Measuring the size of infinite collections of natural numbers: Was Cantor's theory of infinite number inevitable?

Review of Symbolic Logic 2 (4):612-646 (2009)
Abstract
Cantorsizesizesizewhole principle). This second intuition was not developed mathematically in a satisfactory way until quite recently. In this article I begin by reviewing the contributions of some thinkers who argued in favor of the assignment of different sizes to infinite collections of natural numbers (Thabit ibn Qurra, Grosseteste, Maignan, Bolzano). Then, I review some recent mathematical developments that generalize the partdel) or for the rational nature of the Cantorian generalization as opposed to that, based on the part–whole principle, envisaged by Bolzano (Kitcher)
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DOI 10.1017/S1755020309990128
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References found in this work BETA
Paradoxien des Unendlichen.Bernard Bolzano - 2012 - Felix Meiner Verlag.
The Nature of Mathematical Knowledge.Philip Kitcher - 1983 - Oxford University Press.
Principles of Mathematics.Bertrand Russell - 1903 - Cambridge University Press.
Wissenschaftslehre. [REVIEW]Bernard Bolzano - 2001 - Revue de Métaphysique et de Morale 2 (18):134-136.
Collected Works.Kurt Gödel - 1986 - Oxford University Press.

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Citations of this work BETA
Fair Infinite Lotteries.Sylvia Wenmackers & Leon Horsten - 2013 - Synthese 190 (1):37-61.
Set Size and the Part-Whole Principle.Matthew W. Parker - 2013 - Review of Symbolic Logic (4):1-24.

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