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Deflationism/VsDeflationism: is it possible that most of our present scientific concepts have less power in a deflationist perspective? - Field: perhaps this is so: deflationism shows that there is no best translation of Newtonian terms into modern language. - New Vocabulary/Field: can often be captured with old vocabulary plus higher-order quantification. This is e.g. a Ramsey sentence.
Applying/Explaining/Observing/Field: our observation practice explains how our physical vocabulary applies to all that and only that to which it applies to. - This explains why some non-standard models are unintended.
Undefined/Language/McGee/Field: having non-standard models. - Solution: extension by predicate: e.g. "standard natural number". - FieldVs: that is cheating. - New axioms with new vocabulary are not better than new axioms in the old vocabulary. - it would be cheating to assume that the new predicates have certain extensions. - (Still FieldVsIndeterminism).
Pure Mathematics/Application/Field: E.g. Number theory: is not applicable to the world. - For example, set theory: must allow primordial elements for the application. - Solution: "impure mathematics": Functions that map physical objects to numbers - Then the comprehension axioms must also contain non-mathematical vocabulary. E.g. instances of the separation axiom.
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