Logic in Grammar

Abstract

This book explores the relation between language and logic through an analysis of polarity sensitivity and free choice effects. A wide variety of items are considered, with the intent of identifying the common core of the Polarity System as well as the choices that determine the stunningly diverse array of its manifestations. Sensitivity to polarity and freedom of choice are analyzed as a form of grammaticized Scalar Implicature. This requires a reassessment of how the different components of language (i.e. syntax, semantics and pragmatics) interact. But perhaps the most surprising outcome of t Logical Syntax of Language his book concers the relation of syntax to logic. In his classic, Carnap defines syntax as a lexicon and a set of formation rule and logic proper as a set of inference rules. Modern linguistics in the generative tradition has maintained a similar modular set up: a combinatorial apparatus generates structures over which semantic/pragmatic relations (like entailment, presuppositions and implicatures) are defined. This book argues that a wide array of structures that are typically perceived and analyzed as syntactically deviant owe in fact their status to their logical properties, i.e. whether they are contradictory/analytically true in specific ways (‘G-trivial’). This alters the Carnapian view, as the characterization of ‘grammatical structure’ now requires a more direct role of logical inferences. The functional lexicon of grammar comes with a set of inference rules that crucially and directly determine grammaticality patterns. Logic in Grammar presents the results of a decade’s work on semantics, pragmatics and syntax. It extends the author’s long-term project on how humans categorize the world and how they reason. It is, in sum, a mind-opening contribution to the understanding of the fundamental operations of language and thought, a book that will interest linguists, philosophers, and cognitive scientists alike.

Universal Quantifier PPIs

“…According to a recent line of thinking (Krifka 1995;Lahiri 1998;Chierchia 2006Chierchia , 2013, and others), Negative Polarity Items (NPIs) that are only fine in Downward Entailing (DE) contexts are ruled out outside DE contexts, since then their semantics would give rise to a contradiction.…”

“…Following Chierchia's (2006Chierchia's ( , 2013 implementation of this idea, NPIs are equipped with an uninterpretable feature [uσ] that obligatorily introduces all its domain and scalar alternatives and that must be checked by a covert c-commanding exhaustifier that carries an interpretable feature [σ] (or [σ,D]). Chierchia then argues that the combination of these two requirements triggers a semantic contradiction for every NPI outside a DE context.…”

“…An exhaustifier that is applied to some proposition states that all stronger alternatives of that proposition are false. Chierchia (2013) introduces two exhaustification operators, O and E. O is the covert counterpart of only; E is the overt counterpart of even.…”

“…According to Chierchia (2006Chierchia ( , 2013, this contradiction arises as such NPIs both obligatorily introduce domain alternatives and trigger the presence of a covert exhaustifier. Following this line of reasoning, I argue it should be expected that elements with the same properties that denote the highest endpoint of a scale, such as universal quantifiers, are Positive Polarity Items (PPIs).…”

Are All Concessive Scalar Particles the Same? Probing into Spanish "Siquiera"

“…We will adopt Crnic's AT LEAST operator, but will work within a two-tier system that computes ordinary meanings ( · o ) and alternatives ( · alt ) in tandem (Rooth 1985;Krifka 1995;Chierchia 2013). The ordinary meaning of AT LEAST is as before.…”