|Explanation: making a statement in relation to an event, a state, a change or an action that was described before by a deviating statement. The statement will often try to involve circumstances, history, logical premises, causes and causality. See also description, statements, theories, understanding, literal truth, best explanation, causality, cause, completeness.|
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Explanation/Field: a) Definition intrinsic explanation/Field: does not contain causally irrelevant entities (namely: mathematical entities) - b) Definition extrinsic explanation/Field: also contains causally irrelevant entities. For example, the attribution of finite sentences for the behavior of animals. - Every good extrinsic explanation is based on a good intrinsic explanation. - Field/(s): therefore only causally relevant should occur in the explanation. - in short: intrinsic explanation: causal.
Problem: then the properties of electrons cannot contain anything that requires mathematical entities.
Explanation/Application/Physics/Mathematics/Field: new: different than in Sience without numbers: Physics itself has an explanatory function. - You need theories to explain physical phenomena. - This makes a nominalistic theory of proof superfluous. - Platonism: Here the proof theory is an instrument of discovery, not just explanation. - Nominal Model Theory: Problem: one cannot explain the applicability solely from the concept of conservativity. Therefore we need modal logic as an analog of Platonist model theory. Then model theory is like physics. Otherwise, it is like the theory of proof: then we would not need a nominalistic analog of the model theory because it does not serve as an explanation, but only in order to find out something about possibility. - Then, in turn, we do not need to accept the truth of the statements.
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