Papers on Negation and Quantifiers

Here is a series of five papers I have written recently concerning negation, quantifiers and negating quantifiers. They are all syntax/semantics interface papers, with a substantial semantic component. The constant theme throughout is the application of the basic framework of Collins and Postal 2014 to various phenomena. 

The relevant principle from Collins and Postal 2014 is the following:

If X has a semantic type ending in <t>, then

NEG takes X with semantic value: λP1….λPn […]

And returns Y with semantic value: λP1…λPn ➖[…]

I only include in this list singled-authored papers dealing with the syntax/semantics interface. I have a series of other papers on the syntax of negation with Francis Blanchette, Paul Postal and Elvis Yevudey. Let me know if you need any of these papers. I would be happy to send them to you, and to discuss them with you.

2023 Negating Gradable Adjectives. Natural Language Semantics.

(https://rdcu.be/debuX)

Abstract: In this short paper, I analyze the syntax and semantics of the prefix un- with gradable adjectives like unhappy and compare it to the syntax and semantics of not. Within the framework of Collins and Postal 2014, I propose that un- and not have the same semantics but negate different constituents, accounting for differences in interpretation.

2022 Scalar Modifiers of Quantifier Phrases. Glossa 7(1), 1-20.

(https://www.glossa-journal.org/article/id/6162/)

Abstract: This paper analyzes the syntax and semantics of scalar modifiers of quantifier phrases in expressions like almost every student, absolutely every student and nowhere near every student. The semantics is based on scales (positive and negative) of generalized quantifiers.

2020 Outer Negation of Universal Quantifier Phrases. Journal of Linguistics and Philosophy. (https://doi.org/10.1007/s10988-019-09269-4)

Abstract: This paper discusses two ways of negating DP quantifier phrases. In one way, NEG modifies the quantifier D directly with the structure [[NEG D] NP] (inner negation). In the other way, NEG modifies the whole DP with the structure [NEG DP] (outer negation). I give evidence based on negative polarity items that negated universal quantifier phrases like not every student involve outer negation (contra Hoeksema 1986, 1987).

2017 A Scope Freezing Effect with Negated Quantifier Phrases. Natural Language 

Semantics 25, 315-327.

Abstract: I document a scope freezing effect found with negated quantifier phrases (distinct from the scope freezing effect discussed in Collins 2016a). In a sentence with a negated quantifier phrase of the form [NEG DP1], no quantifier phrase DP2 can take scope between NEG and DP1. I show how this scope freezing effect can be explained in terms of the analysis of negated quantifier phrases given in Collins and Postal (2014) and Collins (2016a).

2016 Not even. Natural Language Semantics 24, 291-303.

Abstract: This paper proposes an analysis of the semantics of even that is consistent with the assumptions about the syntax and semantics of negation in Collins and Postal (Classical NEG raising, MIT Press, Cambridge, 2014). First, I review the distribution of negation, showing how negation may modify quantificational expressions where it gives rise to scope freezing effects. Second, I discuss the fact that even-phrases can be modified by negation, as in Not even John is there. On the basis of this fact, I argue that even is a quantifier. Lastly, I show that my data provides new empirical support for the assumption that there are two kinds of even, depending on the role played by focus in the scalar presupposition.