Joachim Lambek: The Interplay of Mathematics, Logic, and Linguistics
Joachim Lambek: The Interplay of Mathematics, Logic, and Linguistics

Author: Claudia Casadio

Publisher: Springer Nature

Published: 2021-04-21

Total Pages: 432

ISBN-13: 3030665453

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This book is dedicated to the life and work of the mathematician Joachim Lambek (1922–2014). The editors gather together noted experts to discuss the state of the art of various of Lambek’s works in logic, category theory, and linguistics and to celebrate his contributions to those areas over the course of his multifaceted career. After early work in combinatorics and elementary number theory, Lambek became a distinguished algebraist (notably in ring theory). In the 1960s, he began to work in category theory, categorical algebra, logic, proof theory, and foundations of computability. In a parallel development, beginning in the late 1950s and for the rest of his career, Lambek also worked extensively in mathematical linguistics and computational approaches to natural languages. He and his collaborators perfected production and type grammars for numerous natural languages. Lambek grammars form an early noncommutative precursor to Girard’s linear logic. In a surprising development (2000), he introduced a novel and deeper algebraic framework (which he called pregroup grammars) for analyzing natural language, along with algebraic, higher category, and proof-theoretic semantics. This book is of interest to mathematicians, logicians, linguists, and computer scientists.

Hermeneutics and Science
Hermeneutics and Science

Author: Márta Fehér

Publisher: Springer Science & Business Media

Published: 2013-04-17

Total Pages: 385

ISBN-13: 9401592934

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Hermeneutics was elaborated as a specific art of understanding in humanities. The discovered paradigmatic, historical characteristics of scientific knowledge, and the role of rhetoric, interpretation and contextuality enabled us to use similar arguments in natural sciences too. In this way a new research field, the hermeneutics of science emerged based upon the works of Husserl, Merleau-Ponty, Heidegger and Gadamer. A dialogue between philosophers and scientists begins in this volume on hermeneutic approaches to physics, biology, ethology, mathematics and cognitive science. Scientific principles, methodologies, discourse, language, and metaphors are analyzed, as well as the role of the lay public and the legitimation of science. Different hermeneutical-phenomenological approaches to perception, experiments, methods, discovery and justification and the genesis of science are presented. Hermeneutics shed a new light on the incommensurability of paradigms, the possibility of translation and the historical understanding of science.

Wittgenstein, Finitism, and the Foundations of Mathematics
Wittgenstein, Finitism, and the Foundations of Mathematics

Author: Mathieu Marion

Publisher: OUP Oxford

Published: 1998-12-17

Total Pages: 272

ISBN-13: 0191568325

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Mathieu Marion offers a careful, historically informed study of Wittgenstein's philosophy of mathematics. This area of his work has frequently been undervalued by Wittgenstein specialists and by philosophers of mathematics alike; but the surprising fact that he wrote more on this subject than on any other indicates its centrality in his thought. Marion traces the development of Wittgenstein's thinking in the context of the mathematical and philosophical work of the times, to make coherent sense of ideas that have too often been misunderstood because they have been presented in a disjointed and incomplete way. In particular, he illuminates the work of the neglected 'transitional period' between the Tractatus and the Investigations. Marion shows that study of Wittgenstein's writings on mathematics is essential to a proper understanding of his philosophy; and he also demonstrates that it has much to contribute to current debates about the foundations of mathematics.

From the Atom to Living Systems
From the Atom to Living Systems

Author: Marina Paola Banchetti-Robino

Publisher: Oxford University Press

Published: 2023-10-17

Total Pages: 305

ISBN-13: 0197598900

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From the Atom to Living Systems represents an original historico-epistemological approach to follow the passage, in the microscopic analysis of reality, from the atomic to the molecular to the macromolecular levels and then to the threshold of life itself. Naturally, some parts of this journey have been developed in other works, some highly specialized and others of a more general nature. However, although this journey has often been traced in specialized scientific detail, the philosophical implications of the journey have not been discussed to any satisfactory degree. This scientific journey does have important philosophical consequences that constitute an integral part of this book, which is framed within the perspective of systems science and the so-called sciences of complexity, which are areas fundamental to 21st century science. In fact, the possibility of studying and understanding the material world through levels of complexity opens a great philosophical space that proposes to provide systemic and complex explanations, rather than reductive accounts that pretend to explain all phenomena through the interactions of elementary particles while considering all phenomena implicit and deterministic. The systemic and complex approach implies substituting unique bottom-up explanations, which move exclusively from the microscopically simple to the macroscopically complex, with a series of explanations that are horizontal within planes of complexity, vertically bottom up between various levels of complexity, vertically top-down, as well as circular in a manner that renders all levels of reality and the disciplines that study them as both autonomous and interconnected.

Feferman on Foundations
Feferman on Foundations

Author: Gerhard Jäger

Publisher: Springer

Published: 2018-04-04

Total Pages: 617

ISBN-13: 3319633341

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This volume honours the life and work of Solomon Feferman, one of the most prominent mathematical logicians of the latter half of the 20th century. In the collection of essays presented here, researchers examine Feferman’s work on mathematical as well as specific methodological and philosophical issues that tie into mathematics. Feferman’s work was largely based in mathematical logic (namely model theory, set theory, proof theory and computability theory), but also branched out into methodological and philosophical issues, making it well known beyond the borders of the mathematics community. With regard to methodological issues, Feferman supported concrete projects. On the one hand, these projects calibrate the proof theoretic strength of subsystems of analysis and set theory and provide ways of overcoming the limitations imposed by Gödel’s incompleteness theorems through appropriate conceptual expansions. On the other, they seek to identify novel axiomatic foundations for mathematical practice, truth theories, and category theory. In his philosophical research, Feferman explored questions such as “What is logic?” and proposed particular positions regarding the foundations of mathematics including, for example, his “conceptual structuralism.” The contributing authors of the volume examine all of the above issues. Their papers are accompanied by an autobiography presented by Feferman that reflects on the evolution and intellectual contexts of his work. The contributing authors critically examine Feferman’s work and, in part, actively expand on his concrete mathematical projects. The volume illuminates Feferman’s distinctive work and, in the process, provides an enlightening perspective on the foundations of mathematics and logic.