Can Başkent

In this work, we offer a formal approach to analyze Lakatosian heuristics. We first give overviews of Lakatosian heuristics based on Lakatos's seminal work Proofs and Refutations and subset space logic which is a bimodal epistemic logic. Then, we establish the connection between Lakatosian heuristics and subset space logic by making use of an extended version of subset space logic which was suggested earlier. We then conclude with discussing the merits of our approach. © 2012 Elsevier B.V., All rights reserved.

This book explores the two major elements of Hintikka’s model of inquiry: underlying game theoretical motivations and the central role of questioning. The chapters build on the Hintikkan tradition extending Hintikka’s model and present a wide variety of approaches to the philosophy of inquiry from different directions, ranging from erotetic logic to Lakatosian philosophy, from socio-epistemologic approaches to strategic reasoning and mathematical practice. Hintikka's theory of inquiry is a well-known example of a dynamic epistemic procedure. In an interrogative inquiry, the inquirer is given a theory and a question. He then tries to answer the question based on the theory by posing questions to nature or an oracle. The initial formulation of this procedure by Hintikka is rather broad and informal. This volume introduces a carefully selected responses to the issues discussed by Hintikka. The articles in the volume were contributed by various authors associated with a research project on Hintikka's interrogative theory of inquiry conducted in the Institut d’Histoire et de Philosophie des Sciences et des Techniques of Paris, including those who visited to share their insight.

This book presents the state of the art in the fields of formal logic pioneered by Graham Priest. It includes advanced technical work on the model and proof theories of paraconsistent logic, in contributions from top scholars in the field. Graham Priest’s research has had a considerable influence on the field of philosophical logic, especially with respect to the themes of dialetheism—the thesis that there exist true but inconsistent sentences—and paraconsistency—an account of deduction in which contradictory premises do not entail the truth of arbitrary sentences. Priest’s work has regularly challenged researchers to reappraise many assumptions about rationality, ontology, and truth. This book collects original research by some of the most esteemed scholars working in philosophical logic, whose contributions explore and appraise Priest’s work on logical approaches to problems in philosophy, linguistics, computation, and mathematics. They provide fresh analyses, critiques, and applications of Priest’s work and attest to its continued relevance and topicality. The book also includes Priest’s responses to the contributors, providing a further layer to the development of these themes.

This book discusses major milestones in Rohit Parikh’s scholarly work. Highlighting the transition in Parikh’s interest from formal languages to natural languages, and how he approached Wittgenstein’s philosophy of language, it traces the academic trajectory of a brilliant scholar whose work opened up various new avenues in research. This volume is part of Springer’s book series Outstanding Contributions to Logic, and honours Rohit Parikh and his works in many ways. Parikh is a leader in the realm of ideas, offering concepts and definitions that enrich the field and lead to new research directions. Parikh has contributed to a variety of areas in logic, computer science and game theory. In mathematical logic his contributions have been in recursive function theory, proof theory and non-standard analysis; in computer science, in the areas of modal, temporal and dynamic logics of programs and semantics of programs, as well as logics of knowledge; in artificial intelligence in the area of belief revision; and in game theory in the formal analysis of social procedures, with a strong undercurrent of philosophy running through all his work. This is not a collection of articles limited to one theme, or even directly connected to specific works by Parikh, but instead all papers are inspired and influenced by Parikh in some way, adding structures to and enriching “Parikh-land”.

Paraconsistent logics are the formal systems in which absurdities do not trivialise the logic. In this paper, we give Hintikka-style game theoretical semantics for a variety of paraconsistent and non-classical logics. For this purpose, we consider Priest’s Logic of Paradox, Dunn’s First-Degree Entailment, Routleys’ Relevant Logics, McCall’s Connexive Logic and Belnap’s four-valued logic. We also present a game theoretical characterisation of a translation between Logic of Paradox/Kleene’s K3 and S5. We underline how non-classical logics require different verification games and prove the correctness theorems of their respective game theoretical semantics. This allows us to observe that paraconsistent logics break the classical bidirectional connection between winning strategies and truth values.

Lakatos’s seminal work Proofs and Refutations introduced the methods of proofs and refutations by discussing the history and methodological development of Euler’s formula V — E+F = 2 for three dimensional polyhedra. Lakatos considered the history of polyhedra illustrating a good example for his philosophy and methodology of mathematics and geometry. In this study, we focus on the mathematical and topological properties which play a role in Lakatos’s methodological approach. For each example and counterexample given by Lakatos, we briefly outline its topological counterpart. We thus present the mathematical background and basis of Lakatos’s philosophy of mathematical methodology in the case of Euler’s formula, and thereby develop some intuitions about the function of his notions of positive and negative heuristics.

The Brandenburger–Keisler paradox is a self-referential paradox in epistemic game theory which can be viewed as a two-person version of Russell’s Paradox. Yablo’s Paradox, according to its author, is a non-self referential paradox, which created a significant impact. This paper gives a Yabloesque, non-self-referential paradox for infinitary players within the context of epistemic game theory. The new paradox advances both the Brandenburger–Keisler and Yablo results. Additionally, the paper constructs a paraconsistent model satisfying the paradoxical statement.