On Wittgenstein"s "One of the Most Fundamental\ud Language Games�

My interest in this topic springs from the controversy that\ud Wittgenstein"s language games have sparked in gametheoretic\ud approaches to logic. Hintikka (1996) has argued\ud that semantic games and language games share a mutual\ud concern on how language and the world are related. Such\ud links are codified in the practices of language games, and\ud are operationalised in semantic games by the mathematical\ud theory of games

Question-Answer Structures in Cognition

[Abstract] Peirce’s semeiotic was all about cognitive studies of the mind. His anthropomorphism states that the study of the structures of the world must go through the study of the structures of the mind shaped by experience. This was labelled much later as? Descriptive taphysics? What is the correct method of such an investigation? Peirce thought that all our knowledge-seeking activities must be conducted in terms of Socratic processes of questions and answers. The mind is a dialogical creatory of signs. Rather than? Putting questions to Nature?, the method of doing philosophy, that is pragmaticism, is therefore? Putting questions to mind? In Peirce’s proof of pragmaticism, the crucial steps characterize abduction in terms of signs that give their objects as conclusive answers to questions. Questions are experiments on various ways of finding solutions in our thoughts. And logic is the theory of the inner nature of habits which cater for those solution

Recent studies on signs: Commentary and perspectives

In this commentary, I reply to the fourteen papers published in the Sign Systems Studies special issue on Peirce’s Theory of Signs, with a view on connecting some of their central themes and theses and in putting some of the key points in those papers into a wider perspective of Peirce’s logic and philosophy

Signs systematically studied: Invitation to Peirce’s theory

This introductory presentation reviews noteworthy topics and concepts in Peirce’s interrelated kingdoms of the theory of signs, their classification, categories, logic and semeiotic

Some Logical Notations for Pragmatic Assertions

The pragmatic notion of assertion has an important inferential role in logic. There are also many notational forms to express assertions in logical systems. This paper reviews, compares and analyses languages with signs for assertions, including explicit signs such as Frege’s and Dalla Pozza’s logical systems and implicit signs with no specific sign for assertion, such as Peirce’s algebraic and graphical logics and the recent modification of the latter termed Assertive Graphs. We identify and discuss the main ‘points’ of these notations on the logical representation of assertions, and evaluate their systems from the perspective of the philosophy of logical notations. Pragmatic assertions turn out to be useful in providing intended interpretations of a variety of logical systems

Editors\u27 Introduction

The idea of interpreting quantifiers in terms of a game between two players was first suggested at the end of the 19th century by one of the inventors of quantification theory, C. S. Peirce, but it laid buried in his papers until it was discovered in the 1980s. His idea was independently discovered in the 1950s, when Leon Henkin suggested a game semantics for infinitary languages. Paul Lorenzen introduced his Dialogspiele at the same time, while his student Kuno Lorenz introduced the vocabulary of game theory that led to our modern conception of game semantics shortly after. The idea is to provide an explanation of the meaning of the logical connectives and quantifiers in terms of rules for non-collaborative, zero-sum games between two agents, one of whom argues for the validity of the claim against moves from the other, and to define truth in terms of the existence of a winning strategy for the defender

A Scholastic-Realist Modal-Structuralism

How are we to understand the talk about properties of structures the existence of which is conditional upon the assumption of the reality of those structures? Mathematics is not about abstract objects, yet unlike fictionalism, modal-structuralism respects the truth of theorems and proofs. But it is nominalistic with respect to possibilia. The problem is that, for fear of reducing possibilia to actualities, the second-order modal logic that claims to axiomatise modal existence has no real semantics. There is no cross-identification of higher-order mathematical entities and thus we cannot know what those entities are. I suggest that a scholastic notion of realism, interspersed with cross-identification of higher-order entities, can deliver the semantics without collapse. This semantics of modalities is related to Peirce's logic and his pragmaticist philosophy of mathematics.Comment comprendre le discours sur les propriétés de structures, dont l'existence dépend de ce que l'on suppose la réalité de ces structures ? Les mathématiques ne portent pas sur des objets abstraits, pourtant le structuralisme modal respecte la vérité des théorèmes et des preuves, contrairement au fictionalisme. Il est en revanche nominaliste quant aux possibilia. Le problème est que, de peur de réduire les possibilia à des actualités, la logique modale du second ordre qui prétend axiomatiser l'existence modale ne possède pas réellement de sémantique. Il n'existe pas d'identification croisée des entités mathématiques d'ordre supérieur et ainsi nous ne pouvons savoir ce que sont ces entités. Je suggère qu'une notion scolastique de réalisme, émaillé d'identification croisée d'entités d'ordre supérieur, peut nous fournir une sémantique sans s'écrouler. La sémantique des modalités est liée à la logique de Peirce et à sa philosophie pragmaticiste des mathématiques