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Definition substantivalism/Field: asserts that literal speech about space can be taken at face value, even without physical objects. Then it is also useful to say that the space is empty.
FieldVsSubstantivalism: is forced to answer a relationist in his own terms.
Substantivalism/Field: (the thesis that there are empty spacetime regions). - Space time regions are known as causally active: e.g. field theories such as classical electromagnetism or the general relativity theory or quantum field theory. - Resnik: not "What properties of the spacetime points ..?" - But "What is the structure of space-time?" FieldVsResnik: that's wrong. The theory of the electromagnetic field is also that of the properties of the parts of the space time that are not occupied by objects.
Definition Substantivalism/Field: Thesis: empty space exists. - Definition Relationism: Thesis: there is no empty space. - Part-relation: exists in both.
Substantivalism/Field: favors the field theory.
Substantivalism/Newton pro: E.g. bucket experiment: shows that we need the concept of absolute acceleration and the one of the equality of place over time - (space that exists through time).
Field pro substantivalism: there is empty space time. - Spacetimepoints are entities in their own right. - Field: that is compatible with the nominalism. - VsRelationism: this cannot accept Hilbert's axioms. VsRelationism: cannot accept physical fields. - Platonism: assumes at fields spacetime points with properties. - VsRelationism: this one cannot do it.
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