Elena Dragalina Chernaya

The purpose of this paper is twofold: (1) to clarify Ludwig Wittgenstein’s thesis that colours possess logical structures, focusing on his ‘puzzle proposition’ that “there can be a bluish green but not a reddish green”, (2) to compare modeltheoretical and gametheoretical approaches to the colour exclusion problem. What is gained, then, is a new gametheoretical framework for the logic of ‘forbidden’ (e.g., reddish green and bluish yellow) colours. My larger aim is to discuss phenomenological principles of the demarcation of the bounds of logic as formal ontology of abstract objects.

According to Alfred Tarski’s classical definition, logical consequence is necessary and formal. This paper focuses on the question: In what sense (if any) is material consequence a logical relation? For Tarski, material consequence has no modal force. Treating all terms (of a language with a fixed domain) as logical, he reduces logical consequence to material consequence. Thus, Tarskian material consequence seems to be a logical oxymoron designed to emphasize the importance of the distinction between logical and extra-logical terms for the definition of logical consequence. Historically, however, there have been different approaches to material consequences. This paper attempts to provide an investigation into the parallels between Tarski’s dichotomy of formal and material consequence and the modern.

This paper addresses Ludwig Wittgenstein’s claim that “there can never be surprises in logic” (TLP 6.1251) from a perspective of the distinction between substantial and dynamic models of formality. It attempts to provide an interpretation of this claim as stressing the dynamic formality of logic. Focusing on interactive interpretation of compositionality as dynamic formality, it argues for the advantages of dynamic, i.e., game-theoretical approach to some binary semantical phenomena. Firstly, model-theoretical and game-theoretical interpretations of binary quantifiers are compared. Secondly, the paper offers an analysis of Wittgenstein’s idea that mixed colours (e.g., bluish green, reddish yellow, etc.) possess logical structures. To answer some experimental challenges, it provides a game-theoretical interpretation of the colours opponency in Payoff Independence (PI) logic. Comparing Nikolay Vasiliev’s logical principles and Wittgenstein’s internal properties and relations, Wittgenstein’s approach is argued for as an attempt of modelling a balance between logic and the empirical.

This paper attempts to provide an interpretation of Ludwig Wittgenstein’s logical study of colour concepts at different stages of the evolution of his approach to logic, language, and colour perception. It endeavors to reveal the influence of this study on the demarcation of the boundaries of logic and logical space. Firstly, I try to clarify Wittgenstein’s idea of logical space in «Tractatus Logico- Philosophicus» focusing on the concept of internal relations and the colour exclusion problem. Secondly, I address the “middle” Wittgenstein’s phenomenology of colours and his attempts to explain the necessity of propositions like “There cannot be a reddish-green” by reference to the geometry of colour, particularly to the colour octahedron. Thirdly, I argue for the advantages of languagegame approach to the logic of colour concepts as an attempt of modelling a balance between logic and the empirical. This paper addresses, finally, Wittgenstein’s idea that mixed colours (e.g., bluish green, reddish green, etc.) possess logical structures. The paper offers an analysis of Wittgensteinian perspective on the interpretation of reports about reddish-green and other “Martian” colours experimental perception.