|Objectivity: is a property of determinations about facts. It is assumed that the properties attributed to the facts are determined by the facts and are not, or as little as, influenced by the attributing person. In order to determine whether this requirement is fulfilled, consideration must be given to the methods of access to information. This goes beyond the facts considered._____________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. |
Def Objectivity/Mathematics/Gyro/Putnam/Field: should consist in that we believe only the true axioms. (s) objectivity, i.e. subjective, based on propositional attitudes, simultaneously on truth). - Problem: the axioms also refer to the ontology.
Objectivity does not have to be explained in terms of the truth of the axioms - this is not possible in the associated modal propositions.
Objectivity/mathematics/set theory/Field: even if we accept "ε" as fixed, the platonic (!) view does not have to assume that the truths are objectively determinated. - Because there are other totalities over which the quantors can go in a set theory.
Putnam: further: there is no reason to keep "ε" fixed. FieldVsPutnam: confusion of the view that the reference is fixed (e.g. causally) with the view that it is defined by a description theory that contains the word "cause".
Objectivity/truth/Mathematics/Field: Thesis: even if there are no mathematical objects, why should it not be the case that there is exactly one value of n for which An - modally interpreted - is objectively true?
Mathematical objectivity/Field: for them we do not need to accept the existence of mathematical objects if we presuppose the objectivity of logic. - But objectively correct are only sentences of mathematics which can be proved from the axioms.
Mathematical concepts are not causally connected with their predicates. - ((s) But conceptually) - E.g. For each choice of a power of the continuum, we can find properties and relations for our set theoretical concepts (here: vocabulary) that make this choice true and another choice wrong.
The defense of axioms is enough to make mathematics (without objects) objective, but only with the broad notion of consistency: that a system is consistent if not every sentence is a consequence of it.
Objectivity/quantity theory/element relation/Field: to determine the specific extension of "e" and "quantity" we also need the physical applications - also for "finity".
Arbitrariness/arbitrary/scalar types/scalar field/mass density/Field: mass density is a very special scalar field which is, because of its logarithmic structure, less arbitrary than the scale for the gravitational potential - ((s) > objectivity, > logarithm.) Logarithmic structures are less arbitrary - Mass density: needs more basic 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.
Realism, Mathematics and Modality Oxford New York 1989
Truth and the Absence of Fact Oxford New York 2001
Science without numbers Princeton New Jersey 1980
"Realism and Relativism", The Journal of Philosophy, 76 (1982), pp. 553-67
Theories of Truth, Paul Horwich, Aldershot 1994