|Mathematical Entities: mathematical entities are research objects of mathematics, which cannot be regarded as material objects. Nevertheless, there are discussions about the status of their existence. Whereas Platonism assumes its (permanent) existence as intellectual objects or universals, this permanence is denied, e.g. by intuitionism, which assumes that mathematical entities exist only at the moment of their construction._____________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. |
|Big I J. Bigelow, R. Pargetter Science and Necessity Cambridge 1990
Big I 380
Numbers/Armstrong/Bigelow/Pargetter: Armstrong Thesis: Numbers are causally inactive. (Field ditto).
Mathematics/Realism/Bigelow/Pargetter: some mathematical entities are even observable!
Numbers: even they are involved in the causal processes. If objects did not instantiate the quantities they instantiate, other changes would have occurred. Thus at least proportions are causally involved. (s) FieldVsNumbers as causal agents, but not FieldVsProportions).
Counterfactual Dependence/Bigelow/Pargetter: thus we can again set up sequences of counterfactual conditionals, 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 to then convert the results into completely abstract mathematics.
Field/Bigelow/Pargetter: wants to avoid this detour.
BigelowVsField: his project is superfluous if we realize that mathematics are 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.
AR II = Disp
D. M. Armstrong
Dispositions, Tim Crane, London New York 1996
What is a Law of Nature? Cambridge 1983