Online research in philosophy

Rodriguez-Pereyra (2006) argues for the disjunction thesis but against the conjunction thesis. I argue that accepting the disjunction thesis undermines his argument against the conjunction thesis.

In English, a non-wh-question may have a disjunctive phrase explicitly providing the choices that the question ranges over. For example, in (1), the disjunction or not indicates that the the choice is between the positive and the negative polarity for the relevant proposition, as spelled out in the yes/no (yn)-question reading (2) and in the answers (2a,b). Another example is (3). The disjunction in (3) can be understood as providing the choices that the question ranges over, hence giving rise to the alternative (alt-)reading in (4) and eliciting the answers in (4a,b). (Cf. Karttunen (1977) and Higginbotham (1993) for the semantics of yn/alt-questions).

There is a requirement which a disjunction must satisfy in order to constitute a felicitous contribution to an ordinary conversation: its disjuncts must be interpretable as relevant alternatives. When such an interpretation is not available, the disjunction is highly anomalous. The disjuncts of sentence (1), for example, appear unrelated to one another, and the disjunction is concomitantly odd. The effect is similar when the disjuncts are related but do not constitute distinct alternatives, perhaps by virtue of one disjunct entailing another, as in (2).

This study is concerned with the properties of the disjunction operator, or, and the acquisition of these properties by English-speaking children. Previous research has concluded that adult truth conditions for logical connectives are acquired relatively late in the course of language development. With particular reference to disjunction, the results of several studies have led to two claims. First, it has been argued that the full range of truth-conditions associated with inclusive-or is not initially available to children; instead, children are supposed to interpret disjunction using the truth conditions that are associated with exclusive-or (e.g., Beilin and Lust 1975; Braine and Rumain 1981, 1983; Paris 1973). A second, related claim is that even when children respond as if they have access to the complete range of truth conditions, their responses result from the failure to distinguish or from and (Paris, 1973).

Two quite simple identities for exclusive disjunction and the biconditional are proven by mathematical induction. This proof is independently reprised in R.E. Jennings' /The Genealogy of Disjunction/ (OUP, 1994) pp. 6-7, esp. p. 7 which points out the consequences for the biconditional of the proof that runs from pages 6-7.

I argue that the conjunctive distribution of permissibility over or, which is a puzzling feature of free-choice permission is just one instance of a more general class of conjunctive occurrences of the word, and that these conjunctive uses are more directly explicable by the consideration that or is a descendant of oper than by reference to the disjunctive occurrences which logicalist prejudices may tempt us to regard as semantically more fundamental. I offer an account of how the disjunctive uses of or may have come about through an intermediate discourse-adverbial use of or, drawing a parallel with but, which, etymologically, is disjunctive rather than conjunctive and whose conjunctive uses seem to represent just such a discourse-adverbial application.

This study is concerned with the acquisition of the disjunction operator, or, in English. Two mutually inconsistent claims have been made about the acquisition of disjunction. One claim is that the acquisition of the adult truth conditions for logical connectives, including disjunction, is a late and not fully universal, achievement. With particular reference to disjunction, the findings from several studies are interpreted as showing that only the truth conditions associated with exclusive-or are available to young children (e.g., Beilin and Lust 1975; Braine and Rumain 1981, 1983; Paris 1973). There is a related claim, that even when children respond as if they have access to a broader range of truth conditions, namely those associated with inclusive-or, children's adult-like responses are the result of a failure to distinguish or from and (Paris 1973). A different conclusion was reached in a recent study by Chierchia, Crain, Guasti and Thornton (1998), who conducted a series of experiments which revealed children's adult-like knowledge of logical connectives, including disjunction. To reconcile the findings from the Chierchia et al. study and those of previous research, Chierchia et al. (1998) draw upon a distinction between semantic and pragmatic knowledge. They argue that the acquisition of logical connectives is simply a process of mapping the appropriate truth conditions (associated with logical connectives in classical logic) onto the particular words of the language to which the child is exposed. In understanding sentences, however, children are also influenced by the pragmatic norms they follow. In many..

This study is concerned with the acquisition of the disjunction operator, or, in English. Two mutually inconsistent claims have been made about the acquisition of disjunction. One claim is that the acquisition of the adult truth conditions for logical connectives, including disjunction, is a late and not fully universal, achievement. With particular reference to disjunction, the findings from several studies are interpreted as showing that only the truth conditions associated with exclusive-or are available to young children (e.g., Beilin and Lust 1975; Braine and Rumain 1981, 1983; Paris 1973). There is a related claim, that even when children respond as if they have access to a broader range of truth conditions, namely those associated with inclusive-or, children's adult-like responses are the result of a failure to distinguish or from and (Paris 1973).

Since Horn (1972) the notion of conversational implicature proposed by Grice has been put to use to explain certain interpretive differences between expressions in natural language and their counterparts in formal logic. For example, the sentences in (1) seem to convey more than they would be expected to if the natural language disjunction or had the same meaning as the logical disjunction ∨, or if the quantificational determiner some was interpreted as the existential quantifier ∃.

We present a series of arguments for logical nativism, focusing mainly on the meaning of disjunction in human languages. We propose that all human languages are logical in the sense that the meaning of linguistic expressions corresponding to disjunction (e.g. English or , Chinese huozhe, Japanese ka ) conform to the meaning of the logical operator in classical logic, inclusive- or . It is highly implausible, we argue, that children acquire the (logical) meaning of disjunction by observing how adults use disjunction. Findings from studies of child language acquisition and from cross-linguistic research invite the conclusion that children do not learn to be logical—it comes naturally to them.