fixing frege princeton monographs in philosophy

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Fixing Frege

Author : John P. Burgess
ISBN : 9780691187068
Genre : Philosophy
File Size : 53. 75 MB
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The great logician Gottlob Frege attempted to provide a purely logical foundation for mathematics. His system collapsed when Bertrand Russell discovered a contradiction in it. Thereafter, mathematicians and logicians, beginning with Russell himself, turned in other directions to look for a framework for modern abstract mathematics. Over the past couple of decades, however, logicians and philosophers have discovered that much more is salvageable from the rubble of Frege's system than had previously been assumed. A variety of repaired systems have been proposed, each a consistent theory permitting the development of a significant portion of mathematics. This book surveys the assortment of methods put forth for fixing Frege's system, in an attempt to determine just how much of mathematics can be reconstructed in each. John Burgess considers every proposed fix, each with its distinctive philosophical advantages and drawbacks. These systems range from those barely able to reconstruct the rudiments of arithmetic to those that go well beyond the generally accepted axioms of set theory into the speculative realm of large cardinals. For the most part, Burgess finds that attempts to fix Frege do less than advertised to revive his system. This book will be the benchmark against which future analyses of the revival of Frege will be measured.

G Del S Disjunction

Author : Leon Horsten
ISBN : 9780191077685
Genre : Mathematics
File Size : 32. 9 MB
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The logician Kurt Gödel in 1951 established a disjunctive thesis about the scope and limits of mathematical knowledge: either the mathematical mind is not equivalent to a Turing machine (i.e., a computer), or there are absolutely undecidable mathematical problems. In the second half of the twentieth century, attempts have been made to arrive at a stronger conclusion. In particular, arguments have been produced by the philosopher J.R. Lucas and by the physicist and mathematician Roger Penrose that intend to show that the mathematical mind is more powerful than any computer. These arguments, and counterarguments to them, have not convinced the logical and philosophical community. The reason for this is an insufficiency if rigour in the debate. The contributions in this volume move the debate forward by formulating rigorous frameworks and formally spelling out and evaluating arguments that bear on Gödel's disjunction in these frameworks. The contributions in this volume have been written by world leading experts in the field.

Philosophical Myths Of The Fall

Author : Stephen Mulhall
ISBN : 9781400826650
Genre : Philosophy
File Size : 89. 3 MB
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Did post-Enlightenment philosophers reject the idea of original sin and hence the view that life is a quest for redemption from it? In Philosophical Myths of the Fall, Stephen Mulhall identifies and evaluates a surprising ethical-religious dimension in the work of three highly influential philosophers--Nietzsche, Heidegger, and Wittgenstein. He asks: Is the Christian idea of humanity as structurally flawed something that these three thinkers aim simply to criticize? Or do they, rather, end up by reproducing secular variants of the same mythology? Mulhall argues that each, in different ways, develops a conception of human beings as in need of redemption: in their work, we appear to be not so much capable of or prone to error and fantasy, but instead structurally perverse, living in untruth. In this respect, their work is more closely aligned to the Christian perspective than to the mainstream of the Enlightenment. However, all three thinkers explicitly reject any religious understanding of human perversity; indeed, they regard the very understanding of human beings as originally sinful as central to that from which we must be redeemed. And yet each also reproduces central elements of that understanding in his own thinking; each recounts his own myth of our Fall, and holds out his own image of redemption. The book concludes by asking whether this indebtedness to religion brings these philosophers' thinking closer to, or instead forces it further away from, the truth of the human condition.

Philosophy Of Mathematics

Author : Vincent F. Hendricks
ISBN : 8799101351
Genre : Mathematics
File Size : 76. 59 MB
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Philosophy of Mathematics: 5 Questions is a collection of short interviews based on 5 questions presented to some of the most influential and prominent scholars in this field. We hear their views aim, scope, use, the future direction and how their work fits in these respects.

Mathematical Reviews

Author :
ISBN : UOM:39015067193329
Genre : Mathematics
File Size : 59. 93 MB
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The Philosophical Review

Author : Jacob Gould Schurman
ISBN : STANFORD:36105121703750
Genre : Philosophy
File Size : 55. 41 MB
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Joyce In The Belly Of The Big Truck Workbook

Author : Joyce A. Cascio
ISBN : 0976237318
Genre :
File Size : 39. 86 MB
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American Book Publishing Record

Author :
ISBN : UOM:39015066043251
Genre : American literature
File Size : 66. 26 MB
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Funktion Begriff Bedeutung

Author : Gottlob Frege
ISBN : 9783647231150
Genre : Philosophy
File Size : 32. 35 MB
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Als diese fünf Aufsätze Gottlob Freges 1962 in der Kleinen Vandenhoeck-Reihe erstmals erschienen, war Gottlob Frege noch weithin unbekannt. Damals bedurfte es noch einer ausführlichen Begründung der Bedeutung Freges für die Gegenwartsphilosophie. Heute sind seine Schriften zu Klassikern geworden, die für kühne Thesen mit vorbildlicher Klarheit argumentieren. Der Band enthält die Texte Funktion und Begriff; Über Sinn und Bedeutung; Über Begriff und Gegenstand; Was ist eine Funktion? sowie Über die wissenschaftliche Berechtigung einer Begriffsschrift. Ein ausführliches Vorwort des Herausgebers und Frege-»Entdeckers« Günther Patzig und ein Register erleichtern dem Benutzer den Zugang.

Name Und Notwendigkeit

Author : Saul A. Kripke
ISBN : 3518286560
Genre : Name - Analytische Philosophie
File Size : 20. 12 MB
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