The Limits of Abstraction PDF Download

Author: Kit Fine
Publisher: Clarendon Press
ISBN: 0199246181
Category : Mathematics
Languages : en
Pages : 214

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Book Description
"The Limits of Abstraction breaks new ground both technically and philosophically, and is essential reading for all those working on the philosophy of mathematics."--BOOK JACKET.

Author: Tim Button
Publisher:
ISBN: 0199672172
Category : Mathematics
Languages : en
Pages : 277

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Book Description
Tim Button explores the relationship between minds, words, and world. He argues that the two main strands of scepticism are deeply related and can be overcome, but that there is a limit to how much we can show. We must position ourselves somewhere between internal realism and external realism, and we cannot hope to say exactly where.

Author: Noson S. Yanofsky
Publisher: MIT Press
ISBN: 026252984X
Category : Science
Languages : en
Pages : 419

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Book Description
This exploration of the scientific limits of knowledge challenges our deep-seated beliefs about our universe, our rationality, and ourselves. “A must-read for anyone studying information science.” —Publishers Weekly, starred review Many books explain what is known about the universe. This book investigates what cannot be known. Rather than exploring the amazing facts that science, mathematics, and reason have revealed to us, this work studies what science, mathematics, and reason tell us cannot be revealed. In The Outer Limits of Reason, Noson Yanofsky considers what cannot be predicted, described, or known, and what will never be understood. He discusses the limitations of computers, physics, logic, and our own intuitions about the world—including our ideas about space, time, and motion, and the complex relationship between the knower and the known. Yanofsky describes simple tasks that would take computers trillions of centuries to complete and other problems that computers can never solve: • perfectly formed English sentences that make no sense • different levels of infinity • the bizarre world of the quantum • the relevance of relativity theory • the causes of chaos theory • math problems that cannot be solved by normal means • statements that are true but cannot be proven Moving from the concrete to the abstract, from problems of everyday language to straightforward philosophical questions to the formalities of physics and mathematics, Yanofsky demonstrates a myriad of unsolvable problems and paradoxes. Exploring the various limitations of our knowledge, he shows that many of these limitations have a similar pattern and that by investigating these patterns, we can better understand the structure and limitations of reason itself. Yanofsky even attempts to look beyond the borders of reason to see what, if anything, is out there.

Author: Nathan Ballantyne
Publisher:
ISBN: 019084728X
Category : Philosophy
Languages : en
Pages : 345

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Book Description
Epistemology and inquiry -- Regulative epistemology in the seventeenth century -- How do epistemic principles guide? -- How to know our limits -- Disagreement and debunking -- Counterfactual interlocutors -- Unpossessed evidence -- Epistemic trespassing -- Novices and expert disagreement -- Self-defeat? -- The end of inquiry.

Author: Jack L. Goldsmith
Publisher: Oxford University Press
ISBN: 0199883378
Category : Law
Languages : en
Pages : 271

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Book Description
International law is much debated and discussed, but poorly understood. Does international law matter, or do states regularly violate it with impunity? If international law is of no importance, then why do states devote so much energy to negotiating treaties and providing legal defenses for their actions? In turn, if international law does matter, why does it reflect the interests of powerful states, why does it change so often, and why are violations of international law usually not punished? In this book, Jack Goldsmith and Eric Posner argue that international law matters but that it is less powerful and less significant than public officials, legal experts, and the media believe. International law, they contend, is simply a product of states pursuing their interests on the international stage. It does not pull states towards compliance contrary to their interests, and the possibilities for what it can achieve are limited. It follows that many global problems are simply unsolvable. The book has important implications for debates about the role of international law in the foreign policy of the United States and other nations. The authors see international law as an instrument for advancing national policy, but one that is precarious and delicate, constantly changing in unpredictable ways based on non-legal changes in international politics. They believe that efforts to replace international politics with international law rest on unjustified optimism about international law's past accomplishments and present capacities.

