David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Philosophia Mathematica 2 (1):5-15 (1994)
For 20th century mathematicians, the role of Cantor's sets has been that of the ideally featureless canvases on which all needed algebraic and geometrical structures can be painted. (Certain passages in Cantor's writings refer to this role.) Clearly, the resulting contradication, 'the points of such sets are distinc yet indistinguishable', should not lead to inconsistency. Indeed, the productive nature of this dialectic is made explicit by a method fruitful in other parts of mathematics (see 'Adjointness in Foundations', Dialectia 1969). This role of Cantor's theory is compared with the role of Galois theory in algebraic geometry.
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
Øystein Linnebo & Richard Pettigrew (2011). Category Theory as an Autonomous Foundation. Philosophia Mathematica 19 (3):227-254.
Similar books and articles
S. J. Mcleish (1997). The Forth Part of the Back and Forth Map in Countable Homogeneous Structures. Journal of Symbolic Logic 62 (3):873-890.
Christopher Menzel (1984). Cantor and the Burali-Forti Paradox. The Monist 67 (1):92-107.
Jan Kraszewski (2001). Properties of Ideals on the Generalized Cantor Spaces. Journal of Symbolic Logic 66 (3):1303-1320.
Marcus Rossberg & Philip A. Ebert (2010). Cantor on Frege's Foundations of Arithmetic : Cantor's 1885 Review of Frege's Die Grundlagen der Arithmetik. History and Philosophy of Logic 30 (4):341-348.
J. Ferreiros (2004). The Motives Behind Cantor’s Set Theory: Physical, Biological and Philosophical Questions. Science in Context 17 (1/2):1–35.
Claire Ortiz Hill (1997). Did Georg Cantor Influence Edmund Husserl? Synthese 113 (1):145-170.
I. Grattan-Guinness (1982). Psychology in the Foundations of Logic and Mathematics: The Cases of Boole, Cantor and Brouwer. History and Philosophy of Logic 3 (1):33-53.
Added to index2009-01-28
Total downloads33 ( #96,521 of 1,725,474 )
Recent downloads (6 months)3 ( #211,098 of 1,725,474 )
How can I increase my downloads?