Even though dialetheism (the idea that some sentences are true and false) has been accepted as a plausible solution to paradoxes, it is commonly remarked that systems such as LP have expressive limitations. In particular, LP cannot express the concept of being “just true”; if the predicate is added to the theory, a new Liar paradox leads to triviality. Beall (2013) proposed to add, instead of a “just true” operator, a series of shrieking rules, such as “A and ¬A entail triviality”. Unlike predicates or operators, rules cannot be diagonalized, so there are no new liar paradoxes. In a recent paper, Scharp (2018) observes that dialetheism with shrieking rules is still not a convincing theory. In particular, he observes that once contradictions are allowed, the meaning of “John is tall” will always be ambiguous between “John is tall (and maybe also not-tall)” and “John is just tall”. This is worse for complex sentences: “John is playing with a friend at a park” will mean “John is just playing with a just friend at a just park”. Defining “just true” with rules involving entailment and triviality makes the theory even less familiar for ordinary speakers. A solution to the Liar paradox cannot imply such a huge reform of language.

In this paper, I claim that Scharp is not right. First, because recent experiments (Alxatib & Pelletier, 2011) have determined that dialetheias are commonly adopted in natural language for borderline situations (“x is tall and not tall” is usually a way of claiming that x is borderline tall). Second, because the possibility of dialetheias does not imply a general ambiguity of every predicate, but rather a widening of the acknowledged open texture of predicates (in particular, gradable predicates). Third, because a theory of just true does not need to be so complicated or theory-loaded; Logics of Formal Inconsistency show that just true is a simple concept. Finally, because the idea of reforming the language just for giving room to the Liar paradox is a misconception of the goals of paraconsistency; in particular, as the Brazilian school always claimed, and the linguistic evidence shows, true contradictions can also emerge in non-paradoxical scenarios.

References

Alxatib, S. & Pelletier, J. (2011) “The psychology of vagueness: borderline cases and contradictions”, Mind and Language 26(3): 287-326.

Beall, J.C. “Shrieking against gluts: the solution to the ‘just true’ problem”. Analysis 73: 438-445.

Scharp, J. (2018) “Shrieking in the face of revenge”, Analysis, forthcoming.