I 272f
Def Objectivity/Mathematics/Gyro/Putnam/Field: objectivity should consist in that we believe only the true axioms.
Problem: the axioms also refer to the ontology.
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Axioms, >
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.
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Modalities, >
Propositions.
I 277
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 quantifiers can go in a set theory.
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Platonism, >
Quantifiers, >
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 it 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.
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Provability, >
Correctness.
II 319
Mathematical concepts are not causally connected with their predicates. 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.
Cf. >
Truthmakers.
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".
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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.
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Field theory.