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This book traces the development of formal logic from its origins inancient Greece to the present day. The authors first discuss the work oflogicians from Aristotle to Frege, showing how they were influenced by thephilosophical or mathematical ideas of their time. They then examinedevelopments in the present century. |
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This book consists of Gregory Vlastos' studies on a variety of themes in Plato's metaphysics, epistemology, ethics, and social philosophy. |
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[INTRODUCTION] Like the terms 'dialectic', 'Aufhebung' (or 'sublation'), and 'Geist', the term 'concrete universal' has a distinctively Hegelian ring to it. But unlike these others, it is particularly associated with the British strand in Hegel's reception history, as having been brought to prominence by some of the central British Idealists. It is therefore perhaps inevitable that, as their star has waned, so too has any use of the term, while an appreciation of the problematic that lay behind it has seemingly (...) |
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In this book, Malcolm presents a new and radical interpretation of Plato's earlier dialogues. He argues that the few cases of self-predication contained therein are acceptable simply as statements concerning universals, and that therefore Plato is not vulnerable in these cases to the Third Man Argument. In considering the middle dialogues, Malcolm takes a conservative stance, rejecting influential current doctrines which portray the Forms as being not self-predicative. He shows that the middle dialogues do indeed take Forms to be both (...) |
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First-order logic. The origin of modern foundational studies. Frege's system and the paradoxes. The teory of types. Zermelo-Fraenkel set theory. Hilbert's program and Godel's incompleteness theorems. The foundational systems of W.V. Quine. Categorical algebra. |
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The book draws on the astonishing scope and depths of Hegel's Lectures on Aesthetics, exploring the multifaceted issue of art and the absolute. Why does Hegel ascribe absoluteness to art? What can such absoluteness mean? |
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Did Plato abandon, or sharply modify, the Theory of Forms in later life? In the _Phaedo, Symposium, _and _Republic_ it is generally agreed that Plato held that universals exist. But in Parmenides, he subjected that theory to criticism. If the criticism were valid, and Plato knew so, then the _Parmenides_ marks a turning point in his thought. If, however, Plato became aware that there are radical differences in the logical behaviour of concepts, and the later dialogues are a record of (...) |
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Category Theory has developed rapidly. This book aims to present those ideas and methods which can now be effectively used by Mathe maticians working in a variety of other fields of Mathematical research. This occurs at several levels. On the first level, categories provide a convenient conceptual language, based on the notions of category, functor, natural transformation, contravariance, and functor category. These notions are presented, with appropriate examples, in Chapters I and II. Next comes the fundamental idea of an adjoint (...) |
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Gregory Vlastos was one of the twentieth century's most influential scholars of ancient philosophy. Over a span of more than fifty years, he published essays and book reviews that established his place as a leading authority on early Greek philosophy. The two volumes that comprise Studies in Greek Philosophy include nearly forty contributions by this acknowledged master of the philosophical essay. Many of these pieces are now considered to be classics in the field. Perhaps more than any other modern scholar, (...) |
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Did Plato abandon, or sharply modify, the Theory of Forms in later life? In the Phaedo, Symposium, and Republic it is generally agreed that Plato held that universals exist. But in Parmenides, he subjected that theory to criticism. If the criticism were valid, and Plato knew so, then the Parmenides marks a turning point in his thought. If, however, Plato became aware that there are radical differences in the logical behaviour of concepts, and the later dialogues are a record of (...) |
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Offering clear and reliable guidance to the ideas of philosophers from antiquity to the present day and to the major philosophical systems around the globe, he Oxford Companion to Philosophy is the definitive philosophical reference work for readers at all levels. For ten years the original volume has served as a stimulating introduction for general readers and as an indispensable guide for students and scholars. A distinguished international assembly of 249 philosophers contributed almost 2,000 entries, and many of these have (...) |
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This paper offers an interpretation of self-Predication (the idea that justice is just) in plato, Given that self-Predication is accepted as obvious both by plato and by his audience, Which entails that "all" self-Predications are clearly, Though not trivially, True. More strongly, It is suggested that "only" self-Predications can be accepted as clearly true by plato. This is to deny that plato had at his disposal an articulated notion of predication, And his middle theory of forms, Primarily the relation of (...) |
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