Free PDF BookThe Rise of Modern Logic from Leibniz to Frege (Handbook of the History of Logic)

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Published on: 2004-03-08
Released on: 2004-03-08
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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 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. Paraconsistent Logic (Stanford Encyclopedia of Philosophy) 1. Paraconsistency. A logic is said to be paraconsistent iff its logical consequence relation is not explosive. Paraconsistency is thus a property of a consequence ... George Boole - Wikipedia Wikisource contiene una pagina dedicata a George Boole; contiene immagini o altri file su ; Collegamenti esterni. Voce sulla Stanford Encyclopedia of Philosophy ... History of logic - Wikipedia The history of logic deals with the study of the development of the science of valid inference . Formal logics developed in ancient times in China India and Greece. Mathematical logic - Wikipedia Mathematical logic is a subfield of mathematics exploring the applications of formal logic to mathematics. It bears close connections to metamathematics the ... Razonamiento diagramtico - Wikipedia la enciclopedia libre razonamiento diagramtico: lenguaje: characteristica universalis: demostraciones ... El lenguaje tiene sus reglas de construccin llamadas reglas sintcticas. Aristotle - New World Encyclopedia Given the volume of Aristotle's work it is not possible to adequately summarize his views in anything less than a book. This article focuses on the aspects of his ... Leibniz: Logic Internet Encyclopedia of Philosophy Leibniz: Logic. The revolutionary ideas of Gottfried Wilhelm Leibniz (1646-1716) on logic were developed by him between 1670 and 1690. The ideas can be divided into ... Philosophy - New World Encyclopedia The Nature of Philosophy Methods and definitions. Philosophy has almost as many definitions as there have been philosophers both as a subject matter and an activity. Metaphilosophy Contemporary Internet Encyclopedia of ... Contemporary Metaphilosophy. What is philosophy? What is philosophy for? How should philosophy be done? These are metaphilosophical questions metaphilosophy being ... What is Analytic Philosophy? - Oxford Handbooks [UNTITLED] Preface; Notes on Contributors; What is Analytic Philosophy? The Historiography of Analytic Philosophy; Chronology of Analytic Philosophy and its ...
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