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Philosophy and History 1 (2):156-158 (1968)

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Abstract mathematical tools and machines for mathematics.Jean-Pierre Marquis - 1997 - Philosophia Mathematica 5 (3):250-272.details In this paper, we try to establish that some mathematical theories, like K-theory, homology, cohomology, homotopy theories, spectral sequences, modern Galois theory (in its various applications), representation theory and character theory, etc., should be thought of as (abstract) machines in the same way that there are (concrete) machines in the natural sciences. If this is correct, then many epistemological and ontological issues in the philosophy of mathematics are seen in a different light. We concentrate on one problem which immediately follows (...) Download Export citation Bookmark 10 citations
Epistemic optimism.Mihai Ganea - 2008 - Philosophia Mathematica 16 (3):333-353.details Michael Dummett's argument for intuitionism can be criticized for the implicit reliance on the existence of what might be called absolutely undecidable statements. Neil Tennant attacks epistemic optimism, the view that there are no such statements. I expose what seem serious flaws in his attack, and I suggest a way of defending the use of classical logic in arithmetic that circumvents the issue of optimism. I would like to thank an anonymous referee for helpful comments. CiteULike Connotea Del.icio.us What's this? Download Export citation Bookmark
Hao Wang as philosopher and interpreter of gödel.Charles Parsons - 1998 - Philosophia Mathematica 6 (1):3-24.details The paper undertakes to characterize Hao Wang's style, convictions, and method as a philosopher, centering on his most important philosophical work From Mathematics to Philosophy, 1974. The descriptive character of Wang's characteristic method is emphasized. Some specific achievements are discussed: his analyses of the concept of set, his discussion, in connection with setting forth Gödel's views, of minds and machines, and his concept of ‘analytic empiricism’ used to criticize Carnap and Quine. Wang's work as interpreter of Gödel's thought and the (...) Download Export citation Bookmark 4 citations
William Tait. The provenance of pure reason. Essays on the philosophy of mathematics and on its history.Charles Parsons - 2009 - Philosophia Mathematica 17 (2):220-247.details William Tait's standing in the philosophy of mathematics hardly needs to be argued for; for this reason the appearance of this collection is especially welcome. As noted in his Preface, the essays in this book ‘span the years 1981–2002’. The years given are evidently those of publication. One essay was not previously published in its present form, but it is a reworking of papers published during that period. The Introduction, one appendix, and some notes are new. Many of the essays (...) Download Export citation Bookmark 1 citation
Paper machines.Daniele Mundici & Wilfried Seig - 1995 - Philosophia Mathematica 3 (1):5-30.details Machines were introduced as calculating devices to simulate operations carried out by human computers following fixed algorithms. The mathematical study of (paper) machines is the topic of our essay. The first three sections provide necessary logical background, examine the analyses of effective calculability given in the thirties, and describe results that are central to recursion theory, reinforcing the conceptual analyses. In the final section we pursue our investigation in a quite different way and focus on principles that govern the operations (...) Download Export citation Bookmark 3 citations

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