Review of Symbolic Logic (4):1-24 (2013)

Matthew Parker
London School of Economics
Recent work has defended “Euclidean” theories of set size, in which Cantor’s Principle (two sets have equally many elements if and only if there is a one-to-one correspondence between them) is abandoned in favor of the Part-Whole Principle (if A is a proper subset of B then A is smaller than B). It has also been suggested that Gödel’s argument for the unique correctness of Cantor’s Principle is inadequate. Here we see from simple examples, not that Euclidean theories of set size are wrong, but that they must be either very weak and narrow or largely arbitrary and misleading.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
Reprint years 2013
DOI 10.1017/s1755020313000221
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

References found in this work BETA

Mathematics as a Science of Patterns.Michael David Resnik - 1997 - Oxford, England: New York ;Oxford University Press.
What is Cantor's Continuum Problem?Kurt Gödel - 1947 - In Solomon Feferman, John Dawson & Stephen Kleene (eds.), Journal of Symbolic Logic. Oxford University Press. pp. 176--187.
Fair Infinite Lotteries.Sylvia Wenmackers & Leon Horsten - 2013 - Synthese 190 (1):37-61.

View all 21 references / Add more references

Citations of this work BETA

Infinitesimal Probabilities.Vieri Benci, Leon Horsten & Sylvia Wenmackers - 2016 - British Journal for the Philosophy of Science 69 (2):509-552.
Symmetry Arguments Against Regular Probability: A Reply to Recent Objections.Matthew Parker - 2018 - European Journal for Philosophy of Science 9 (1):8.
Symmetry Arguments Against Regular Probability: A Reply to Recent Objections.Matthew Parker - 2019 - European Journal for Philosophy of Science 9 (1):1-21.
Infinitesimal Probabilities.Sylvia Wenmackers - 2016 - In Richard Pettigrew & Jonathan Weisberg (eds.), The Open Handbook of Formal Epistemology. PhilPapers Foundation. pp. 199-265.

View all 10 citations / Add more citations

Similar books and articles

New V, ZF and Abstraction.Stewart Shapiro & Alan Weir - 1999 - Philosophia Mathematica 7 (3):293-321.
A Note on Finiteness in the Predicative Foundations of Arithmetic.Fernando Ferreira - 1999 - Journal of Philosophical Logic 28 (2):165-174.
Formulating the Precautionary Principle.Neil A. Manson - 2002 - Environmental Ethics 24 (3):263-274.
If Logic, Definitions and the Vicious Circle Principle.Jaakko Hintikka - 2012 - Journal of Philosophical Logic 41 (2):505-517.


Added to PP index

Total views
1,108 ( #5,228 of 2,497,979 )

Recent downloads (6 months)
53 ( #15,512 of 2,497,979 )

How can I increase my downloads?


My notes