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Author: Solomon Feferman
Publisher: Oxford University Press, USA
ISBN: 0195080300
Category : Logic, Symbolic and mathematical
Languages : en
Pages : 353
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Book Description
In this collection of essays written over a period of twenty years, Solomon Feferman explains advanced results in modern logic and employs them to cast light on significant problems in the foundations of mathematics. Most troubling among these is the revolutionary way in which Georg Cantor elaborated the nature of the infinite, and in doing so helped transform the face of twentieth-century mathematics. Feferman details the development of Cantorian concepts and the foundational difficulties they engendered. He argues that the freedom provided by Cantorian set theory was purchased at a heavy philosophical price, namely adherence to a form of mathematical platonism that is difficult to support. Beginning with a previously unpublished lecture for a general audience, Deciding the Undecidable, Feferman examines the famous list of twenty-three mathematical problems posed by David Hilbert, concentrating on three problems that have most to do with logic. Other chapters are devoted to the work and thought of Kurt Gödel, whose stunning results in the 1930s on the incompleteness of formal systems and the consistency of Cantors continuum hypothesis have been of utmost importance to all subsequent work in logic. Though Gödel has been identified as the leading defender of set-theoretical platonism, surprisingly even he at one point regarded it as unacceptable. In his concluding chapters, Feferman uses tools from the special part of logic called proof theory to explain how the vast part--if not all--of scientifically applicable mathematics can be justified on the basis of purely arithmetical principles. At least to that extent, the question raised in two of the essays of the volume, Is Cantor Necessary?, is answered with a resounding no. This volume of important and influential work by one of the leading figures in logic and the foundations of mathematics is essential reading for anyone interested in these subjects.
Author: Solomon Feferman
Publisher: Oxford University Press, USA
ISBN: 0195080300
Category : Logic, Symbolic and mathematical
Languages : en
Pages : 353
Get Book
Book Description
In this collection of essays written over a period of twenty years, Solomon Feferman explains advanced results in modern logic and employs them to cast light on significant problems in the foundations of mathematics. Most troubling among these is the revolutionary way in which Georg Cantor elaborated the nature of the infinite, and in doing so helped transform the face of twentieth-century mathematics. Feferman details the development of Cantorian concepts and the foundational difficulties they engendered. He argues that the freedom provided by Cantorian set theory was purchased at a heavy philosophical price, namely adherence to a form of mathematical platonism that is difficult to support. Beginning with a previously unpublished lecture for a general audience, Deciding the Undecidable, Feferman examines the famous list of twenty-three mathematical problems posed by David Hilbert, concentrating on three problems that have most to do with logic. Other chapters are devoted to the work and thought of Kurt Gödel, whose stunning results in the 1930s on the incompleteness of formal systems and the consistency of Cantors continuum hypothesis have been of utmost importance to all subsequent work in logic. Though Gödel has been identified as the leading defender of set-theoretical platonism, surprisingly even he at one point regarded it as unacceptable. In his concluding chapters, Feferman uses tools from the special part of logic called proof theory to explain how the vast part--if not all--of scientifically applicable mathematics can be justified on the basis of purely arithmetical principles. At least to that extent, the question raised in two of the essays of the volume, Is Cantor Necessary?, is answered with a resounding no. This volume of important and influential work by one of the leading figures in logic and the foundations of mathematics is essential reading for anyone interested in these subjects.
Author: Thomas DeGloma
Publisher: University of Chicago Press
ISBN: 022617591X
Category : Social Science
Languages : en
Pages : 254
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Book Description
The chorus of the Christian hymn “Amazing Grace” reads, “I once was lost, but now am found, / Was blind but now I see.” Composed by a minister who formerly worked as a slave trader, the song expresses his experience of divine intervention that ultimately caused him to see the error of his ways. This theme of personal awakening is a feature of countless stories throughout history, where the “lost” and the “blind” are saved from darkness and despair by suddenly seeing the light. In Seeing the Light, Thomas DeGloma explores such accounts of personal awakening, in stories that range from the discovery of a religious truth to remembering a childhood trauma to embracing a new sexual orientation. He reveals a common social pattern: When people discover a life-changing truth, they typically ally with a new community. Individuals then use these autobiographical stories to shape their stances on highly controversial issues such as childhood abuse, war and patriotism, political ideology, human sexuality, and religion. Thus, while such stories are seemingly very personal, they also have a distinctly social nature. Tracing a wide variety of narratives through nearly three thousand years of history, Seeing the Light uncovers the common threads of such stories and reveals the crucial, little-recognized social logic of personal discovery.
Author: Martin Heidegger
Publisher: Indiana University Press
ISBN: 0253004454
Category : Philosophy
Languages : en
Pages : 348
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Book Description
Heidegger’s radical thinking on the meaning of truth in a “clear and comprehensive critical edition” (Philosophy in Review). Martin Heidegger’s 1925–26 lectures on truth and time provided much of the basis for his momentous work, Being and Time. Not published until 1976—three months before Heidegger’s death—as volume 21 of his Complete Works, it is nonetheless central to Heidegger’s overall project of reinterpreting Western thought in terms of time and truth. The text shows the degree to which Aristotle underlies Heidegger’s hermeneutical theory of meaning. It also contains Heidegger’s first published critique of Husserl and takes major steps toward establishing the temporal bases of logic and truth. Thomas Sheehan’s elegant and insightful translation offers English-speaking readers access to this fundamental text for the first time.
