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# đź“™ Handbook of the History of Logic. Volume 3: The Rise of Modern Logic: From Leibniz to Frege by Dov M. Gabbay, John Woods (eds.) â€” epub download

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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 andRussell 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.

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- Author:
**Dov M. Gabbay, John Woods (eds.)** - Year:
**2004** - Publisher:
**Elsevier** - Language:
**English** - ISBN:

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**50 141 114** - Format:
**pdf**

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Logic is now widely recognized as one of the foundational disciplines of computing and has applications in virtually all aspects of the subject, from software engineering and hardware to programming languages and artificial intelligence. The Handbook of L...

Logic is now widely recognized as one of the foundational disciplines of computing and has applications in virtually all aspects of the subject, from software engineering and hardware to programming languages and artificial intelligence. The Handbook of ...

The Logic of Language opens a new perspective on logic. Pieter Seuren argues that the logic of language derives from the lexical meanings of the logical operators. These meanings, however, prove not to be consistent. Seuren solves this problem through an ...

Logic is now widely recognized as one of the foundational disciplines of computing and has applications in virtually all aspects of the subject, from software engineering and hardware to programming languages and artificial intelligence. The Handbook of L...

Logic is now widely recognized as one of the foundational disciplines of computing and has applications in virtually all aspects of the subject, from software engineering and hardware to programming languages and artificial intelligence. The Handbook of ...

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Logic is, and should be, the core subject area of modern mathematÂ ics. The blueprint for twentieth century mathematical thought, thanks to Hilbert and Bourbaki, is the axiomatic development of the subject. As a result, logic plays a central conceptual ro...

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Maxillofacial imaging has evolved dramatically over the past two decades with development of new cross-sectional imaging techniques. Traditional maxillofacial imaging was based on plain films and dental imaging. However, todayâ€™s advanced imaging technique...

Malaria is still a major global health problem, killing more than 1 million people every year. Almost all of these deaths are caused by Plasmodium falciparum, one of the four species of malaria parasites infecting humans. This high burden of mortality fal...

The second edition of Cleft Lip and Palate: Diagnosis and Management is an unparalleled review of treatment concepts in all areas of cleft involvement presented by an international team of experienced clinicians. This text can never be duplicated since it...

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When one is asked to review a manuscript in order of the different parts of the skeleton and comprises to write a foreword,one always asks oneself,â€śIs there about 600 pages. anything special about this book?â€ťâ€śDoes it supply The reader will ?nd something a...

The intestine is colonized by an impressive community of commensals, that has profound effects on the immune funtions. The relationship between gut microbiota and the immune system is one of reciprocity: commensals have important contribution in nutrient ...

Reoviridae family members are large, complex viruses that infect human, animals, plants and insects. They are unique in that they lack lipid envelopes and package their genomes of discrete double-stranded segments of RNA within multi-layered capsids. Lack...

This richly illustrated book provides a comprehensive survey of the growing role of medical imaging studies in the detection, staging, grading, tissue characterization, and post-treatment follow-up of soft tissue tumors. For each tumor group, imaging find...

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