## Philosophy Lexicon of Arguments | |||

Author | Item | Excerpt | Meta data |
---|---|---|---|

Field, Hartry Books on Amazon |
Objectivity | I 272f Definition 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. --- I 274 Objectivity does not have to be explained in terms of the truth of the axioms - this is not possible in the associated modal propositions. --- I 277 Objectivity/mathematics/quantum 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". --- II 316 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? --- II 316 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. --- II 319 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. --- II 320 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. --- II 340 Objectivity/quantity theory/element relation/Field: to determine the specific extension of "e" and "quantity" we also need the physical applications - also for "finity". --- III 79 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. |
Fie I H. Field Realism, Mathematics and Modality Oxford New York 1989 Fie II H. Field Truth and the Absence of Fact Oxford New York 2001 Fie III H. Field Science without numbers Princeton New Jersey 1980 |

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Ed. Martin Schulz, access date 2017-05-01