Author: Caspar John Hare
Publisher: Oxford University Press, USA
ISBN: 0199691991
Category : Philosophy
Languages : en
Pages : 242

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Book Description
Caspar Hare presents a bold and original approach to questions of what we ought to do, and why we ought to do it. He breaks with tradition to argue that we can tackle difficult problems in normative ethics by starting with a principle that is humble and uncontroversial. Being moral involves wanting particular other people to be better off.

Author: Graham Priest
Publisher: Oxford University Press
ISBN: 9780199254057
Category : Philosophy
Languages : en
Pages : 344

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Book Description
Graham Priest presents an expanded edition of his exploration of the nature and limits of thought. Embracing contradiction and challenging traditional logic, he engages with issues across philosophical borders, from the historical to the modern, Eastern to Western, continental to analytic.

Author: Barbara H. Fried
Publisher: Oxford University Press
ISBN: 0192587099
Category : Philosophy
Languages : en
Pages : 397

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Book Description
Facing Up to Scarcity offers a powerful critique of the nonconsequentialist approaches that have been dominant in Anglophone moral and political thought over the last fifty years. In these essays Barbara H. Fried examines the leading schools of contemporary nonconsequentialist thought, including Rawlsianism, Kantianism, libertarianism, and social contractarianism. In the realm of moral philosophy, she argues that nonconsequentialist theories grounded in the sanctity of "individual reasons" cannot solve the most important problems taken to be within their domain. Those problems, which arise from irreducible conflicts among legitimate (and often identical) individual interests, can be resolved only through large-scale interpersonal trade-offs of the sort that nonconsequentialism foundationally rejects. In addition to scrutinizing the internal logic of nonconsequentialist thought, Fried considers the disastrous social consequences when nonconsequentialist intuitions are allowed to drive public policy. In the realm of political philosophy, she looks at the treatment of distributive justice in leading nonconsequentialist theories. Here one can design distributive schemes roughly along the lines of the outcomes favoured--but those outcomes are not logically entailed by the normative premises from which they are ostensibly derived, and some are extraordinarily strained interpretations of those premises. Fried concludes, as a result, that contemporary nonconsequentialist political philosophy has to date relied on weak justifications for some very strong conclusions.

Author: Liane Carlson
Publisher: Columbia University Press
ISBN: 0231548974
Category : Religion
Languages : en
Pages : 232

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Book Description
Central to the historicizing work of recent decades has been the concept of contingency, the realm of chance, change, and the unnecessary. Following Nietzsche and Foucault, genealogists have deployed contingency to show that all institutions and ideas could have been otherwise as a critique of the status quo. Yet scholars have spent very little time considering the genealogy of contingency itself—or what its history means for its role in politics. In Contingency and the Limits of History, Liane Carlson historicizes contingency by tying it to its theological and etymological roots in “touch,” contending that much of its critical, disruptive power is specific to our current historical moment. She returns to an older definition of contingency found in Christian theology that understands it as the lot of mortal creatures, who suffer, feel, bleed, and change, in contrast to a necessary, unchanging, impassible God. Far from dying out, Carlson reveals, this theological past persists in continental philosophy, where thinkers such as Novalis, Schelling, Merleau-Ponty, and Serres have imagined contingency as a type of radical destabilization brought about by the body’s collision with a changing world. Through studies of sickness, loneliness, violation, and love, she shows that different experiences of contingency can lead to dramatically dissimilar ethical and political projects. A strikingly original reconsideration of one of continental philosophy and critical theory’s most cherished concepts, this book reveals the limits of historicist accounts.

Author: Joel David Hamkins
Publisher: MIT Press
ISBN: 0262542234
Category : Mathematics
Languages : en
Pages : 350

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Book Description
An introduction to the philosophy of mathematics grounded in mathematics and motivated by mathematical inquiry and practice. In this book, Joel David Hamkins offers an introduction to the philosophy of mathematics that is grounded in mathematics and motivated by mathematical inquiry and practice. He treats philosophical issues as they arise organically in mathematics, discussing such topics as platonism, realism, logicism, structuralism, formalism, infinity, and intuitionism in mathematical contexts. He organizes the book by mathematical themes--numbers, rigor, geometry, proof, computability, incompleteness, and set theory--that give rise again and again to philosophical considerations.