## Dictionary of Arguments | |||

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Arbitrariness: A. Arbitrariness is an everyday expression for a non-justified behavior or the refusal to give a reason for a behavior. For example, arbitrariness can arise in unfounded favor. B. In the narrower sense, arbitrariness is something subject to the will. Arbitrary action can be simulated by overriding regularities and thereby undermining expectability. See also conventions._____________ 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. | |||

Author | Item | Summary | Meta data |
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I 24 Identity/Identification/Field: in many areas, there is the problem of the continuous arbitrariness of identifications. - In mathematics, however, it is stronger than with physical objects. I 181 Intensity relations between pairs or triples, etc. of points. - Advantage: that avoids attributing intensities to points and thus an arbitrary choice of a numerical scale for intensities. - - - III 32 Addition/Multiplication: not possible in Hilbert's geometry. - (Only with arbitrary zero and arbitrary 1) - Solution: intervals instead of points. - - - II 310 Non-Classical Degrees of Belief/Uncertainty/Field: E.g. that every "decision" about the power of the continuum is arbitrary is a good reason to not assume classical degrees of belief. - (Moderate non-classical logic: That some instances of the sentence cannot be asserted by the excluded third party). - - - III 31 Figure/Points/Field: no Platonist will identify real numbers with points on a physical line. - That would be too arbitrary ( "what line?"). - What should be zero - what is supposed to be 1? III 32 f Hilbert/Geometry/Axioms/Field: multiplication of intervals: not possible, because for that we would need an arbitrary "standard interval". - Solution: Comparing products of intervals. - generalization/Field: is then possible on products of spacetime intervals with scalar intervals. ((s) E.g. temperature difference, pressure difference). - Field: therefore, spacetime points must not be regarded as real numbers. III 48 FieldVsTensor: arbitrary. - Solution/Field: simultaneity. III 65 Def Equally Divided Region/Equally Split/Evenly Divided Evenly/Equidistance/Field: (all distances within the region equal: R: is a spacetime region all of whose points lie on a single line, and that for each point x of R the strict st-between (between in relation to spacetime) two points of R lies, there are points y and z of R, such that a) is exactly one point of R strictly st-between y and z, and that is x, and -b) xy P-Cong xz (Cong = congruent) - ((s) This avoids any arbitrary (length) units - E.g. "fewer" points in the corresponding interval or "the same number." - ((s) but not between temperature and space units (Which common measure?) - But definitely in mixed products - Then: "the mixed product... is smaller than the mixed product..." - Equidistance in each separate region: scalar/spatio-temporal. III 79 Arbitrariness/Arbitrary/Scales Types/Scalar/Mass Density/Field: mass density is a very special scalar field which, due to its logarithmic structure, is "less arbitrary" than the scale for the gravitational potential. - ((s) >objectivity, >logarithm) - Logarithmic structures are less arbitrary. - Mass density: needs more fundamental concepts than other scalar fields. - Scalar field: E.g. height. _____________ 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. The note [Author1]Vs[Author2] or [Author]Vs[term] is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition. |
Field I H. Field Realism, Mathematics and Modality Oxford New York 1989 Field II H. Field Truth and the Absence of Fact Oxford New York 2001 Field III H. Field Science without numbers Princeton New Jersey 1980 Field IV Hartry Field "Realism and Relativism", The Journal of Philosophy, 76 (1982), pp. 553-67 InTheories of Truth, Paul Horwich, Aldershot 1994 |

> Counter arguments against **Field**

Ed. Martin Schulz, access date 2019-02-20