Author: Paul Tomassi
Publisher: Routledge
ISBN: 1134705921
Category : Education
Languages : en
Pages : 428
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Book Description
Bringing elementary logic out of the academic darkness into the light of day, Paul Tomassi makes logic fully accessible for anyone attempting to come to grips with the complexities of this challenging subject. Including student-friendly exercises, illustrations, summaries and a glossary of terms, Logic introduces and explains: * The Theory of Validity * The Language of Propositional Logic * Proof-Theory for Propositional Logic * Formal Semantics for Propositional Logic including the Truth-Tree Method * The Language of Quantificational Logic including the Theory of Descriptions. Logic is an ideal textbook for any logic student: perfect for revision, staying on top of coursework or for anyone wanting to learn about the subject. Related downloadable software for Macs and PCs is available for this title at www.logic.routledge.com.
Author: Penelope Rush
Publisher: Cambridge University Press
ISBN: 1107039649
Category : Mathematics
Languages : en
Pages : 279
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Book Description
This wide-ranging collection of essays explores the nature of logic and the key issues and debates in the metaphysics of logic.
Author: Robert M. Martin
Publisher: Broadview Press
ISBN: 9781551116358
Category : Philosophy
Languages : en
Pages : 274
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Book Description
This accessible, SHORT introduction to symbolic logic includes coverage of sentential and predicate logic, translations, truth tables, and derivations. The author’s engaging style makes this the most informal of introductions to formal logic. Topics are explained in a conversational, easy-to-understand way for readers not familiar with mathematics or formal systems, and the author provides patient, reader-friendly explanations—even with the occasional bit of humour. The first half of the book deals with all the basic elements of Sentential Logic: the five truth-functional connectives, formation rules and translation into this language, truth-tables for validity, logical truth/falsity, equivalency, consistency and derivations. The second half deals with Quantifier Logic: the two quantifiers, formation rules and translation, demonstrating certain logical characteristics by “Finding an Interpretation” and derivations. There are plenty of exercises scattered throughout, more than in many texts, arranged in order of increasing difficulty and including separate answer keys.
Author: Shahid Rahman
Publisher: Springer Science & Business Media
ISBN: 1402028083
Category : Philosophy
Languages : en
Pages : 618
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Book Description
The first volume in this new series explores, through extensive co-operation, new ways of achieving the integration of science in all its diversity. The book offers essays from important and influential philosophers in contemporary philosophy, discussing a range of topics from philosophy of science to epistemology, philosophy of logic and game theoretical approaches. It will be of interest to philosophers, computer scientists and all others interested in the scientific rationality.
Author: Eugenia Cheng
Publisher: Basic Books
ISBN: 154167250X
Category : Mathematics
Languages : en
Pages : 321
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Book Description
How both logical and emotional reasoning can help us live better in our post-truth world In a world where fake news stories change election outcomes, has rationality become futile? In The Art of Logic in an Illogical World, Eugenia Cheng throws a lifeline to readers drowning in the illogic of contemporary life. Cheng is a mathematician, so she knows how to make an airtight argument. But even for her, logic sometimes falls prey to emotion, which is why she still fears flying and eats more cookies than she should. If a mathematician can't be logical, what are we to do? In this book, Cheng reveals the inner workings and limitations of logic, and explains why alogic -- for example, emotion -- is vital to how we think and communicate. Cheng shows us how to use logic and alogic together to navigate a world awash in bigotry, mansplaining, and manipulative memes. Insightful, useful, and funny, this essential book is for anyone who wants to think more clearly.
Author: John Sallis
Publisher: Indiana University Press
ISBN: 025301364X
Category : Philosophy
Languages : en
Pages : 311
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Book Description
The Shakespearean image of a tempest and its aftermath forms the beginning as well as a major guiding thread of Logic of Imagination. Moving beyond the horizons of his earlier work, Force of Imagination, John Sallis sets out to unsettle the traditional conception of logic, to mark its limits, and, beyond these limits, to launch another, exorbitant logic—a logic of imagination. Drawing on a vast range of sources, including Plato, Aristotle, Kant, Hegel, Nietzsche, and Freud, as well as developments in modern logic and modern mathematics, Sallis shows how a logic of imagination can disclose the most elemental dimensions of nature and of human existence and how, through dialogue with contemporary astrophysics, it can reopen the project of a philosophical cosmology.
Author: John L. Casti
Publisher:
ISBN: 0786747609
Category : Science
Languages : en
Pages : 222
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Book Description
Kurt Gödel was an intellectual giant. His Incompleteness Theorem turned not only mathematics but also the whole world of science and philosophy on its head. Shattering hopes that logic would, in the end, allow us a complete understanding of the universe, Gödel's theorem also raised many provocative questions: What are the limits of rational thought? Can we ever fully understand the machines we build? Or the inner workings of our own minds? How should mathematicians proceed in the absence of complete certainty about their results? Equally legendary were Gödel's eccentricities, his close friendship with Albert Einstein, and his paranoid fear of germs that eventually led to his death from self-starvation. Now, in the first book for a general audience on this strange and brilliant thinker, John Casti and Werner DePauli bring the legend to life.
