Bulletin of Symbolic Logic 2 (1):1-71 (1996)

Akihiro Kanamori
Boston University
Set theory is an autonomous and sophisticated field of mathematics, enormously successful not only at its continuing development of its historical heritage but also at analyzing mathematical propositions cast in set-theoretic terms and gauging their consistency strength. But set theory is also distinguished by having begun intertwined with pronounced metaphysical attitudes, and these have even been regarded as crucial by some of its great developers. This has encouraged the exaggeration of crises in foundations and of metaphysical doctrines in general. However, set theory has proceeded in the opposite direction, from a web of intensions to a theory of extensionpar excellence, and like other fields of mathematics its vitality and progress have depended on a steadily growing core of mathematical structures and methods, problems and results. There is also the stronger contention that from the beginning set theory actually developed through a progression ofmathematicalmoves, whatever and sometimes in spite of what has been claimed on its behalf.What follows is an account of the development of set theory from its beginnings through the creation of forcing based on these contentions, with an avowedly Whiggish emphasis on the heritage that has been retained and developed by current set theory. The whole transfinite landscape can be viewed as the result of Cantor's attempt to articulate and solve the Continuum Problem.
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DOI 10.2307/421046
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References found in this work BETA

Word and Object.Willard Van Orman Quine - 1960 - Les Etudes Philosophiques 17 (2):278-279.
Model Theory.Michael Makkai, C. C. Chang & H. J. Keisler - 1991 - Journal of Symbolic Logic 56 (3):1096.
The Iterative Conception of Set.George Boolos - 1971 - Journal of Philosophy 68 (8):215-231.
Principia Mathematica.A. N. Whitehead & B. Russell - 1927 - Erkenntnis 2 (1):73-75.

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Citations of this work BETA

Empiricism, Scientific Change and Mathematical Change.Otávio Bueno - 2000 - Studies in History and Philosophy of Science Part A 31 (2):269-296.
On Arbitrary Sets and ZFC.José Ferreirós - 2011 - Bulletin of Symbolic Logic 17 (3):361-393.
Hilbert and Set Theory.Burton Dreben & Akihiro Kanamori - 1997 - Synthese 110 (1):77-125.
The Early Development of Set Theory.José Ferreirós - unknown - Stanford Encyclopedia of Philosophy.

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