Philosophy Dictionary of ArgumentsHome
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| Scales: Scales in physics refer to the different sizes and magnitudes of physical phenomena. They can be classified into length scales, time scales, energy scales, and mass scales._____________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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Gerhard Schurz on Scales - Dictionary of Arguments
I 76 Def Quasi-order/Schurz: must satisfy three axioms: (i) reflexivity (ii) transitivity (iii) Connexity: i.e. everything is comparable to everything. (x)(y)(x ≤My v y ≤M x). From this follows the antisymmetry of ≤M. And it follows that ≤M is an equivalence relation. Def Order/Schurz: This order is a quasi-order in which no two objects have the same rank. Ordinal Scale: Whether the conditions of transitivity and connexity are met is an empirical question. I 77 Interval scale/measurement/Schurz: Example temperature scale: (expansion of the mercury column). Pointe: here there is no zero point, which could be found by mere observation. Ex Celsius: arbitrary choice of the zero point (freezing of water) and the degree division: (divided a hundred times until boiling). Fahrenheit/zero: is -32° a 1°F is 5/9°C. Meaningless: to say, Ex a liquid is twice as warm at 20° as one is at 10° C. The whole ratio depends on the arbitrary choice of the zero point. Fahrenheit: Here you would have the ratio 68° to 50° instead. Solution: Ex If one had three liquids, with 10°, 20° and 30°, then the statement that the temperature difference between b and a is as large as that between b and c and half as large as that between a and c has a meaning, because it is valid independently of the zero point! Interval scale/interval/difference/objectivity/zero/Schurz: truncates when forming the difference of two temperature values. Only these interval statements are objective. Ratio/Schurz: ratio statements are not objective because the zero point is arbitrary. Also e.g. location and time measurements are interval scaled, because the zero point of a spatial coordinate system or time scale is arbitrary. Meaningless: to say, "the year 2000 is twice as late as the year 1000". In contrast: Ratio scale/absolute zero/Schurz: Here the absolute zero is objectively given: Ex Mass, volume, length (as opposed to location) duration, (as opposed to time) are ratio scaled quantities. Meaningful: Bsp An object of 100 kg is twice as heavy as one of 50 kg. These ratio statements have objective meaning. Extensive size/Schurz: are such quantities on the ratio scale because they grow by joining (concatenating) objects into larger wholes. I 78 Ratio scale/Schurz: The empirical metrization of extensive quantities leads to ratio scales. Here, however, the numerical absolute value of the quantity is still arbitrary, depending on the arbitrary choice of unit. Meaningless: Ex to say the magnitude value of Peter's weight is 100. This is true only if the unit of mass is chosen as one kilogram. If one chooses 1 gram, the absolute value would be 100 000. Measure/measure/unit//Carnap: subtle problem: one must also justify that the unit chosen is constant in time. (Carnap 1976(1), 88-100). Absolute scale: simple counting scale where the unit is "one piece". Scale/Mathematics/Scale transformation/Schurz: In mathematics, the difference between the various types of scales is specified by the permissible scale transformations. These determine the degree of arbitrariness,. Def scale level/order: absolute, ratio, interval, ordinal, nominal scale. Here the level becomes lower and lower, because the scales become more and more comprehensive. Def Metricability/Schurz: Ex An extensive comparative size feature ≤M Ex "longer than" over an object area D in the form of a ratio scale is metricable, iff ≤M is a monotonous quasi-order over D and the Def Archimedean condition is fulfilled, i.e. every object b, no matter how large, must be outweighed by sufficiently many copies of an object a, no matter how small. Def derived metrization: traced back to the metrization of other terms: E.g. density to the quotient of mass by volume. theory derived metrization: theory dependent. I 79 Ex temperature scale according to Kelvin, change of scale level due to theoretical considerations. >Measurement, >Order, >Method, >Monotony. 1. Carnap, R. (1976). Einführung in die Philosophie der Naturwissenschaft, 3. Aufl. München: Nymphenburger. (Engl. Orig. 1966)._____________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. |
Schu I G. Schurz Einführung in die Wissenschaftstheorie Darmstadt 2006 |
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Ed. Martin Schulz, access date 2024-04-19