Modern Logic

  • Mod. Log.
  • Volume 1, Number 4 (1991), 302-318.

Is Cantorian set theory an iterative conception of set?

María J. Frápolli

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Abstract

The aim of this paper is to argue against the view that Cantor's is an iterative conception of set. I shall distinguish between the theory found in Grundlagen and Beiträge, which I call the "first theory," and that expounded in Cantor's correspondence with Dedekind and with Jourdain. I consider that Cantor's first theory encloses a naive and unrestricted concept of set, and that the set-theoretical paradoxes do therefore follow from it. In this sense, I do not support the idea that Cantorian set theory is an iterative conception of set, as maintained by Boolos, Parsons and Vang, among others, or Hallett's interpretation, which considers it from the outset as a theory of limitation of size.

Article information

Source
Mod. Log., Volume 1, Number 4 (1991), 302-318.

Dates
First available in Project Euclid: 6 March 2008

Permanent link to this document
https://projecteuclid.org/euclid.rml/1204834738

Mathematical Reviews number (MathSciNet)
MR1112351

Zentralblatt MATH identifier
0747.03003

Subjects
Primary: 04-03
Secondary: 01A55: 19th century 01A60: 20th century 03A05: Philosophical and critical {For philosophy of mathematics, see also 00A30}

Citation

Frápolli, María J. Is Cantorian set theory an iterative conception of set?. Mod. Log. 1 (1991), no. 4, 302--318. https://projecteuclid.org/euclid.rml/1204834738


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