Philosophy Lexicon of Arguments

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II 227
Vagueness/revision of the logic/Field: some authors: to allow double negation, to prohibit explicit contradictions, thus also not to allow negations of the law of the excluded middle (l.e.m.). - then old version: if Jones is a limiting case, so we cannot claim either "bald" or "not-bald", so we can now - new: neither claim: E.g. "Jones is bald or not bald" nor "It is not the case that Jones is either bald or not bald." - On the other hand: Field: with definite-operator (definite): "It is not the case that Jones is either definitely bald or definitely not bald". - Without law of the excluded middle: "neither bald nor not bald".
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II 228
Limiting case/vagueness/definite-Operator/Field: we need the definite-operator to avoid a limiting case of the a limiting case.
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II 228
Definition weakly true/vagueness/truth/Truth-Predicate/Field: to be able to say general things about borderline cases. - Not only that somebody represents a certain limiting case. - (> generalization.) - Definition paradigmatic borderline case: definitely a borderline case. - Not weakly true/deflationism: e.g. "Either bald or not-bald is true". Then the Truth-predicate itself inherits the vagueness. - It's not definitely true whether or not. - Definition strongly true/Field: assuming, Jones is a limiting case: then neither "bald" nor its negation (strongly) - plus classical logic: then the disjunction "bald or not bald" should be true even in strong interpretation - Law of the excluded middle: if we give it up: a) weakly true: then the disjunction is not true - b) strongly true: then the disjunction is without truth value. - Strongly true: is less vague, does not inherit the vagueness. - Correctness: which interpretation is the correct one is only dependent on utility. - Pro weak truth: allows infinite conjunction and disjunction. - This corresponds more to the theory of validity. - Only the weak Truth-concept is supplied by the disquotation scheme. - Deflationism: additionally requires the definite-operator to declare the predicate strongly true.
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II 230
Inflationism/Vagueness/FieldVsInflationism: Problem: the I. needs a thing that is "neither bald nor not bald". - Inflationism: explains e.g. "weakly true" compositional. Supervaluation/Sorites/Inflationism: "candidate of an extension". - Definition strongly true: is a sentence with a vague predicate then iff it is true relative to each of the candidates of an extension - then limiting case without definite-operator: "Jones is bald in some extensions but not in all".
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II 233
Vagueness/Ontology/Field: Thesis: is a deficiency of language, not of the world.
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II 234
Vagueness/radical non-classical logic/Field: here we do not need a definite-operator or distinction between strong/weak truth: e.g. Jones is a limiting case iff it is not the case that he is either bald or not bald. - Deflationism/Field: seems to save a lot of trouble, because there is no definite-operator, one would have to understand. - Vs: that deceives: the trouble is only postponed: here the logical rules for "not", etc. are much more complicated. - + II 228 weakly true.

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 2017-05-24