Tag Archives: Philosophy of HP

Re: Paper and slides on indefiniteness of CH

Dear Sy,

OK! Now we’re getting somewhere. Your position begins like this:

  1. The relevant concept is the familiar iterative conception, which includes a rough idea of maximality in ‘height’ and ‘width’.
  2. To give an intrinsic justification or intrinsic evidence for a set-theoretic principle is to show that it is implicit in the concept in (1).
  3. The HP is a method for extracting more of the implicit content of the concept in (1) than has heretofore been possible.

The next step is to look into the mechanisms by which (3) is accomplished. Could you give a nice clear example and walk us through it step by step? (I realize you’ve written a lot in this vicinity already, but it seems to me that if we’re going to understand how the machinery is really supposed to work, we need to slow down and carefully examine each step in a nice illustrative case.)

All best,