Language, Logic, and Mathematics in Schopenhauer

Language, Logic, and Mathematics in Schopenhauer
Author: Jens Lemanski
Publisher: Springer Nature
Total Pages: 318
Release: 2020-06-08
Genre: Mathematics
ISBN: 3030330907

The chapters in this timely volume aim to answer the growing interest in Arthur Schopenhauer’s logic, mathematics, and philosophy of language by comprehensively exploring his work on mathematical evidence, logic diagrams, and problems of semantics. Thus, this work addresses the lack of research on these subjects in the context of Schopenhauer’s oeuvre by exposing their links to modern research areas, such as the “proof without words” movement, analytic philosophy and diagrammatic reasoning, demonstrating its continued relevance to current discourse on logic. Beginning with Schopenhauer’s philosophy of language, the chapters examine the individual aspects of his semantics, semiotics, translation theory, language criticism, and communication theory. Additionally, Schopenhauer’s anticipation of modern contextualism is analyzed. The second section then addresses his logic, examining proof theory, metalogic, system of natural deduction, conversion theory, logical geometry, and the history of logic. Special focus is given to the role of the Euler diagrams used frequently in his lectures and their significance to broader context of his logic. In the final section, chapters discuss Schopenhauer’s philosophy of mathematics while synthesizing all topics from the previous sections, emphasizing the relationship between intuition and concept. Aimed at a variety of academics, including researchers of Schopenhauer, philosophers, historians, logicians, mathematicians, and linguists, this title serves as a unique and vital resource for those interested in expanding their knowledge of Schopenhauer’s work as it relates to modern mathematical and logical study.

Language, Logic, and Mathematics in Schopenhauer

Language, Logic, and Mathematics in Schopenhauer
Author: Jens Lemanski
Publisher: Birkhäuser
Total Pages: 326
Release: 2020-06-09
Genre: Mathematics
ISBN: 9783030330897

The chapters in this timely volume aim to answer the growing interest in Arthur Schopenhauer’s logic, mathematics, and philosophy of language by comprehensively exploring his work on mathematical evidence, logic diagrams, and problems of semantics. Thus, this work addresses the lack of research on these subjects in the context of Schopenhauer’s oeuvre by exposing their links to modern research areas, such as the “proof without words” movement, analytic philosophy and diagrammatic reasoning, demonstrating its continued relevance to current discourse on logic. Beginning with Schopenhauer’s philosophy of language, the chapters examine the individual aspects of his semantics, semiotics, translation theory, language criticism, and communication theory. Additionally, Schopenhauer’s anticipation of modern contextualism is analyzed. The second section then addresses his logic, examining proof theory, metalogic, system of natural deduction, conversion theory, logical geometry, and the history of logic. Special focus is given to the role of the Euler diagrams used frequently in his lectures and their significance to broader context of his logic. In the final section, chapters discuss Schopenhauer’s philosophy of mathematics while synthesizing all topics from the previous sections, emphasizing the relationship between intuition and concept. Aimed at a variety of academics, including researchers of Schopenhauer, philosophers, historians, logicians, mathematicians, and linguists, this title serves as a unique and vital resource for those interested in expanding their knowledge of Schopenhauer’s work as it relates to modern mathematical and logical study.

Introduction to Logic and Logical Discourse

Introduction to Logic and Logical Discourse
Author: Satya Sundar Sethy
Publisher: Springer Nature
Total Pages: 283
Release: 2021-06-12
Genre: Philosophy
ISBN: 9811626898

This book focuses on logic and logical language. It examines different types of words, terms and propositions in detail. While discussing the nature of propositions, it illustrates the procedures used to determine the truth and falsity of a proposition, and the validity and invalidity of an argument. In addition, the book provides a clear exposition of the pure and mixed form of syllogism with suitable examples. The book encompasses sentential logic, predicate logic, symbolic logic, induction and set theory topics. The book is designed to serve all those involved in teaching and learning courses on logic. It offers a valuable resource for students and researchers in philosophy, mathematics and computer science disciplines. Given its scope, it is an essential read for everyone interested in logic, language, formulation of the hypotheses for the scientific enquiries and research studies, and judging valid and invalid arguments in the natural language discourse.

