In §93 of The Principles of Mathematics, Bertrand Russell observes that “the variable is a very complicated logical entity, by no means easy to analyze correctly”. This assessment is borne out by the fact that even now we have no fully satisfactory understanding of the role of variables in a compositional semantics for first-order logic. In standard Tarskian semantics, variables are treated as meaning-bearing entities; moreover, they serve as the basic building blocks of all meanings, which are constructed out of (...) variable assignments. But this has disquieting consequences, including Fine’s antinomy of the variable and an undue dependence of meanings on language. Here I develop an alternative, Fregean version of predicate logic that uses the traditional quantifier–variable apparatus for the expression of generality, possesses a fully compositional, non-representational semantics, and is not subject to the antinomy of the variable. The advantages of Fregean over Tarskian predicate logic are due to the former’s treating variables not as meaningful lexical items, but as mere marks of punctuation, similar to parentheses. I submit that this is indeed how the variables of predicate logic should be construed. (shrink)

ABSTRACT In this paper, I ask whether quantifiers are intensional operators, with variable assignments playing the role of indices. Certain formulations of extensional type theory suggest an affirmative answer, but the most satisfactory among them suffer from a contamination of their semantic ontology with syntactic material. I lay out ‘Fregean’ versions of extensional type theory that are free from syntactic contamination and suggest a negative answer to our question.

This paper argues that verb phrase ellipsis requires contrast. The central observation is that ellipsis is ungrammatical in tautologous conditionals; e.g., *_If John wins, then he does_. Ellipsis is correctly ruled out by a focus-based theory of ellipsis (Rooth 1992a, b ), but one that crucially imports focus’s requirement for contrast: an elliptical constituent must have an antecedent that is not merely an alternative to it, but a ‘proper’ alternative. An explanation in terms of contrast failure proves superior to alternative (...) explanations in terms of triviality and matching form. Showing as much catalogues what counts for contrast in ellipsis, encompassing negation, questions, and intensionality. Subjecting ellipsis to a contrast requirement is in direct conflict with the traditional analysis of MaxElide effects (Takahashi and Fox 2005 ), favouring alternative explanations (e.g., Jacobson 2019a, b ), perhaps in terms of contrast itself (Griffiths 2019 ). Overall, this paper establishes that contrast has explanatory power in ellipsis licensing. (shrink)

This paper argues for the hypothesis of direct compositionality (as in, e.g., Montague 1974), according to which the combinatory syntactic rules specify a set of well-formed expressions while the semantic combinatory rules work in tandem to directly supply a model-theoretic interpretation to each expression as it is "built" in the syntax. (This thus obviates the need for any level like LF and, concomitantly, for any rules mapping surface structures to such a level.) I focus here on one related group of (...) phenomena: the interaction of "paycheck" pronouns with Weak Crossover effects and i-within-i effects. These interactions were studied in Jacobson (1977) as they show up in Back-Peters sentences. There I argued that these interactions show that paycheck pronouns have a complex representation at LF; here I show that all of the observations in this earlier work are compatible with the hypothesis of direct compositionality. The key tool is the adoption of a variation-free semantics (a semantics which makes no use of variables as part of the semantic machinery). In addition to the general consequences for the syntax/semantics interface, there are two other main results. First, I provide new arguments for a variable-free semantics. For example, it will be shown that under this view the paycheck reading of a pronoun comes for free; most other theories posit additional mechanisms and/or an additional lexical meaning for pronouns, and thus paycheck and regular pronouns are only accidentally homophonous. Second, I reiterate one of the central points in Jacobson (1977): this is that the first pronoun in a Bach-Peters sentence is indeed a paycheck pronoun, and hence nothing special needs to be said about these sentences nor does any new machinery need to be invoked for them. (shrink)

There have been a variety of arguments over the decades both for and against syntactic Neg Raising. Two recent papers :559–576, 2018; Crowley in Nat Lang Semant 27, 1–17, 2019) focus on the interaction of NR effects with ellipsis. These papers examine similar types of data, but come to opposite conclusion: Jacobson shows that the ellipsis facts provide evidence against syntactic NR, whereas Crowley argues in favor of syntactic NR. The present paper revisits the evidence, showing that the key case (...) in Crowley that he uses to argue for syntactic NR contains a confound, while the broader set of evidence in Jacobson continues to support the non-syntactic account. In addition, I reply here to an argument for syntactic NR due originally to Prince and Smaby and elaborated on by Crowley. The key generalization can be shown to disappear once contexts are carefully controlled for. Moreover, Crowley extends the Prince/Smaby argument to show that no inference-based account of NR can survive, but this conclusion rests on the claim that there are cases where ever is vacuous; I show that this is not the case. I also consider the question—discussed in much previous literature—of why under the syntactic approach to NR the class of predicates allowing NR is limited to just those which easily support an Excluded Middle inference. Crowley attempts to provide a principled explanation, speculating that NR is allowed just in case it is ‘semantically vacuous’. I argue that this proposal is problematic and so the challenge to syntactic approaches remains. Finally, I provide a new argument against syntactic NR which centers on the behavior of guess. (shrink)