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Logical knowledge/Field/(s): knowledge about the fact that something is logically true (e.g. that the axioms are consistent), but not the axioms themselves. - FieldVsKripke: we then introduce a non-Kripkean concept of logical truth, according to which some non-trivial assertions about possibility are part of the logic. - Then the consistency of axioms becomes a logical truth. - Induction/Field: extra-logical means: empirical - because we find no contradiction.
Logical Knowledge/Frege: Problem: whereby do I know that it is logically possible that the axioms of quantum theory are true: by asserting that I know that there are actually entities asserted by the axioms. - FieldVsFrege: if these entities existed, how could one know then that they are in this relationship and not in another?
Pure Logical Knowledge/Field: must be knowledge that makes no existence assumptions.
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