Radical Anti‐disquotationalism

Abstract

Consider a self-referential utterance, u, of the sentence 'u is not true'. According to one widespread and appealing intuition when one makes a semantically paradoxical utterance such as u one simply does not succeed in saying anything. Call this the no proposition theory.No proposition theorists reject the disquotational assumption that utterances of 'u is not true' say that u is not true on the grounds that some utterances of 'u is not true' do not say anything at all. However, they may nonetheless subscribe to a qualified version of the principle that says that if an utterance of 'u is not true' says anything at all it says that u is not true. In this paper I shall show that such views are in the unfortunate position of not being able to state their own view. An examination of these paradoxes suggests a view in which paradoxical utterances such as u do say things, although they do not say what you might expect them to (in this case, that u is not true). I shall show, moreover, that this phenomena falls out of general considerations about the relation between language and the world, and that as a result failures of disquotational principles are much more widespread than many have thought.In this paper we will be primarily be investigating the corner of philosophical space that accepts classical logic, understood broadly to include the classical rules for quantification into sentence position. 1

Higher-order free logic and the Prior-Kaplan paradox

“…This seems very much in line with a solution entertained, albeit in a compressed way, by Kripke to his own puzzle.59 As argued in a lot more detail in Bacon[1].60 The ordering technique we have in mind is one according to which if 'expresses' expresses expressing then expressing comes immediately below expressing in the ordering. Ruling out loops and infinite descending sequences together would still guarantee no more than a partial order; further arguments would be needed to…”

“…By contrast, there's another school of thought, often attributed to Russell, in which each relational type is further stratified into levels indexed by the natural numbers. 1 That is, instead of a single type of relations (τ 1 , ..., τ n ), for any ramified types, τ 1 , ..., τ n , there is a whole hierarchy of relations of different levels, written (τ 1 , ..., τ n )/k for k ∈ N. 2 So instead of a single type of proposition, we have infinitely many ramified propositional types, ()/0, ()/1, ()/2 and so on. One way to think of these types, borrowing a metaphor from Kaplan [11], is to think of the zero level propositional type as containing only propositions concerning the distribution of earth, wind, fire and water.…”

“…One could also insist that despite appearances Kaplan wrote two or more things at midnight (see, for example, Bradwardine[3], Dorr[7], Slater[23]). Or one might insist that while Kaplan didn't say what he seemed to say, he succeeded in saying something else Smith[24], Bacon[1]. The challenge for these kinds of responses is to offer some guidance as to what the additional or alternative contents are 13.…”

Higher-order free logic and the Prior-Kaplan paradox

“…One could also insist that despite appearances Kaplan wrote two or more things at midnight (see, for example, Bradwardine [3], Dorr [7], Slater [23]). Or one might insist that while Kaplan didn't say what he seemed to say, he succeeded in saying something else Smith [24], Bacon [1]. The challenge for these kinds of responses is to offer some guidance as to what the additional or alternative contents are.…”

“…60 Notice that even if a 58 This seems very much in line with a solution entertained, albeit in a compressed way, by Kripke to his own puzzle. 59 As argued in a lot more detail in Bacon [1]. 60 The ordering technique we have in mind is one according to which if 'expresses' expresses expressing then expressing comes immediately below expressing in the ordering.…”