Tolerance and Mixed Consequence in the S’valuationist Setting

Pragmatic Interpretations of Vague Expressions: Strongest Meaning and Nonmonotonic Consequence

“…Notice first that C(T a ∧ ¬T a) = 1 2 = 0 = F(T a ∧ ¬T a). 9 Our pragmatic interpretation rule does not account for the 'scalar implicature' that from '(p ∧ ¬p) ∨ q' we conclude that only one of the disjuncts is as true as possible. It is easy to change the pragmatic interperation rule to account for this-and for embedded implicatures-as well (by changing '…”

“…[12]) that it cannot account for so-called penumbral connections: it fails to predict that T a ∧ ¬T a and T a ∨ ¬T a should always be unacceptable (because contradictory) and acceptable (because tautological), respectively. But, as noted above, and as discussed in TCS and [9], these sentences are in fact not always unacceptable or always acceptable. Our pragmatic analysis in TCS predicts the experimental observations much better.…”

Vagueness, Truth and Permissive Consequence

“…1 Bennett in particular put forward a notion of 'arguable entailment' for supervaluations, which he defined as follows: "if all of the premises are 'unequivocally' true, then the conclusion is 'in some sense' true". Although Bennett does not present it in that way, the definition can be seen to combine the notions of super-truth and sub-truth that are familiar from the literature on vagueness (see [Hyde, 1997], [Cobreros et al, 2012a]). Even closer to our proposal, in an underappreciated book Nait-Abdallah investigated the interplay between two notions of truth in a trivalent setting, which he calls classical truth (for the value 1) and potential truth (for values > 0), which correspond exactly to the notions of strict truth and tolerant truth we are about to review and that we introduced independently.…”

“…More specifically, we intend to show the fruitfulness of this notion for the prospect of getting a unified treatment of the paradoxes of vagueness and of the paradoxes of self-referential truth. The notion of permissive consequence we are concerned with was originally introduced with an aim to solving the sorites paradox (see [Zardini, 2008]), and in order to account for the semantics and pragmatics of vague predicates more generally (see , 1 [Cobreros et al, 2012b], [Cobreros et al, 2012a]). It soon became apparent, however, that it could be applied in a natural way to the treatment of the semantic paradoxes and in particular to the Liar Paradox (see [Ripley, 2011], [Cobreros et al,201xb]).…”

Unifying the Philosophy of Truth

“…The general form of such a consequence relation was introduced and investigated independently by Frankowski (in (Frankowski 2004), based on earlier work by (Malinowski 1990) on the dual notion of quasi-consequence) and by Zardini in , with rather minimalist assumptions about the algebra of truth-values in each case. Although Bennett does not present it in that way, the definition can be seen to combine the notions of super-truth and sub-truth that are familiar from the literature on vagueness (see (Hyde 1997), (Cobreros et al 2012a)). Different logics correspond to this notion of permissive consequence depending on the algebra under consideration.…”