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Truth/Realism/Field: does not want to claim truth as a metaphorical concept about the theory but instead the theory itself. - The existence of mathematical entities follows from the theory itself, not from the truth of the theory (in the sense of correspondence theory).
Realism/Variant/Field: here: Thesis: "There are sentences in our language that are true, but for which we shall never have a reason to believe them." - Then you need a T-concept to generalize. (> Infinite conjunction/disjunction). - Anti-realism/variant: would be the opposite position here: to identify truth with justifiability in the long run. - (> ideal justification).
Horwich I 405 f
Metaphysical Realism/Field: three game styles. Metaphysical realism 1: there are mind-independent objects - metaphysical realism 2: There is only one correct description (FieldVs) - metaphysical realism 3: correspondence theory - a refutation of metaphysical realism 3 is not yet one of metaphysical realism 1.
PutnamVsMetaphysical Realism: Thesis: metaphysical realism leads to a dichotomy facts/values. -> Relativism - this refutes itself. - Dichotomy between evaluative (pseudo-facts, nonfactual) and non-evaluative facts. - FieldVsPutnam/Field per relativism: we can refer the relativism to purely evaluative statements (not facts). - Garfinkel: the relativism itself is no valuation. - Internal Realism/Putnam: our standards of rationality are objectively correct.
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
P. Horwich (Ed.)
Theories of Truth Aldershot 1994