The Schopenhauerian Mind

The Schopenhauerian Mind
Author: David Bather Woods
Publisher: Taylor & Francis
Total Pages: 592
Release: 2023-11-14
Genre: Philosophy
ISBN: 1000987450

Arthur Schopenhauer (1788-1860) is now recognised as a figure of canonical importance to the history of philosophy. Schopenhauer founded his system on a highly original interpretation of Kant’s philosophy, developing an entirely novel and controversial worldview guided centrally by his striking conception of the human will and of art and beauty. His influence extends to figures as diverse as Fredrich Nietzsche, Ludwig Wittgenstein and Iris Murdoch within philosophy, and Richard Wagner, Thomas Hardy, Sigmund Freud, Thomas Mann, Samuel Beckett and Jorge Luis Borges outside it. The Schopenhauerian Mind is an outstanding, wide-ranging collection that explores the rich nature of Schopenhauer's ideas, texts, influences, and legacy. Comprising 38 original chapters by an international team of contributors, the volume is organised into five clear parts: Knowledge and Reality Aesthetics and the Arts Ethics, Politics, and Salvation Before Schopenhauer After Schopenhauer The Schopenhauerian Mind covers all the key areas and concepts of Schopenhauer’s philosophy, including fields omitted in previous studies. It is essential reading for students of nineteenth-century philosophy, Continental philosophy and philosophy of art and aesthetics, and also of interest to those in related disciplines such as literature and religion.

Logic from Kant to Russell

Logic from Kant to Russell
Author: Sandra Lapointe
Publisher: Routledge Studies in Nineteenth-Century Philosophy
Total Pages: 256
Release: 2018
Genre: PHILOSOPHY
ISBN: 9780815396321

The scope and method of logic as we know it today eminently reflect the ground-breaking developments of set theory and the logical foundations of mathematics at the turn of the 20th century. Unfortunately, little effort has been made to understand the idiosyncrasies of the philosophical context that led to these tremendous innovations in the 19thcentury beyond what is found in the works of mathematicians such as Frege, Hilbert, and Russell. This constitutes a monumental gap in our understanding of the central influences that shaped 19th-century thought, from Kant to Russell, and that helped to create the conditions in which analytic philosophy could emerge. The aim of Logic from Kant to Russell is to document the development of logic in the works of 19th-century philosophers. It contains thirteen original essays written by authors from a broad range of backgrounds--intellectual historians, historians of idealism, philosophers of science, and historians of logic and analytic philosophy. These essays question the standard narratives of analytic philosophy's past and address concerns that are relevant to the contemporary philosophical study of language, mind, and cognition. The book covers a broad range of influential thinkers in 19th-century philosophy and analytic philosophy, including Kant, Bolzano, Hegel, Herbart, Lotze, the British Algebraists and Idealists, Moore, Russell, the Neo-Kantians, and Frege.

Archaeology of Logic

Archaeology of Logic
Author: Andrew Schumann
Publisher: CRC Press
Total Pages: 440
Release: 2023-04-27
Genre: Science
ISBN: 100087107X

The question arises whether logic was given to us by God or whether it is the result of human evolution. I believe that at least the modus ponens rule ( A and if A then B implies B) is inherent in humans, but probably many other modern systems (e.g., resource logic, non - monotonic logic etc.) are the result of humans adapating to the environment. It is therefore of interest to study and compare the way logic is used in ancient cultures as well as the way logic is going to be used in our 21st century. This welcome book studies and compares the way formation of logic in three cultures: Ancient Greek (4th century B.C.), Judaic (1st century B.C. – 1st century A.D.) and Indo-Buddhist (2nd century A.D.) The book notes that logic became especially popular during the period of late antiquity in countries covered by the international trade of the Silk Road. This study makes a valuable contribution to the history of logic and to the very understanding of the origions and nature of logical thinking. -Prof. Dov Gabbay, King's College London, UK Andrew Schumann in his book demonsrates that logic step-by-step arose in different places and cultural circles. He argues that if we apply a structural-genealogical method, as well as turn to various sources, particularly, religious, philosophical, linguistic, etc., then we can obtain a more general and more adequate picture of emengence and development of logic. This book is a new and very valuable contribution to the history of logic as a manifestation of the human mind. - Prof. Jan Wolenski, Jagiellonian University, Poland The author of the Archaeology of Logic defends the claim, calling it "logic is aftter all", which sees logical competence as a practical skill that people began to learn in antiquity, as soom as they realized that avoiding cognitive biases in their reasoning would make their daily activities more successful. The in-depth reading of the book with its diving into the comparative quotations in the long dead or hardly known to most of us languages like Sumerian-Akkadian, Aramatic, Hebrew and etc, will be rewarded by the response that the logical competence is diverse and it can be trained, despite the inevitabilitiy of the reasoning fallacies; and that critical discussions and agaonal character of the social lide are the necessary tools for that. - Prof. Elena Lisanyuk

