction of the equivalence result. This is followed by a chapter that demonstrates the use of the algorithm in showing how to transform a specific winning strategy into a CCT-demonstration of the axiom of choice. The fifth chapter develops the algorithm from CTT-demonstrations to dialogical strategies. This brief concludes by introducing elements of discussion which are to be developed in subsequent work.

On Hypothetical Judgements and Leibniz’s Notion of Conditional Right

Sebastien Magnier provides a remarkable analysis of the notion of conditional right with the help of public announcement logic that he generalizes for the logical study of legal norms. Magnier’s main idea, motivated by the earlier exhaustive textual and systematic work of Matthias Armgardt and the subsequent studies carried out by Alexandre Thiercelin, involves Leibniz’s notion of certification, which plays a central role in the famous De conditionibus. Magnier proposes to render the notion of certification of A as there is public evidence for A. More generally, the meanings of “conditional right” and “conditional legal norm” are established by means of identifying a specific kind of dialogical interaction during a legal trial constituted by games of giving and asking for reasons. This yields a theory of meaning rooted in the practice itself of legal debates.