|Abstraction: Subsumption of objects by non-consideration of certain properties. See also equivalence relation, concretion, concreta, indiscernibility._____________Annotation: The above characterizations of concepts are neither definitions nor exhausting presentations of problems related to them. Instead, they are intended to give a short introduction to the contributions below. – Lexicon of Arguments.|
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Abstractions/Figures/Armstrong/Bigelow/Pargetter: Numbers are causally inactive.
Mathematics/Realism/Bigelow/Pargetter: some mathematical entities are even observable.
Causation/Mathematics/BigelowVsArmstrong/Bigelow/Pargetter: in fact, people are not causes, but they are involved in causal processes.
Numbers: they are also involved in causal processes. If objects did not instantiate the quantities they instanced, other changes would have occurred. Thus at least proportions are causally involved. ((s) FieldVsNumbers as causal agents, but not Vs proportions).
Contrafactual dependence/Bigelow/Pargetter: one can again set up consequences of contrafactual conditions, e.g. For the lever laws of Archimedes. This also provides why-explanations.
Numbers/causality/Bigelow/Pargetter: this shows that numbers play a fundamental role in causal explanations.
BigelowVsField: (a propos Field, Science without numbers): he falsely assumes that physics first starts with pure empiricism, in order to convert the results into completely abstract mathematics.
Field/Bigelow/Pargetter: wants to avoid this detour.
BigelowVsField: his project is superfluous when we realize that mathematics is only a different description of the physical proportions and relations and no detour._____________Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution.
J. Bigelow, R. Pargetter
Science and Necessity Cambridge 1990