Over 350 ingenious problems involving classical logic: logic expressed in symbols; syllogisms and the sorites diagrammed; logic as a game played with 2 diagrams and a set of counters.

Lewis Carroll the author of the world famous Alice in Wonderland is well known even today for his fiction, but his tenure as professor of mathematics at Oxford university is less well known as is his love of logic problems. Carroll was a mathematician at heart; he deeply loved and was fascinated by the subject. At first it may seem odd that a creator of such nonsensical writings would have such an interest in this area, although the logic involved in maths appealed to the very clever mind of Dodgson, and logical oddities are at the root of a lot of the wit in the Alice books.

The present volume of the Handbook of the History of Logic is designed to establish 19th century Britain as a substantial force in logic, developing new ideas, some of which would be overtaken by, and other that would anticipate, the century's later capitulation to the mathematization of logic. British Logic in the Nineteenth Century is indispensable reading and a definitive research resource for anyone with an interest in the history of logic.- Detailed and comprehensive chapters covering the entire range of modal logic - Contains the latest scholarly discoveries and interpretative insights that answer many questions in the field of logic

This book contains scores of intriguing puzzles and paradoxes from Lewis Carroll, the author of Alice in Wonderland, whose interests ranged from inventing new games like Arithmetical Croquet to important problems in symbolic logic and propositional calculus. Written by Carroll expert and well-known mathematics author Martin Gardner, this tour through Carroll's inventions is both fun and informative.

This edited volume presents a comprehensive history of modern logic from the Middle Ages through the end of the twentieth century. In addition to a history of symbolic logic, the contributors also examine developments in the philosophy of logic and philosophical logic in modern times. The book begins with chapters on late medieval developments and logic and philosophy of logic from Humanism to Kant. The following chapters focus on the emergence of symbolic logic with special emphasis on the relations between logic and mathematics, on the one hand, and on logic and philosophy, on the other. This discussion is completed by a chapter on the themes of judgment and inference from 1837-1936. The volume contains a section on the development of mathematical logic from 1900-1935, followed by a section on main trends in mathematical logic after the 1930s. The volume goes on to discuss modal logic from Kant till the late twentieth century, and logic and semantics in the twentieth century; the philosophy of alternative logics; the philosophical aspects of inductive logic; the relations between logic and linguistics in the twentieth century; the relationship between logic and artificial intelligence; and ends with a presentation of the main schools of Indian logic. The Development of Modern Logic includes many prominent philosophers from around the world who work in the philosophy and history of mathematics and logic, who not only survey developments in a given period or area but also seek to make new contributions to contemporary research in the field. It is the first volume to discuss the field with this breadth of coverage and depth, and will appeal to scholars and students of logic and its philosophy.

Algebraic Art explores the invention of a peculiarly Victorian account of the nature and value of aesthetic form, and it traces that account to a surprising source: mathematics. The nineteenth century was a moment of extraordinary mathematical innovation, witnessing the development of non-Euclidean geometry, the revaluation of symbolic algebra, and the importation of mathematical language into philosophy. All these innovations sprang from a reconception of mathematics as a formal rather than a referential practice—as a means for describing relationships rather than quantities. For Victorian mathematicians, the value of a claim lay not in its capacity to describe the world but its internal coherence. This concern with formal structure produced a striking convergence between mathematics and aesthetics: geometers wrote fables, logicians reconceived symbolism, and physicists described reality as consisting of beautiful patterns. Artists, meanwhile, drawing upon the cultural prestige of mathematics, conceived their work as a 'science' of form, whether as lines in a painting, twinned characters in a novel, or wavelike stress patterns in a poem. Avant-garde photographs and paintings, fantastical novels like Flatland and Lewis Carroll's children's books, and experimental poetry by Swinburne, Rossetti, and Patmore created worlds governed by a rigorous internal logic even as they were pointedly unconcerned with reference or realist protocols. Algebraic Art shows that works we tend to regard as outliers to mainstream Victorian culture were expressions of a mathematical formalism that was central to Victorian knowledge production and that continues to shape our understanding of the significance of form.

This book provides a comprehensive introduction to the essential elements of standard (classical) symbolic logic. Key topics covered include: · The characteristic nature and scope of logic as a discipline · The construction of a series of distinctly named formal languages suitable for formal translation · Semantic models · The construction of decision procedures · The execution of proof-theoretic arrangements like natural deduction and proof-sequent systems The book covers both the semantics and proof theory of the standard sentential (propositional) logic and predicate (first-order) logic. Other topics covered include: parsing trees, extraction of alternative notations (for instance, Polish notation), Fitch-style proof-theory, sequent and ‘tree’ proof systems, comparisons and contrasts with intuitionistic logic, and presentations of predicate logic models. An ancillary chapter on elements of set theory is conveniently placed at the end and includes insights into the Zermelo-Fraenkel systematization of set theory. The philosophy of logic is also explored. Exercises in the text provide instruction on mathematical induction for the construction of formula, tests for the well-formedness of Polish notation, and functional completeness. Symbolic Logic is essential reading for all philosophy students taking intermediate level formal logic courses and will also appeal to diligent first year students of logic. The text is replete with exercises on both the formal machinery and the philosophical aspects of logic.

During the Victorian era, industrial and economic growth led to a phenomenal rise in productivity and invention. That spirit of creativity and ingenuity was reflected in the massive expansion in scope and complexity of many scientific disciplines during this time, with subjects evolving rapidly and the creation of many new disciplines. The subject of mathematics was no exception and many of the advances made by mathematicians during the Victorian period are still familiar today; matrices, vectors, Boolean algebra, histograms, and standard deviation were just some of the innovations pioneered by these mathematicians. This book constitutes perhaps the first general survey of the mathematics of the Victorian period. It assembles in a single source research on the history of Victorian mathematics that would otherwise be out of the reach of the general reader. It charts the growth and institutional development of mathematics as a profession through the course of the 19th century in England, Scotland, Ireland, and across the British Empire. It then focuses on developments in specific mathematical areas, with chapters ranging from developments in pure mathematical topics (such as geometry, algebra, and logic) to Victorian work in the applied side of the subject (including statistics, calculating machines, and astronomy). Along the way, we encounter a host of mathematical scholars, some very well known (such as Charles Babbage, James Clerk Maxwell, Florence Nightingale, and Lewis Carroll), others largely forgotten, but who all contributed to the development of Victorian mathematics.