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Theory/Nominalism/strong/weak/stronger/weaker/(s): strong theory: has more consequences - if mathematical entities (mE) are to be dispensed with, a Platonist theory can have no (physical) consequences which a nominalistic (only physical entities entities) does not have.
Equivalence/Platonism/Nominalism/Field: Question: in what sense are Platonist (e.g. "direction 1 = direction 2") and nominalistic statement (c1 is parallel to c2) equivalent? Problem: if there are no directions, the second cannot be a consequence of the first.
Nominalism/Field/N.B.: will not claim N* (without mathematical entities), but the stronger N.
Nominalism/Field: is compatible with the assumption of space-time points and empty regions -
Nominalism pro substantivalism.
Regions/Points/Field: Solution for the nominalists: individual calculus/Goodman: Regions as sums of points. - But then there are no empty regions. - The region then does not need to be connected or measurable.
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