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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.

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.

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.

This volume analyzes how vagueness occurs and matters as a specific problem in the context of theories that are primarily about something else. Topics include vagueness and metaphysics, vagueness and logic, vagueness and linguistics, and vagueness and law.

Accordingly, the sociological and historical interpretation - volves in fact two kinds of discontinuity which are closely related: the discontinuity of science as such and the discontinuity of the more inclusive political and social context of its development.