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.).
>
Negation, >
Double negation, >
Contradictions, >
Stronger/Weaker, >
Excluded middle.
Then old version: if Jones is a limiting case for "Jones is bald", 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".
II 228
Limiting case/vagueness/definite-Operator/Field: we need the definite-operator to avoid a limiting case of the a limiting case.
>
dft-operator, >
Terminology/Field.
II 228
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 is 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.
>
Correctness.
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: deflationism additionally requires the definite-operator to declare the predicate strongly true.
>
Deflationism.
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.
>
Inflationism.
Supervaluation/Sorites/Inflationism: "candidate of an extension".
>
Supervaluation.
Def strongly true: is a sentence with a vague predicate then iff it is true relative to each of the candidates of an extension. - Then the limiting case without definite-operator: "Jones is bald in some extensions but not in all".
II 233
Vagueness/Ontology/Field: Thesis: vgueness is a deficiency of language, not of the world.
>
Language dependence.
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:...++...
