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Switch to: Citations
References in:
Mathematical knowledge is context dependent
Grazer Philosophische Studien 76 (1):91-107 (2008)
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In response to Jaffe and Quinn [math.HO/9307227], the author discusses forms of progress in mathematics that are not captured by formal proofs of theorems, especially in his own work in the theory of foliations and geometrization of 3-manifolds and dynamical systems. |
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'To think often, and never to retain it so much as one moment, is a very useless sort of thinking' In An Essay concerning Human Understanding, John Locke sets out his theory of knowledge and how we acquire it. Eschewing doctrines of innate principles and ideas, Locke shows how all our ideas, even the most abstract and complex, are grounded in human experience and attained by sensation of external things or reflection upon our own mental activities. A thorough examination of (...) |
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A scholarly edition of Essay Concerning Human Understanding by P. H. Nidditch. The edition presents an authoritative text, together with an introduction, commentary notes, and scholarly apparatus. |
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This book argues against the view that mathematical knowledge is a priori,contending that mathematics is an empirical science and develops historically,just as ... |
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Recent years have seen an explosion of interest in the semantics of knowledge-attributing sentences, not just among epistemologists but among philosophers of language seeking a general understanding of linguistic context sensitivity. Despite all this critical attention, however, we are as far from consensus as ever. If we have learned anything, it is that each of the standard views—invariantism, contextualism, and sensitive invariantism—has its Achilles’ heel: a residuum of facts about our use of knowledge attributions that it can explain only with (...) |
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is the second-order theory of the part-whole relation. It can express such hypotheses about the size of Reality as that there are inaccessibly many atoms. Take a non-empty class to have exactly its non-empty subclasses as parts; hence, its singleton subclasses as atomic parts. Then standard set theory becomes the theory of the member-singleton function—better, the theory of all singleton functions—within the framework of megethology. Given inaccessibly many atoms and a specification of which atoms are urelements, a singleton function exists, (...) |
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David Lewis (1941-2001) was Class of 1943 University Professor of Philosophy at Princeton University. His contributions spanned philosophical logic, philosophy of language, philosophy of mind, philosophy of science, metaphysics, and epistemology. In On the Plurality of Worlds, he defended his challenging metaphysical position, "modal realism." He was also the author of the books Convention, Counterfactuals, Parts of Classes, and several volumes of collected papers. |
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This paper uses the knowledge account of assertion (KAA) in defense of epistemological contextualism. Part 1 explores the main problem afflicting contextualism, what I call the "Generality Objection." Part 2 presents and defends both KAA and a powerful new positive argument that it provides for contextualism. Part 3 uses KAA to answer the Generality Objection, and also casts other shadows over the prospects for anti-contextualism. |
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A guide to the practical art of plausible reasoning, this book has relevance in every field of intellectual activity. Professor Polya, a world-famous mathematician from Stanford University, uses mathematics to show how hunches and guesses play an important part in even the most rigorously deductive science. He explains how solutions to problems can be guessed at; good guessing is often more important than rigorous deduction in finding correct solutions. Vol. I, on Induction and Analogy in Mathematics, covers a wide variety (...) |
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A Non-Technical Introduction to Ethnomethodological Investigations of the Foundations of Mathematics through the Use of a Theorem of Euclidean Geometry* I ... |
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Ordinary mathematical proofs—to be distinguished from formal derivations—are the locus of mathematical knowledge. Their epistemic content goes way beyond what is summarised in the form of theorems. Objections are raised against the formalist thesis that every mainstream informal proof can be formalised in some first-order formal system. Foundationalism is at the heart of Hilbert's program and calls for methods of formal logic to prove consistency. On the other hand, ‘systemic cohesiveness’, as proposed here, seeks to explicate why mathematical knowledge is (...) |
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This book is concerned with `the problem of existence in mathematics'. It develops a mathematical system in which there are no existence assertions but only assertions of the constructibility of certain sorts of things. It explores the philosophical implications of such an approach through an examination of the writings of Field, Burgess, Maddy, Kitcher, and others. |
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