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Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the eighth publication in the Perspectives in Logic series, brings together several directions of work in model theory between the late 1950s and early 1980s. It contains expository papers by pre-eminent researchers. Part I provides an introduction to the subject as a whole, as well as to the basic theory and examples. The rest of the book addresses finitary languages with additional quantifiers, infinitary languages, second-order logic, logics of topology and analysis, and advanced topics in abstract model theory. Many chapters can be read independently.
Clark Butler presents an innovative analysis of Hegel's most challenging work in Hegel's Logic—the first major English-language treatment of Hegel's Science of Logic to appear in nearly fifteen years. Although earlier commentators on the Logic have considered standard analytical philosophy-and with it modern logic-in opposition to Hegel. Butler views it as a legitimate approach in terms of which Hegel needs to be understood. This interpretation allows him to address the rigor of Hegel's thought on several levels as at once an exercise in purely conceptual redefinition and a full-bodied work in metaphysical ontology and even theology. The result is an account of the Logic intelligible to analytical philosophers as well as non-specialists.
An argument that what is usually dismissed as the “mystical shell” of Hegel's thought—the concept of absolute knowledge—is actually its most “rational kernel.” This book sets out from a counterintuitive premise: the “mystical shell” of Hegel's system proves to be its most “rational kernel.” Hegel's radicalism is located precisely at the point where his thought seems to regress most. Most current readings try to update Hegel's thought by pruning back his grandiose claims to “absolute knowing.” Comay and Ruda invert this deflationary gesture by inflating what seems to be most trivial: the absolute is grasped only in the minutiae of its most mundane appearances. Reading Hegel without presupposition, without eliminating anything in advance or making any decision about what is essential and what is inessential, what is living and what is dead, they explore his presentation of the absolute to the letter. The Dash is organized around a pair of seemingly innocuous details. Hegel punctuates strangely. He ends the Phenomenology of Spirit with a dash, and he begins the Science of Logic with a dash. This distinctive punctuation reveals an ambiguity at the heart of absolute knowing. The dash combines hesitation and acceleration. Its orientation is simultaneously retrospective and prospective. It both holds back and propels. It severs and connects. It demurs and insists. It interrupts and prolongs. It generates nonsequiturs and produces explanations. It leads in all directions: continuation, deviation, meaningless termination. This challenges every cliché about the Hegelian dialectic as a machine of uninterrupted teleological progress. The dialectical movement is, rather, structured by intermittency, interruption, hesitation, blockage, abruption, and random, unpredictable change—a rhythm that displays all the vicissitudes of the Freudian drive.
In recent years, mathematical logic has developed in many directions, the initial unity of its subject matter giving way to a myriad of seemingly unrelated areas. The articles collected here, which range from historical scholarship to recent research in geometric model theory, squarely address this development. These articles also connect to the diverse work of Väänänen, whose ecumenical approach to logic reflects the unity of the discipline.
Georg Wilhelm Friedrich Hegel gave many lectures in logic at Berlin University between 1818 and his untimely death in 1831. Edited posthumously by Hegel's son, Karl, these lectures were published in German in 2001 and now appear in English for the first time. Because they were delivered orally, Lectures on Logic is more approachable and colloquial than much of Hegel's formal philosophy. The lectures provide important insight into Hegel's science of logic, dialectical method, and symbolic logic. Clark Butler's smooth translation helps readers understand the rationality of Hegel's often dark and difficult thought. Readers at all levels will find a mature and particularly clear presentation of Hegel's systematic philosophical vision.
Logical pluralism is the view that different logics are equally appropriate, or equally correct. Logical relativism is a pluralism according to which validity and logical consequence are relative to something. In Varieties of Logic, Stewart Shapiro develops several ways in which one can be a pluralist or relativist about logic. One of these is an extended argument that words and phrases like 'valid' and 'logical consequence' are polysemous or, perhaps better, are cluster concepts. The notions can be sharpened in various ways. This explains away the 'debates' in the literature between inferentialists and advocates of a truth-conditional, model-theoretic approach, and between those who advocate higher-order logic and those who insist that logic is first-order. A significant kind of pluralism flows from an orientation toward mathematics that emerged toward the end of the nineteenth century, and continues to dominate the field today. The theme is that consistency is the only legitimate criterion for a theory. Logical pluralism arises when one considers a number of interesting and important mathematical theories that invoke a non-classical logic, and are rendered inconsistent, and trivial, if classical logic is imposed. So validity is relative to a theory or structure. The perspective raises a host of important questions about meaning. The most significant of these concern the semantic content of logical terminology, words like 'or', 'not', and 'for all', as they occur in rigorous mathematical deduction. Does the intuitionistic 'not', for example, have the same meaning as its classical counterpart? Shapiro examines the major arguments on the issue, on both sides, and finds them all wanting. He then articulates and defends a thesis that the question of meaning-shift is itself context-sensitive and, indeed, interest-relative. He relates the issue to some prominent considerations concerning open texture, vagueness, and verbal disputes. Logic is ubiquitous. Whenever there is deductive reasoning, there is logic. So there are questions about logical pluralism that are analogous to standard questions about global relativism. The most pressing of these concerns foundational studies, wherein one compares theories, sometimes with different logics, and where one figures out what follows from what in a given logic. Shapiro shows that the issues are not problematic, and that is usually easy to keep track of the logic being used and the one mentioned.
Luft's update of Hibben's classic work on Hegel's Encyclopedia Logic; one of the clearest, most illuminating, most helpful, and most popular expositions of this rich and difficult text.
Winner of the 2020 Hegelpd-Prize presented by the University of Padova Research Group In this book, Angelica Nuzzo proposes a reading of Hegel's Logic as "logic of transformation" and "logic of action," and supports this thesis by looking to works of literature and history as exemplary of Hegel's argument and method. By examining Melville's Billy Budd, Molière's Tartuffe, Beckett's Endgame, Elizabeth Bishop's and Giacomo Leopardi's late poetry along with Thucydides' History in this way, Nuzzo finds an unprecedented and productive way to render Hegel's Logic alive and engaging. She argues that Melville's Billy Budd is the most successful embodiment of the abstract movement of thinking presented in Hegel's Logic, connecting Billy Budd's stutter to the puzzlingly inarticulate beginning of Hegel's Logic, "Being, pure Being," identical with "Nothing," and argues that the Logic serves as an especially appropriate tool for understanding the sudden violent action that strikes Claggart dead. Through these and other readings, Nuzzo finds a fresh way to address interpretive issues that have remained unresolved for almost two centuries in Hegel scholarship, and also presents well-known works of literature in an entirely new light. This account of Hegel's Logic is framed by the need for an interpretive tool able to orient our understanding of the contemporary world as mired in an unprecedented global crisis. How can the story of our historical present—the tragedy or the comedy we all play parts in—be told? What is the inner logic of our changing world?
This translation of The Science of Logic (also known as 'Greater Logic') includes the revised Book I (1832), Book II (1813) and Book III (1816). Recent research has given us a detailed picture of the process that led Hegel to his final conception of the System and of the place of the Logic within it. We now understand how and why Hegel distanced himself from Schelling, how radical this break with his early mentor was, and to what extent it entailed a return (but with a difference) to Fichte and Kant. In the introduction to the volume, George Di Giovanni presents in synoptic form the results of recent scholarship on the subject, and, while recognizing the fault lines in Hegel's System that allow opposite interpretations, argues that the Logic marks the end of classical metaphysics. The translation is accompanied by a full apparatus of historical and explanatory notes.