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Author: Penelope Maddy
Publisher: Clarendon Press
ISBN: 0191518972
Category : Philosophy
Languages : en
Pages : 265
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Book Description
Our much-valued mathematical knowledge rests on two supports: the logic of proof and the axioms from which those proofs begin. Naturalism in Mathematics investigates the status of the latter, the fundamental assumptions of mathematics. These were once held to be self-evident, but progress in work on the foundations of mathematics, especially in set theory, has rendered that comforting notion obsolete. Given that candidates for axiomatic status cannot be proved, what sorts of considerations can be offered for or against them? That is the central question addressed in this book. One answer is that mathematics aims to describe an objective world of mathematical objects, and that axiom candidates should be judged by their truth or falsity in that world. This promising view—realism—is assessed and finally rejected in favour of another—naturalism—which attends less to metaphysical considerations of objective truth and falsity, and more to practical considerations drawn from within mathematics itself. Penelope Maddy defines this naturalism, explains the motivation for it, and shows how it can be helpfully applied in the assessment of candidates for axiomatic status in set theory. Maddy's clear, original treatment of this fundamental issue is informed by current work in both philosophy and mathematics, and will be accessible and enlightening to readers from both disciplines.
Author: Penelope Maddy
Publisher: Clarendon Press
ISBN: 0191518972
Category : Philosophy
Languages : en
Pages : 265
Get Book Here
Book Description
Our much-valued mathematical knowledge rests on two supports: the logic of proof and the axioms from which those proofs begin. Naturalism in Mathematics investigates the status of the latter, the fundamental assumptions of mathematics. These were once held to be self-evident, but progress in work on the foundations of mathematics, especially in set theory, has rendered that comforting notion obsolete. Given that candidates for axiomatic status cannot be proved, what sorts of considerations can be offered for or against them? That is the central question addressed in this book. One answer is that mathematics aims to describe an objective world of mathematical objects, and that axiom candidates should be judged by their truth or falsity in that world. This promising view—realism—is assessed and finally rejected in favour of another—naturalism—which attends less to metaphysical considerations of objective truth and falsity, and more to practical considerations drawn from within mathematics itself. Penelope Maddy defines this naturalism, explains the motivation for it, and shows how it can be helpfully applied in the assessment of candidates for axiomatic status in set theory. Maddy's clear, original treatment of this fundamental issue is informed by current work in both philosophy and mathematics, and will be accessible and enlightening to readers from both disciplines.
Author: Phillip E. Johnson
Publisher: InterVarsity Press
ISBN: 9780830819294
Category : Religion
Languages : en
Pages : 252
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Book Description
Phillip E. Johnson exposes the flawed underpinnings of naturalism in this discussion of evolution, sex education, abortion, God, the search for a grand unified theory in physics, what our public schools should teach, the basis of law and more.
Author: Mario De Caro
Publisher: Harvard University Press
ISBN: 0674030419
Category : Philosophy
Languages : en
Pages : 351
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Book Description
Today the majority of philosophers in the English-speaking world adhere to the "naturalist" credos that philosophy is continuous with science, and that the natural sciences provide a complete account of all that exists--whether human or nonhuman. The new faith says science, not man, is the measure of all things. However, there is a growing skepticism about the adequacy of this complacent orthodoxy. This volume presents a group of leading thinkers who criticize scientific naturalism not in the name of some form of supernaturalism, but in order to defend a more inclusive or liberal naturalism. The many prominent Anglo-American philosophers appearing in this book--Akeel Bilgrami, Stanley Cavell, Donald Davidson, John Dupr, Jennifer Hornsby, Erin Kelly, John McDowell, Huw Price, Hilary Putnam, Carol Rovane, Barry Stroud, and Stephen White--do not march in lockstep, yet their contributions demonstrate mutual affinities and various unifying themes. Instead of attempting to force human nature into a restricted scientific image of the world, these papers represent an attempt to place human nature at the center of renewed--but still scientifically respectful--conceptions of philosophy and nature.
