Bøger i Logic, Epistemology, and the Unity of Science serien

This volume develops a theory of meaning and a semantics for both mathematical and empirical sentences inspired to Chomsky¿s internalism, namely to a view of semantics as the study of the relations of language not with external reality but with internal, or mental, reality. In the first part a theoretical notion of justification for a sentence A is defined, by induction on the complexity of A; intuitively, justifications are conceived as cognitive states of a particular kind. The main source of inspiration for this part is Heyting¿s explanation of the intuitionistic meaning of logical constants.In the second part the theory is applied to the solution of several foundational problems in the theory of meaning and epistemology, such as Frege¿s puzzle, Mates¿ puzzle about synonymy, the paradox of analysis, Kripke¿s puzzle about belief, the de re/de dicto distinction, the specific/non-specific distinction, Gettier¿s problems, the paradox of knowability, and the characterization oftruth. On a more general philosophical level, throughout the book the author develops a tight critique of the neo-verificationism of Dummett, Prawitz and Martin-Löf, and defends a mentalist interpretation of intuitionism.

This volume collects 22 essays on the history of logic written by outstanding specialists in the field. The book was originally prompted by the 2018-2019 celebrations in honor of Massimo Mugnai, a world-renowned historian of logic, whose contributions on Medieval and Modern logic, and to the understanding of the logical writings of Leibniz in particular, have shaped the field in the last four decades. Given the large number of recent contributions in the history of logic that have some connections or debts with Mugnai's work, the editors have attempted to produce a volume showing the vastness of the development of logic throughout the centuries. We hope that such a volume may help both the specialist and the student to realize the complexity of the history of logic, the large array of problems that were touched by the discipline, and the manifold relations that logic entertained with other subjects in the course of the centuries. The contributions of the volume, in fact, span from Antiquity to the Modern Age, from semantics to linguistics and proof theory, from the discussion of technical problems to deep metaphysical questions, and in it the history of logic is kept in dialogue with the history of mathematics, economics, and the moral sciences at large.

This publication includes an unabridged and annotated translation of two works by Johann Heinrich Lambert (1728¿1777) written in the 1760s: Vorläufige Kenntnisse für die, so die Quadratur und Rectification des Circuls suchen and Mémoire sur quelques propriétés remarquables des quantités transcendentes circulaires et logarithmiques. The translations are accompanied by a contextualised study of each of these works and provide an overview of Lambert¿s contributions, showing both the background and the influence of his work. In addition, by adopting a biographical approach, it allows readers to better get to know the scientist himself. Lambert was a highly relevant scientist and polymath in his time, admired by the likes of Kant, who despite having made a wide variety of contributions to different branches of knowledge, later faded into an undeserved secondary place with respect to other scientists of the eighteenth century. In mathematics, in particular, he is famous for his research on non-Euclidean geometries, although he is likely best known for having been the first who proved the irrationality of pi. In his Mémoire, he conducted one of the first studies on hyperbolic functions, offered a surprisingly rigorous proof of the irrationality of pi, established for the first time the modern distinction between algebraic and transcendental numbers, and based on such distinction, he conjectured the transcendence of pi and therefore the impossibility of squaring the circle.

The first category includes papers on non-classical logics, including intuitionistic logic, constructive logic, basic logic, and substructural logic.

This open access book examines the many contributions of Paul Lorenzen, an outstanding philosopher from the latter half of the 20th century. It features papers focused on integrating Lorenzen's original approach into the history of logic and mathematics. The papers also explore how practitioners can implement Lorenzen¿s systematical ideas in today¿s debates on proof-theoretic semantics, databank management, and stochastics.Coverage details key contributions of Lorenzen to constructive mathematics, Lorenzen¿s work on lattice-groups and divisibility theory, and modern set theory and Lorenzen¿s critique of actual infinity. The contributors also look at the main problem of Grundlagenforschung and Lorenzen¿s consistency proof and Hilbert¿s larger program. In addition, the papers offer a constructive examination of a Russell-style Ramified Type Theory and a way out of the circularity puzzle within the operative justification of logic and mathematics.Paul Lorenzen's name is associated with the Erlangen School of Methodical Constructivism, of which the approach in linguistic philosophy and philosophy of science determined philosophical discussions especially in Germany in the 1960s and 1970s. This volume features 10 papers from a meeting that took place at the University of Konstanz.

This edited book brings together research work in the field of constructive semantics with scholarship on the phenomenological foundations of logic and mathematics.

