FOM: continuum hypothesis, determinate truth value

Harvey Friedman friedman at
Mon Mar 9 06:17:14 EST 1998

Reply to Field 7:59PM 3/7/98

>Similarly, I think that the continuum hypothesis lacks determinate truth
>value.  But by either supervaluationism or the variant just proposed, I can
>assert that either CH or not CH.  And by the variant of supervaluationism I
>can even assert that CH is either true or false.  It's a view that allows
>the proponent of the view that CH is indeterminate to say most of what
>people who believe CH determinate say.  So we can accept the (overwhelming!)
>arguments for the indeterminacy of CH, without any revision of our
>mathematical practice.  All that gets revised is our philosophical
>commentaries on what we are doing.

To understand this better, does this point of view affect what work
logicians, or mathematicians, or philosophers, do, should do, can do, or
want to do, (or not do), with regard to the continuum hypothesis? The Godel
and Cohen work does have such consequences, and some other philosophical
views also have such consequences.

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