Is the Continuum Hypothesis a definite mathematical problem?

Abstract

The purpose of this article is to explain why I believe that the Continuum Hypothesis (CH) is not a definite mathematical problem. My reason for that is that the concept of arbitrary set essential to its formulation is vague or underdetermined and there is no way to sharpen it without violating what it is supposed to be about. In addition, there is considerable circumstantial evidence to support the view that CH is not definite

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References found in this work

What Numbers Could Not Be.Paul Benacerraf - 1965 - Philosophical Review 74 (1):47-73.
Mathematics as a Science of Patterns.Michael David Resnik - 1997 - Oxford, England: New York ;Oxford University Press.
Naturalism in Mathematics.Penelope Maddy - 1997 - Oxford, England: Oxford University Press.

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Citations of this work

Maddy On The Multiverse.Claudio Ternullo - 2019 - In Deniz Sarikaya, Deborah Kant & Stefania Centrone (eds.), Reflections on the Foundations of Mathematics. Berlin: Springer Verlag. pp. 43-78.
An Indeterminate Universe of Sets.Chris Scambler - 2020 - Synthese 197 (2):545-573.

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