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One reason is that TR appeals to tertium non datur (part of the standard practice of logic and set theory), and thus regards, say, the Continuum Hypothesis as either true or false.
I would very much like to hear him prove or even disprove Cantor's continuum hypothesis.
of California at Berkeley) is the identification of a canonical model in which the Continuum Hypothesis is false.
There are questions that remain undecided by the accepted axioms of set theory (what Maddy calls the Independent Questions) that look as if they should have determinate answers; the most well-known example is Cantor's Continuum Hypothesis.
Many readers will be sympathetic to this continuum hypothesis, and recognize that it contrasts sharply with the old positivist picture of scientific reasoning, which tried unsuccessfully to find some special criteria demarcating scientific reasoning from ordinary reasoning that we apply in everyday life situations.
Still in typescript, this text contains the lecture notes for a course Cohen (1934-2007) taught at Harvard in spring 1965, shortly after his work on the continuum hypothesis.
Proving the truth or falsehood of Cantor's continuum hypothesis boils down to answering this: Where does the set of real numbers sit in the hierarchy of infinite sets?