Philosophy Lexicon of Arguments

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Field, Hartry
 
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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.
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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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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".
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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?
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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.
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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.
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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.
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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.

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


> Counter arguments against Field
> Counter arguments in relation to Objectivity



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Ed. Martin Schulz, access date 2017-03-23