|Vagueness, philosophy: there are descriptions of objects or situations that are necessarily not fully determined. For example, the indication whether a given hue is still red or already orange is not always decidable. It is a property of the language to provide vague predicates. Whether vagueness is a property of the world is controversial. See also sorites, indeterminacy, under-determinateness, intensification, penumbra._____________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. |
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".
Limiting case/vagueness/definite-Operator/Field: we need the definite-operator to avoid a limiting case of the a limiting case.
Def 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.) -
Def 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.
Def 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.
Per 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.
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".
Vagueness/Ontology/Field: Thesis: is a deficiency of language, not of the world.
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._____________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.
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