## Philosophy Lexicon of Arguments | |||

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Books on Amazon |
I 78 Proportion/Relation/Bigelow/Pargetter: in any case, we can assume proportions between relations. Problem: but not proportions between properties. Flux/Bigelow/Pargetter: but assumes that speed is a property rather than a relation. Vector: to explain its nature, we now need something that fills the gap between property and relation. 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. 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. |
Big I J. Bigelow, R. Pargetter Science and Necessity Cambridge 1990 |

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Ed. Martin Schulz, access date 2017-09-22