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144What is required of a foundation for mathematics?Philosophia Mathematica 2 (1): 16-35. 1994.The business of mathematics is definition and proof, and its foundations comprise the principles which govern them. Modern mathematics is founded upon set theory. In particular, both the axiomatic method and mathematical logic belong, by their very natures, to the theory of sets. Accordingly, foundational set theory is not, and cannot logically be, an axiomatic theory. Failure to grasp this point leads obly to confusion. The idea of a set is that of an extensional plurality, limited and definite…Read more
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98J. L. Bell, A Primer of Infinitesimal Analysis. Cambridge: Cambridge University Press, 1998, cloth £19.95. ISBN: 0 521 62401 0British Journal for the Philosophy of Science 51 (2): 339-345. 2000.
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79The consistency problem for set theory: An essay on the Cantorian foundations of mathematics (II)British Journal for the Philosophy of Science 28 (2): 137-170. 1977.
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60The Foundations of Mathematics in the Theory of SetsCambridge University Press. 2000.This book will appeal to mathematicians and philosophers interested in the foundations of mathematics.
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57On the consistency problem for set theory: An essay on the Cantorian foundations of classical mathematics (I)British Journal for the Philosophy of Science 28 (1): 1-34. 1977.
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45Cantorian set Theory and Limitation of SizePhilosophical Quarterly 36 (144): 429-434. 1986.This is a book review of Cantorian set theory and limitations of size by Michael Hallett.
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42Frege, Dedekind, and Peano on the Foundations of Arithmetic (review)Philosophical Quarterly 34 (136): 424. 1984.First published in 1982, this reissue contains a critical exposition of the views of Frege, Dedekind and Peano on the foundations of arithmetic. The last quarter of the 19th century witnessed a remarkable growth of interest in the foundations of arithmetic. This work analyses both the reasons for this growth of interest within both mathematics and philosophy and the ways in which this study of the foundations of arithmetic led to new insights in philosophy and striking advances in logic. This hi…Read more
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36First published in 1982, this reissue contains a critical exposition of the views of Frege, Dedekind and Peano on the foundations of arithmetic. The last quarter of the 19th century witnessed a remarkable growth of interest in the foundations of arithmetic. This work analyses both the reasons for this growth of interest within both mathematics and philosophy and the ways in which this study of the foundations of arithmetic led to new insights in philosophy and striking advances in logic. This hi…Read more
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32Global quantification in zermelo-Fraenkel set theoryJournal of Symbolic Logic 50 (2): 289-301. 1985.
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22Luis E. Sanchis. Set theory—an operational approach. Gordon and Breach Science Publishers, Amsterdam etc. 1996, xvi + 279 pp (review)Journal of Symbolic Logic 63 (2): 751-752. 1998.
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14D. A. Gillies, "Frege Dedekind, and Peano on the Foundations of Arithmetic" (review)Philosophical Quarterly 34 (36): 424. 1984.
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10Review: Luis E. Sanchis, Set Theory -- An Operational Approach (review)Journal of Symbolic Logic 63 (2): 751-752. 1998.