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Contradiction / Stalnaker: it is essential that logical falsehoods are absolutely impossible. - This is the condition that they can not be believed. - Problem / Field: Then Cantor could not have established his (later proven to be contradictory) set theory.
Cantor had not "split" belief states that had to be linked. - Rather, they all together explained his actions.
Realism, Mathematics and Modality Oxford New York 1989
Truth and the Absence of Fact Oxford New York 2001
Science without numbers Princeton New Jersey 1980