|Order, philosophy: order is the division of a subject area by distinctions or the highlighting of certain differences as opposed to other differences. The resulting order can be one-dimensional or multi-dimensional, i.e. linear or spatial. Examples are family trees, lexicons, lists, alphabets. It may be that only an order makes certain characteristics visible, e.g. contour lines. Ordering spaces may be more than three-dimensional, e.g. in the attribution of temperatures to color-determined objects. See also conceptual space, hierarchies, distinctness, indistinguishability, stratification, identification, individuation, specification._____________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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Order/Universals/Antisymmetry/Bigelow/Pargetter: the antisymmetry can then establish an order (hierarchy) between infinitely many different universals.
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...
((s) that is, summaries of types are also types).
Definition 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.
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.
Order/Relation/Bigelow/Pargetter: for this theory we need to extend the natural order created by relatios.
Geometry: shows proportions that cannot be displayed in whole numbers.
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.
Real numbers/Bigelow/Pargetter: Assuming that there is no golden section, would there be no real numbers?
Is the existence of real numbers contingent on the existence of quantities?
Aristotle/Bigelow/Pargetter: demands that every quantity must be instantiated to exist
VsAristotle: this seems to make mathematical facts dependent on empirical facts.
Platonism/Bigelow/Pargetter: all quantities exist for him, regardless of whether they are instantiated or not. This guarantees pure mathematics._____________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