The second part is on logic, its Chapters dedicated to the topics from Peirce's Existential Graphs and the philosophy of notation to Husserl's notions of pure logic and transcendental logic.

The second part is on logic, its Chapters dedicated to the topics from Peirce's Existential Graphs and the philosophy of notation to Husserl's notions of pure logic and transcendental logic.

This book is the first in the field of paraconsistency to offer a comprehensive overview of the subject, including connections to other logics and applications in information processing, linguistics, reasoning and argumentation, and philosophy of science.

This book develops a novel generalization of possible world semantics, called 'world line semantics', which recognizes worlds and links between world-bound objects (world lines) as mutually independent aspects of modal semantics.

This book provides a detailed commentary on the classic monograph by Alfred Tarski, and offers a reinterpretation and retranslation of the work using the original Polish text and the English and German translations.

This book examines three connected aspects of Frege's logicism: the differences between Dedekind's and Frege's interpretation of the term 'logic' and related terms and reflects on Frege's notion of function, comparing its understanding and the role it played in Frege's and Lagrange's foundational programs.

This volume tackles Goedel's two-stage project of first using Husserl's transcendental phenomenology to reconstruct and develop Leibniz' monadology, and then founding classical mathematics on the metaphysics thus obtained.

Intuitionistic type theory can be described, somewhat boldly, as a fulfillment of the dream of a universal language for science. In particular, intuitionistic type theory is a foundation for mathematics and a programming language.

This book shows how TIL lends itself to a broad range of applications. It comprises logical analysis of natural language, artificial-intelligence methods of knowledge representation, multi-agent systems in computer science, philosophy of mathematics, and more.

Multimodality is the key to many fertile investigations in modal logic. This book is a philosophically and historically-based introduction to modal logic that will appeal to philosophers, logicians, linguists, mathematicians and computer scientists.

The wealth of proposals about truth and its meaning in natural languages everywhere should open it to analysis and definition, but this book makes the startlingly rare assertion that we can define truth using the latest methods in linguistics and philosophy.

The book provides a historical (with an outline of the history of the concept of truth from antiquity to our time) and systematic exposition of the semantic theory of truth formulated by Alfred Tarski in the 1930s.

This edited book brings together research work in the field of constructive semantics with scholarship on the phenomenological foundations of logic and mathematics.

This book explores the unique relationship between two different approaches to understand the nature of knowledge, reality, and existence. It collects essays that examine the distinctive historical relationship between mathematics and philosophy. Readers learn what key philosophers throughout the ages thought about mathematics. This includes both thinkers who recognized the relevance of mathematics to their own work as well as those who chose to completely ignore its many achievements.The essays offer insight into the role that mathematics played in the formation of each included philosopher's doctrine as well as the impact its remarkable expansion had on the philosophical systems each erected. Conversely, the authors also highlight the ways that philosophy contributed to the growth and transformation of mathematics. Throughout, significant historical examples help to illustrate these points in a vivid way. Mathematics has often been a favored interlocutor of philosophers and a major source of inspiration. This book is the outcome of an international conference held in honor of Roshdi Rashed, a renowned historian of mathematics. It provides researchers, students, and interested readers with remarkable insights into the history of an important relationship throughout the ages.

This book examines the role of acts of choice in classical and intuitionistic mathematics.

This anthology of the very latest research on truth features the work of recognized luminaries in the field, put together following a rigorous refereeing process. Along with an introduction outlining the central issues in the field, it provides a unique and unrivaled view of contemporary work on the nature of truth, with papers selected from key conferences in 2011 such as Truth Be Told (Amsterdam), Truth at Work (Paris), Paradoxes of Truth and Denotation (Barcelona) and Axiomatic Theories of Truth (Oxford).Studying the nature of the concept of ¿truth¿ has always been a core role of philosophy, but recent years have been a boom time in the topic. With a wealth of recent conferences examining the subject from various angles, this collection of essays recognizes the pressing need for a volume that brings scholars up to date on the arguments.Offering academics and graduate students alike a much-needed repository of today¿s cutting-edge work in this vital topic of philosophy, the volume is required reading for anyone needing to keep abreast of developments, and is certain to act as a catalyst for further innovation and research.

onticism is also compared with other, competing theories of vagueness such as semanticism, the view that vagueness exists only in our linguistic representation of the world.Gareth Evans's influential paper of 1978, "Can There Be Vague Objects?" gave a simple but cogent argument against the coherence of ontic vagueness.

This book is about philosophy, mathematics and logic, giving a philosophical account of Pluralism which is a family of positions in the philosophy of mathematics.