@misc{Lexicon of Arguments, title = {Quotation from: Lexicon of Arguments – Concepts - Ed. Martin Schulz, 29 Mar 2024}, author = {Bigelow,John}, subject = {Order}, note = {I 42 Order/Universals/Antisymmetry/Bigelow/Pargetter: the antisymmetry can then establish an order (hierarchy) between infinitely many different universals. Order/Hierarchy: 1. individuals: Definition individual/Bigelow/Pargetter: what is not instantiated by anything. 2. rule: the rest is obtained by the following rule: If t1, t2,.... tn are types, then also (t1, t2... tn) is a type... >Individuals, >Type/Token, >Universals. ((s) that is, summaries of types are also types). Def type/Bigelow/Pargetter: is then a set of universals, which can consist of one to infinitely many. Domain/Bigelow/Pargetter: the union of all types, each type is a subset of the domain. There may also be empty subsets. >Domains, >Sets. I 362 Real Numbers/Bigelow/Pargetter: this theory of proportions as a theory of real numbers was developed by Dedekind and others at the end of the 19th century. >Real numbers. Order/Relation/Bigelow/Pargetter: for this theory we need to extend the natural order created by relatios. >Proportions. Geometry: shows proportions that cannot be displayed in whole numbers. >Geometry. Proportion/terminology/Bigelow/Pargetter: we call proportions ratios that cannot be expressed in whole numbers. Realism/Bigelow/Pargetter: pleads for the assumption that there are objects with the proportions of the golden section rather than claiming there is no golden section. >Realism. Real numbers/Bigelow/Pargetter: Assuming that there is no golden section, would there be no real numbers? I 363 Is the existence of real numbers contingent on the existence of quantities? >Quantity, >Quantities/Physics. Aristotle/Bigelow/Pargetter: demands that every quantity must be instantiated to exist. >Instantiation, >Ontology, >Existence. VsAristotle: this seems to make mathematical facts dependent on empirical facts. >Mathematical entities, >Empiricism. Platonism/Bigelow/Pargetter: all quantities exist for him, regardless of whether they are instantiated or not. This guarantees pure mathematics. >Platonism, >Mathematics.}, note = { Big I J. Bigelow, R. Pargetter Science and Necessity Cambridge 1990 }, file = {http://philosophy-science-humanities-controversies.com/listview-details.php?id=746831} url = {http://philosophy-science-humanities-controversies.com/listview-details.php?id=746831} }