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Author: Alex Citkin
Publisher: MDPI
ISBN: 303943358X
Category : Mathematics
Languages : en
Pages : 298
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Book Description
The book provides a contemporary view on different aspects of the deductive systems in various types of logics including term logics, propositional logics, logics of refutation, non-Fregean logics, higher order logics and arithmetic.
Author: Alex Citkin
Publisher: MDPI
ISBN: 303943358X
Category : Mathematics
Languages : en
Pages : 298
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Book Description
The book provides a contemporary view on different aspects of the deductive systems in various types of logics including term logics, propositional logics, logics of refutation, non-Fregean logics, higher order logics and arithmetic.
Author: Michael Wolff
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110785102
Category : Philosophy
Languages : en
Pages : 438
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Book Description
Wolff's book defends the Kantian idea of a "general logic" whose principles underlie special systems of deductive logic. It thus undermines "logical pluralism," which tolerates the co-existence of divergent systems of modern logic without asking for consistent common principles. Part I of Wolff’s book identifies the formal language in which the most general principles of logic must be expressed. This language turns out to be a version of syllogistic language already used by Aristotle. The universal validity of logical principles, as well as the translatability of other logical languages into this language, are shown to depend only on the meanings of its logical vocabulary. Part II of the book answers the metalogical question concerning the deductive relation between general logic and special logical systems, which also have their own (less general) principles. This part identifies the rules according to which logical rules can be derived from principles. The main result of the book is that the highest principles of logic and metalogics are provided by the syllogistic, when properly understood.
Author: David Binder
Publisher: Springer Nature
ISBN: 3030949265
Category : Philosophy
Languages : en
Pages : 552
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Book Description
This open access book is the first ever collection of Karl Popper's writings on deductive logic. Karl R. Popper (1902-1994) was one of the most influential philosophers of the 20th century. His philosophy of science ("falsificationism") and his social and political philosophy ("open society") have been widely discussed way beyond academic philosophy. What is not so well known is that Popper also produced a considerable work on the foundations of deductive logic, most of it published at the end of the 1940s as articles at scattered places. This little-known work deserves to be known better, as it is highly significant for modern proof-theoretic semantics. This collection assembles Popper's published writings on deductive logic in a single volume, together with all reviews of these papers. It also contains a large amount of unpublished material from the Popper Archives, including Popper's correspondence related to deductive logic and manuscripts that were (almost) finished, but did not reach the publication stage. All of these items are critically edited with additional comments by the editors. A general introduction puts Popper's work into the context of current discussions on the foundations of logic. This book should be of interest to logicians, philosophers, and anybody concerned with Popper's work.
Author: James Wilkinson Miller
Publisher: Routledge
ISBN: 1317375432
Category : Philosophy
Languages : en
Pages : 100
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Book Description
Originally published in 1938. This compact treatise is a complete treatment of Aristotle’s logic as containing negative terms. It begins with defining Aristotelian logic as a subject-predicate logic confining itself to the four forms of categorical proposition known as the A, E, I and O forms. It assigns conventional meanings to these categorical forms such that subalternation holds. It continues to discuss the development of the logic since the time of its founder and address traditional logic as it existed in the twentieth century. The primary consideration of the book is the inclusion of negative terms - obversion, contraposition etc. – within traditional logic by addressing three questions, of systematization, the rules, and the interpretation.
Author: Lizzie Susan Stebbing
Publisher: Routledge
ISBN: 1351349082
Category : Philosophy
Languages : en
Pages : 548
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Book Description
As the author of this volume states, "the science of logic does not stand still." This book was intended to cover the advances made in the study of logic in the first half of the nineteenth century, during which time the author felt there to have been greater advances made than in the whole of the preceding period from the time of Aristotle. Advances which, in her eyes, were not present in contemporary text books. As such, this book offers a valuable insight into the progress of the subject, tracing this frenetic period in its development with a first-hand awareness of its documentary value.