Author: Kai Nielsen
Publisher: Prometheus Books
ISBN: 1615927573
Category : Philosophy
Languages : en
Pages : 506
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Book Description
This elucidation and defense of naturalism argues that an uncompromising secular orientation is the best framework for the search for meaning and interprets religion in purely naturalistic terms. Part One seeks to demonstrate that religious symbols arise from facts about human beings and the societies in which they live, specifically our needs, fears, and aspirations. Part Two examines arguments for and against naturalism, including the defenses of naturalism by Sidney Hook, Ernest Nagel, Antony Flew, and critical reactions to their views. The forceful and rigorously analytical case made by Jean Hampton against naturalism is also examined, resulting in a clarification of the substantial and sound methodological grounds for naturalism and atheism. Part Three considers the strongest intellectual challenge to secularism and naturalism, namely that of Ludwig Wittgenstein and some of his followers - Norman Malcolm, D. Z. Phillips, Hilary Putnam, Rush Rhees, and Peter Winch. Nielsen concludes that none of these critiques diminish the cogency and viability of naturalism as the most reasonable basis for viewing our world today.
Author: William Lane Craig
Publisher: Routledge
ISBN: 1134564511
Category : Philosophy
Languages : en
Pages : 550
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Book Description
Naturalism provides a rigorous analysis and critique of the major varieties of contemporary philosophical naturalism. The authors advocate the thesis that contemporary naturalism should be abandoned, in light of the serious objections raised against it. Contributors draw on a wide range of topics including: epistemology, the philosophy of science, the philosophy of mind and agency, and natural theology.
Author: Penelope Maddy
Publisher:
ISBN: 9780191597961
Category : Mathematics
Languages : en
Pages : 254
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Book Description
Set theory has rendered the notion of self-evident truths to be obsolete in mathematics. Penelope Maddy examines this dilemma using the minimum of technical jargon. Set theory is explained in a manner that can be understood by non-mathematicians.
Author: Mario De Caro
Publisher: Columbia University Press
ISBN: 0231134673
Category : Philosophy
Languages : en
Pages : 378
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Book Description
Normativity concerns what we ought to think or do and the evaluations we make. For scientific naturalists the moral is reached by reducing the normative to the nonnormative. For orthodox nonnaturalists the moral is found in the transcendent realm of norms. This book challenges both sides of this debate.
Author: Brian Lightbody
Publisher: Lexington Books
ISBN: 0739183990
Category : Philosophy
Languages : en
Pages : 148
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Book Description
Philosophers often use the term “naturalism’ in order to describe their work. It is commonplace to see a metaphysical, epistemological and/or ethical position self-described and described by others as one that is “naturalized.” But what, if anything, does the term naturalized add--or subtract---to the position being articulated? I demonstrate in The Problem of Naturalism: Analytic and Continental Perspectives, that the term naturalism connotes such a broad meaning that it is difficult to demarcate naturalism from philosophy itself. Still, many philosophers have tried to provide non-trivial and non-vacuous definitions of the term. My book, by and large, argues that such attempts are unsuccessful. Instead, I argue that naturalism is an attitude and neither a methodology nor a substantive position. I then articulate the guidelines the naturalist needs to follow, as well as the virtues he or she needs to practice, in order for the term naturalism to do any meaningful work. Much of the book explains and then critiques the various attempts to define naturalism in the Anglo-American secondary literature. Some of the criticisms I raise seem to emanate from the internal logic of the naturalistic position being expressed. However, others have emerged from gleaning the work of such Continental thinkers as: Nietzsche, Husserl, Heidegger and Foucault. I use these thinkers in order to expose the unjustified implicit and sometimes explicit assumptions that many naturalistic philosophers presume to hold when they attempt to render a clear, distinct and robust naturalist position.
Author: Jeffrey Wells Roland
Publisher:
ISBN: 9780496962099
Category :
Languages : en
Pages : 202
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Book Description
Thus, unless this burden can be met (and I strongly suspect that it can't be), neither Mathematical Naturalism nor Naturalistic Constructivism successfully naturalizes the epistemology of mathematics.
Author: Michael Cannon Rea
Publisher: Oxford University Press
ISBN: 0199247609
Category : Philosophy
Languages : en
Pages : 256
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Book Description
"Philosophical naturalism has dominated the Western academy for well over a century. According to Michael Rea, however, there is an important sense in which naturalism's status as orthodoxy is without rational foundation, and the costs of embracing it are surprisingly high. The goal of World without Design is to defend these two claims, with special attention to the second." "The first part of the book aims to provide a fair and historically informed characterization of naturalism. The second part argues for the striking thesis that naturalists are committed to rejecting realism about material objects, materialism, and perhaps realism about other minds. Rea concludes by examining two alternative research programs: intuitionism and supernaturalism, and argues for the conclusion that, under certain circumstances, intuitionism is self-defeating."
