|Paradoxes: are contradictions within formally correct statements or sets of statements that lead to an existence assumption, which initially seemed plausible, to be withdrawn. Paradoxes are not errors, but challenges that may lead to a re-formulation of the prerequisites and assumptions, or to a change in the language, the subject domain, and the logical system. See also Russellian paradox, contradictions, range, consistency.|
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|Grover II 201
Paradoxies/Antinomies/Enhanced Liar/Burge/Grover: (Burge 1979, p. 178):
In all variants we started with
a) an incident with a liar-like sentence.
b) then we argued that the sentence is pathological and concluded that it is not true in the wording of the pathological proposition. ((s) Here we are talking about "not true" and not "wrong").
Then we realized that this seems to come down to the following:
c) that the sentence is true at the end!
Burge: Thesis: there seems to be no change involved in the grammar or the linguistic meaning of the expressions.
Grover: that suggests that the changes in evaluation occur in pragmatic terms.
Burge: since the truth value changes without the meaning changing, an indexical element must be at work.
Paradoxies/Parsons/Grover: similar: Thesis: the use of "true" and other semantic expressions related to paradoxes brings about a change of the range (the discourse range).
KripkeVsBurge/Grover: (Kripke 1975): the changeover to b) takes place at a later point in the development of the natural language.
GroverVsBurge: there is actually a transition to be made, but if the prosentential approach (oro-sentence theory) is correct, the inference of Burge is not valid:
Burge/Grover: the transition to b) has the form:
"S" is pathological, hence "S" is not true.
This should be justified by the following:
If "S" is pathological, the sentence is not an assertion.
If "S" is not an assertion, then "S" is neither true nor false.
(14) If "S" is pathological, "S" is not true, and "S" is not false.
Problem/Grover: if "true" were property-attributive (truth was conceived as a property), namely the same property for "true" and "not true" ((s) the property is then attributed or denied) and a property for "false" and "not false", then we must be able to make the transition to "S" is not true".
((s) with "true" or "false" it would only be about attributing or denying a single property!) Grover: does not want any property, of course.
Grover: regardless of whether "true" is property-attributive, if (14) is a necessary condition for an expression to be pathological, then it looks as if Burge was right. For then we could infer that "S" is not true. But:
GroverVsBurge: Perhaps "true" and "false" are not property-attributive, and perhaps (14) is not a necessary condition for being pathological:
Then we can argue instead
If "S" is pathological, then "S" is not true,
We just have something like
Provided "S" is not pathological, either S or not S.
Expressibility/Important Point/Grover: then we do not need the expressibility ((s) completeness) that we seemed to need.
Paradoxies/Liar/GroverVsBurge: Thesis: we can conclude that liar-sentences are pathological, but that does not force us to assume that they are not true.
GroverVsBurge: I did say that his conclusion was not valid, but I think that actually there is no conclusion here, neither valid nor invalid: because if "true" is prosential, then ""S"is not true" does not express any proposition! ((s) Has no antecedent from "S" and that stands for any sentence and therefore for no content "all that he said").
Origins of Objectivity Oxford 2010
D. L. Grover
A Prosentential Theory of Thruth Princeton New Jersey 1992