Philosophy Dictionary of ArgumentsHome
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| Proportions: Proportions are comparisons of two ratios, written as equations with two equal fractions. They are used to solve problems involving rates, ratios, and percentages. See also Measurements, Comparisons, Comparability, Numbers._____________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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J. Bigelow on Proportions - Dictionary of Arguments
I 78 Proportion/Relation/Bigelow/Pargetter: in any case, we can assume proportions between relations. >Relations, >Ontology, >Ontology/Bigelow. Problem: but not proportions between properties. >Properties. Flux/Bigelow/Pargetter: but assumes that speed is a property rather than a relation. >Flux, >Flux/Bigelow. Vector: to explain its nature, we now need something that fills the gap between property and relation. >Vectors. Solution/Bigelow/Pargetter: for all things with the same property, there is a relation; that of accordance! Formally: if Fx and Fy, there is a relation RF, so that x RF y. Properties/Relation/Bigelow/Pargetter: even if two individuals have different properties, there is a relation between them: formal: there is a relation RFG between Fx and Gy... I 79 ...so that x RFG y. At any rate, we assume this in case F and G are vectors of the same kind. For example, rotating homogeneous disk: 1. points on same radius (same direction): each has a different speed. Then there are some that are 1m/sec faster than others. etc. Relation: between properties: because point x has the property (here: speed or location?) it stands in a certain relation to the point y: it is so and so much faster. Properties/Bigelow/Pargetter: are therefore also in proportions. I 80 2. corresponding to points on the same circumference (same speed, different direction). Relations/Property/Bigelow/Pargetter: then we have relations between velocities with respect to size (if the points lie on the same radius) e.g. speed of x has r times the size of the velocity of y: x Pr y. For example, be a point at the same distance from the center of the borderline, then it has the same speed (size). z P0 y The two relations are summarized as follows x Pr y. z P0 y, then we have a derived relation between x and z. Definition derived relation P*/Bigelow/Pargetter: we define it by saying: x P* z iff for a y, x pr y and y p0 z,... I 81 Proportion/properties/Bigelow/Pargetter: on the rotating disk, two points will be placed in this "two-step-proportion" of the form P*. Namely, by virtue of their intrinsic properties. Vectors/Bigelow/Pargetter: the property of instantaneous speed are considered vectors because they are in a family of two-step proportions! n-step Proportion/Bigelow/Pargetter: this can be generalized to proportions that include n steps. This gives us more general vectors. Vector/Bigelow/Pargetter: the vector of a speed of a point on a rotating disk can be represented as an ordered pair of real numbers. General: all ordered n-tuples of real numbers can be understood as vectors. We need some for the flux theory, but not all of them. Vectors/Bigelow/Pargetter: are useful for representing physical properties, because they can be embedded in a network of proportions. I 358 Ratios/Bigelow/Pargetter: are special cases of real numbers. >Real numbers. Conversely however, not all real numbers correspond to ratios. Proportion/Bigelow/Pargetter: is a more general term than ratio and forms the basis for our system of real numbers. Some proportions in the geometry, for example, do not correspond to ratios. E.g. pentagon:...._____________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. Translations: Dictionary of Arguments The note [Concept/Author], [Author1]Vs[Author2] or [Author]Vs[term] resp. "problem:"/"solution:", "old:"/"new:" and "thesis:" is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition. |
Big I J. Bigelow, R. Pargetter Science and Necessity Cambridge 1990 |
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> Counter arguments against Bigelow
> Counter arguments in relation to Proportions
Ed. Martin Schulz, access date 2024-04-18