Re: Paper and slides on indefiniteness of CH

Dear Sy,

Thanks for your helpful comments on my draft, “The Continuum Hypothesis is neither a definite mathematical problem nor a definite logical problem,” and especially for bringing your Hyperuniverse Program (HP) to my attention.  I had seen your 2013 article with Arrigoni on HP back then but had not taken in its point.  I have now read it as well as your Chiemsee slides, and will certainly take it into account in the final version of my paper.

I’m glad that we are in considerable agreement about my fundamental argument that one must distinguish mathematical problems in the ordinary sense from logical problems, and that as of now what I claim in the title is true, even taking HP into consideration.  Is my title misleading since it does not say “as of the time of writing”? The reader will see right away in the abstract and the opening section that what I claim does not exclude the possibility that in the future CH will return as a definite mathematical problem [quite unlikely] or that it will somehow become a definite logical problem.

This is not the place to respond to your many interesting comments on the draft, nor on the substance of the HP and your subsequent exchange with Woodin.  But I would like to make some suggestions regarding your terminology for HP (friendly to my mind).  First all, it seems to me that “preferred models” is too weak to express what you are after.  How about, “premier models” or some such?  (Tapping into the Thesaurus could lead to the best choice.) Secondly, I’m not happy about your use of “intrinsic evidence for set-theoretic truth” both because “intrinsic evidence” is commonly used to refer to the constellation of Gödel’s ideas in that respect (not the line you are taking) as opposed to “extrinsic evidence”, and because “set-theoretic truth” suggests a platonistic view (which you explicitly reject).  I don’t have anything to take its place, but it reminds me of the kinds of methodological maxims that Maddy has promoted, so perhaps a better choice of terminology can be found in her writings in place of that.

Best,
Sol

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