Trivial Languages

Trivial Languages Arvid Båve 0 0 Stockholm University , Stockholm , Sweden I here present and defend what I call the Triviality Theory of Truth (TT), to be understood in analogy with Matti Eklund's Inconsistency Theory of Truth (IT). A specific formulation of (TT) is defended and compared with alternatives found in the literature. A number of objections against the proposed notion of meaningconstitutivity are discussed and held inconclusive. The main focus, however, is on the problem, discussed at length by Gupta and Belnap, that speakers do not accept epistemically neutral conclusions of Curry derivations. I first argue that the facts about speakers' reactions to such Curry derivations do not constitute a problem for (TT) specifically. Rather, they follow from independent, uncontroversial facts. I then propose a solution which coheres with (TT) as I understand it. Finally, I consider a normative reading of their objection and offer a response. The idea that the Liar paradox shows that Bour language is inconsistent^, what is now called the Inconsistency Theory of Truth (IT), goes back at least to Tarski. 1 How exactly to understand the idea that our language is inconsistent is a matter of ongoing debate. I will here expound what I take to be the best rendering of this phrase, by which I mean least contentious explication, which nevertheless captures most of what its adherents take it to involve. However, it is not (IT), but the related Triviality Theory of Truth (TT) that will be the main focus of this paper. As we will see, this theory raises some new questions and has been questioned on grounds irrelevant to (IT). In a nutshell, (TT) says of Curry's paradox (and of the Liar paradox plus ex contradictione quodlibet) what (IT) says about the Liar, namely, that the principles used in the respective paradoxical derivations are - meaning-constitutive. These theories have misleading names, however, for they are not Btheories of truth^ in the ordinary sense: they do attempt to say Bwhat truth is^, or state conditions for something to be true, and they are not intended to provide a solution to the truth-paradoxes, i.e. an answer to the question what goes wrong in the Liar derivation. In fact, they make no claims at all about validity or truth, but rather concern what the word Btrue^ means, and what constitutes someone’s understanding it (or being semantically competent with it). On the versions of (IT) and (TT) discussed here, meaning is typically analysed in terms of understanding (semantic competence), rather than in terms of truth. A common view of this kind is that the meaning of an expression simply is its understanding conditions (see, e.g. Båve (2009) ). This separation of matters of meaning and matters of truth is consonant with (IT) and (TT)’s commitment to rejecting the idea that any meaning-constitutive sentence is true. More on this below. More specifically, (IT) must be distinguished from dialethism and (TT) must similarly be distinguished from what is normally called Btrivialism^, i.e. the view that every sentence/proposition is true.2 (IT) does not entail that there are true contradictions, and (TT) does not entail that every sentence is true, at least not according to their adherents. Indeed, (IT) and (TT) can be seen as attempts to avoid the radical claims of dialethism and trivialism, while doing justice to some of the facts motivating the latter. These two pairs of theories are also related in the following way: if every sentence/ inference that is meaning-constitutive is also true/valid, then: if (IT) is true, so is dialethism and if (TT) is true, so is trivialism. Since adherents of (IT) and (TT) typically want to avoid dialethism and trivialism, they claim that some meaning-constitutive principles (sentences or inferences) are untrue or invalid. As I will be defining (IT) and (TT), moreover, they are also silent on the normative characteristics of meaningconstitutive principles, e.g. whether they ought to be accepted. As theories of understanding, or semantic competence, the main purpose of (IT) and (TT) is to explain linguistic behaviour, in particular, our reactions to the paradoxes. This is a thoroughly psychological matter, and the connection to questions about validity and truth is not obvious. On my preferred versions of (IT) and (TT), they take semantic competence to consist in dispositions to accept certain principles, where acceptance is a psychological relation similar to belief, except it relates speakers to sentences, rather than propositions. It is thus not a behavioural notion and must not be confused with, e.g. assent, which is. While (IT) and (TT) are logically independent, it is rather natural to accept one if one accepts the other. For instance, the main intuition motivating (IT), namely, that Liar reasoning is impeccable, has an obvious counterpart motivating (TT), namely, the intuition that Curry reasoning is impeccable. Still, (TT) raises some new and separate (...truncated)