Kreisel, the continuum hypothesis and second order set theory

Journal of Philosophical Logic 5 (2):281 - 298 (1976)

The major point of contention among the philosophers and mathematicians who have written about the independence results for the continuum hypothesis (CH) and related questions in set theory has been the question of whether these results give reason to doubt that the independent statements have definite truth values. This paper concerns the views of G. Kreisel, who gives arguments based on second order logic that the CH does have a truth value. The view defended here is that although Kreisel's conclusion is correct, his arguments are unsatisfactory. Later sections of the paper advance a different argument that the independence results do not show lack of truth values
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DOI 10.1007/BF00248732
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When Do Some Things Form a Set?Simon Hewitt - 2015 - Philosophia Mathematica 23 (3):311-337.
On the Referential Indeterminacy of Logical and Mathematical Concepts.Otávio Bueno - 2003 - Journal of Philosophical Logic 34 (1):65 - 79.

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