The Waltz of Reason

The Waltz of Reason
Author: Karl Sigmund
Publisher: Basic Books
Total Pages: 346
Release: 2023-12-19
Genre: Mathematics
ISBN: 1541602706

"A mind-bending jaunt ... that makes clear in fascinating detail how math is more than a sum of its parts" (Publishers Weekly) “Let no one ignorant of geometry enter here,” Plato warned would-be philosophers. Mathematician Karl Sigmund agrees. In The Waltz of Reason, he shows how mathematics and philosophy together have shaped our understanding of space, chance, logic, cooperation, voting, and the social contract. Sigmund shows how game theory is integral to moral philosophy, how statistics shaped the meaning of reason, and how the search for a logical basis for math leads to deep questions about the nature of truth itself. But this is no dry tome: Sigmund’s wit and humor shine as brightly as his erudition. The Waltz of Reason is an engrossing history of ideas as vibrant as a ballroom full of dancers, one that empowers as it entertains, following the complex and occasionally dizzying steps of the thinkers who have molded our thought and founded our world.

The Exoteric Square of Opposition

The Exoteric Square of Opposition
Author: Jean-Yves Beziau
Publisher: Springer Nature
Total Pages: 480
Release: 2022-08-23
Genre: Mathematics
ISBN: 3030908232

The theory of the square of opposition has been studied for over 2,000 years and has seen a resurgence in new theories and research since the second half of the twentieth century. This volume collects papers presented at the Sixth World Congress on the Square of Opposition, held in Crete in 2018, developing an interdisciplinary exploration of the theory. Chapter authors explore subjects such as Aristotle’s ontological square, logical oppositions in Avicenna’s hypothetical logic, and the power of the square of opposition to solve theological problems regarding predestination and theodicy. Other topics covered include: Hegel’s opposition to diagrams De Morgan’s unpublished octagon of opposition turnstile figures of opposition institutional model-theoretic treatment of oppositions Lacan’s four formulas of sexuation the theory of oppositional poly-simplexes The Exoteric Square of Opposition will appeal to pure logicians, historians of logic, semioticians, philosophers, theologians, mathematicians, and psychoanalysts.

Logic in Question

Logic in Question
Author: Jean-Yves Béziau
Publisher: Springer Nature
Total Pages: 743
Release: 2023-01-11
Genre: Mathematics
ISBN: 3030944522

This contributed volume collects papers related to the Logic in Question workshop, which has taken place annually at Sorbonne University in Paris since 2011. Each year, the workshop brings together historians, philosophers, mathematicians, linguists, and computer scientists to explore questions related to the nature of logic and how it has developed over the years. As a result, chapter authors provide a thorough, interdisciplinary exploration of topics that have been studied in the workshop. Organized into three sections, the first part of the book focuses on historical questions related to logic, the second explores philosophical questions, and the third section is dedicated to mathematical discussions. Specific topics include: • logic and analogy• Chinese logic• nineteenth century British logic (in particular Boole and Lewis Carroll)• logical diagrams • the place and value of logic in Louis Couturat’s philosophical thinking• contributions of logical analysis for mathematics education• the exceptionality of logic• the logical expressive power of natural languages• the unification of mathematics via topos theory Logic in Question will appeal to pure logicians, historians of logic, philosophers, linguists, and other researchers interested in the history of logic, making this volume a unique and valuable contribution to the field.

A Companion to Schopenhauer

A Companion to Schopenhauer
Author: Bart Vandenabeele
Publisher: John Wiley & Sons
Total Pages: 438
Release: 2015-12-14
Genre: Philosophy
ISBN: 1119144809

A Companion to Schopenhauer provides a comprehensive guide to all the important facets of Schopenhauer’s philosophy. The volume contains 26 newly commissioned essays by prominent Schopenhauer scholars working in the field today. A thoroughly comprehensive guide to the life, work, and thought of Arthur Schopenhauer Demonstrates the range of Schopenhauer’s work and illuminates the debates it has generated 26 newly commissioned essays by some of the most prominent Schopenhauer scholars working today reflect the very latest trends in Schopenhauer scholarship Covers the full range of historical and philosophical perspectives on Schopenhauer’s work Discusses his seminal contributions to our understanding of knowledge, perception, morality, science, logic and mathematics, Platonic Ideas, the unconscious, aesthetic experience, art, colours, sexuality, will, compassion, pessimism, tragedy, pleasure, and happiness