Author:
Publisher: Ardent Media
ISBN:
Category :
Languages : en
Pages : 652
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Book Description
Author: Dov M. Gabbay
Publisher: Elsevier
ISBN: 008053287X
Category : Mathematics
Languages : en
Pages : 781
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Book Description
With the publication of the present volume, the Handbook of the History of Logic turns its attention to the rise of modern logic. The period covered is 1685-1900, with this volume carving out the territory from Leibniz to Frege. What is striking about this period is the earliness and persistence of what could be called 'the mathematical turn in logic'. Virtually every working logician is aware that, after a centuries-long run, the logic that originated in antiquity came to be displaced by a new approach with a dominantly mathematical character. It is, however, a substantial error to suppose that the mathematization of logic was, in all essentials, Frege's accomplishment or, if not his alone, a development ensuing from the second half of the nineteenth century. The mathematical turn in logic, although given considerable torque by events of the nineteenth century, can with assurance be dated from the final quarter of the seventeenth century in the impressively prescient work of Leibniz. It is true that, in the three hundred year run-up to the Begriffsschrift, one does not see a smoothly continuous evolution of the mathematical turn, but the idea that logic is mathematics, albeit perhaps only the most general part of mathematics, is one that attracted some degree of support throughout the entire period in question. Still, as Alfred North Whitehead once noted, the relationship between mathematics and symbolic logic has been an "uneasy" one, as is the present-day association of mathematics with computing. Some of this unease has a philosophical texture. For example, those who equate mathematics and logic sometimes disagree about the directionality of the purported identity. Frege and Russell made themselves famous by insisting (though for different reasons) that logic was the senior partner. Indeed logicism is the view that mathematics can be re-expressed without relevant loss in a suitably framed symbolic logic. But for a number of thinkers who took an algebraic approach to logic, the dependency relation was reversed, with mathematics in some form emerging as the senior partner. This was the precursor of the modern view that, in its four main precincts (set theory, proof theory, model theory and recursion theory), logic is indeed a branch of pure mathematics. It would be a mistake to leave the impression that the mathematization of logic (or the logicization of mathematics) was the sole concern of the history of logic between 1665 and 1900. There are, in this long interval, aspects of the modern unfolding of logic that bear no stamp of the imperial designs of mathematicians, as the chapters on Kant and Hegcl make clear. Of the two, Hcgel's influence on logic is arguably the greater, serving as a spur to the unfolding of an idealist tradition in logic - a development that will be covered in a further volume, British Logic in the Nineteenth Century.
Author: Antonio Piccolomini d'Aragona
Publisher: Springer Nature
ISBN: 3031514068
Category :
Languages : en
Pages : 421
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Author: M. Bunge
Publisher: Springer Science & Business Media
ISBN: 940102667X
Category : Social Science
Languages : en
Pages : 282
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Book Description
The present volume collects some of the talks given at the Bertrand Russell Colloquium on Exact Philosophy, attached to the McGill University Foundations and Philosophy of Science Unit. It also includes a paper, on Bertrand Russell's method of philosophizing, read at the memorial symposium held at Sir Gorge Williams University shortly after the philosopher's death. All the papers appear here for the first time. Unlike many a philosophy of science anthology, this one is not center ed on the philosophy of physics. In fact the papers deal with conceptual and, in particular, philosophical problems that pop up in almost every one of the provinces of the vast territory constituted by the foundations, meth odology and philosophy of science. A couple of border territories which are in the process of being infiltrated have been added for good measure. The inclusion of papers in the philosophy of formal science and in the philosophies of physics and of biology, in a volume belonging to a series devoted to the philosophy and methodology of the social and behavioral sciences, should raise no eyebrows. Because the sciences of man make use of logic and mathematics, they are interested in questions such as whether the formal sciences have anything to do with reality (rather than with our theories about reality) and whether or not logic has kept up with the practice of mathematicians. These two problems are tackled in Part II, on the philosophy of formal science.
Author:
Publisher: UM Libraries
ISBN:
Category : Education, Higher
Languages : en
Pages : 116
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Book Description
