# Conceptual Structuralism and Continuum hypothesis

In Ferefman's paper 'Is the Continuum Hypothesis a definite mathematical problem?', he argues that within the philosophy of conceptual structuralism, the continuum hypothesis is not a definite mathematical problem.

However, Koellner wrote a response to this paper in his paper 'Feferman on the Indefiniteness of CH'. In this, he proposes that it is possible to reach the conclusion that the continuum hypothesis is a definite mathematical problem via conceptual structuralism though he presents no argument for it. Instead, he relates this to the views of Martin and Isaacson.

Does anyone know where I can find an argument that the continuum hypothesis is a definite mathematical problem by the view of a conceptual structuralist?

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Feferman's paper (logic.harvard.edu/EFI_Feferman_IsCHdefinite.pdf) and Koellner's response (logic.harvard.edu/EFI_Feferman_comments.pdf) were both part of a workshop at Harvard, in , called "Exploring the Frontiers of Infinity," and other materials can be found at logic.harvard.edu/efi.php#material. As for conceptual structuralism, the paper "Godel's conceptual realism" (jstor.org/stable/1556750) might be relevant, but I'm not sure - I don't have a totally precise sense of what "conceptual structuralism" means. –  Noah S Mar 26 '13 at 15:05

Koellner is probably referring to Isaacson's paper, The reality of mathematics and the case of set theory. Isaacson appeals to Kreisel's argument that the second-order categoricity of set theory makes the continuum hypothesis a definite problem.

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