The idea that there is a “Number Sense” (Dehaene, 1997) or “Core Knowledge” of number ensconced in a modular processing system (Carey, 2009) has gained popularity as the study of numerical cognition has matured. However, these claims are generally made with little, if any, detailed examination of which modular properties are instantiated in numerical processing. In this article, I aim to rectify this situation by detailing the modular properties on display in numerical cognitive processing. In the process, I review literature (...) from across the cognitive sciences and describe how the evidence reported in these works supports the hypothesis that numerical cognitive processing is modular. I outline the properties that would suffice for deeming a certain processing system a modular processing system. Subsequently, I use behavioral, neuropsychological, philosophical, and anthropological evidence to show that the number module is domain specific, informationally encapsulated, neurally localizable, subject to specific pathological breakdowns, mandatory, fast, and inaccessible at the person level; in other words, I use the evidence to demonstrate that some of our numerical capacity is housed in modular casing. (shrink)

To determine what the speaker in a cooperative dialog meant with his assertion, on top of what he explicitly said, it is crucial that we assume that the assertion he gave was optimal. In determining optimal assertions we assume that dialogs are embedded in decision problems (van Rooij 2003) and use backwards induction for calculating them (Benz 2006). In this paper, we show that in terms of our framework we can account for several types of implicatures in a uniform way, (...) suggesting that there is no need for an independent linguistic theory of generalized implicatures. In the final section, we show how we can embed our theory in the framework of signaling games, and how it relates with other game theoretic analyses of implicatures. (shrink)

Generalized quantifiers are functions from pairs of properties to truth-values; these functions can be used to interpret natural language quantifiers. The space of such functions is vast and a great deal of research has sought to find natural constraints on the functions that interpret determiners and create quantifiers. These constraints have demonstrated that quantifiers rest on number and number sense. In the first part of the paper, we turn to developing this argument. In the remainder, we report on work in (...) neurobiology that test the empirical claims of the theory. In particular, we look at fMRI experiments and behavioral experiments with various patient populations that support the intimate connection between natural language quantification and number sense. (shrink)

Number morphology (e.g., singular vs. plural) is a part of the grammar that captures numerical information. Some languages have morphological Number values, which express few (paucal), two (dual), three (trial) and sometimes (possibly) four (quadral). Interestingly, the limit of the attested morphological Number values matches the limit of non‐verbal numerical cognition. The latter is based on two systems, one estimating approximate numerosities and the other computing exact numerosities up to three or four. We compared the literature on non‐verbal number systems (...) with data on Number morphology from 218 languages. Our observations suggest that non‐verbal numerical cognition is reflected as a core part of language. (shrink)

One approach to understanding how the human cognitive system stores and operates with quantifiers such as “some,” “many,” and “all” is to investigate their interaction with the cognitive mechanisms for estimating and comparing quantities from perceptual input (i.e., nonsymbolic quantities). While a potential link between quantifier processing and nonsymbolic quantity processing has been considered in the past, it has never been discussed extensively. Simultaneously, there is a long line of research within the field of numerical cognition on the relationship between (...) processing exact number symbols (such as “3” or “three”) and nonsymbolic quantity. This accumulated knowledge can potentially be harvested for research on quantifiers since quantifiers and number symbols are two different ways of referring to quantity information symbolically. The goal of the present review is to survey the research on the relationship between quantifiers and nonsymbolic quantity processing mechanisms and provide a set of research directions and specific questions for the investigation of quantifier processing. (shrink)

The verification of a sentence against a visual display in experimental conditions reveals a procedure that is driven solely by the properties of the linguistic input and not by the properties of the context (the set-up of the visual display) or extra-linguistic cognition (operations executed to obtain the truth value). This procedure, according to the Interface Transparency Thesis (ITT) (Lidz et al. in Nat Lang Semant 19(3):227–256, 2011), represents the meaning of an expression at the interface with the ‘conceptual-intentional’ system (...) (Chomsky in The minimalist program. MIT Press, Cambridge, 1995). My experiments provide support for the ITT by replicating in Polish and in Bulgarian the findings of Lidz et al. (Nat Lang Semant 19(3):227–256, 2011) for the English quantifier most. We also obtain new evidence that participants are prompted to switch between verification procedures by a change in the linguistic input (a different superlative quantifier entailed by most), but not by a change in the visual input. Thus, the motivation for the subconscious switch in procedures is not to maximize efficiency. Participants use the procedure associated with each quantifier, and in effect, the same display is verified differently depending on which information the visual system is instructed to use by the semantic representation of the sentence. (shrink)

We examine the verification of simple quantifiers in natural language from a computational model perspective. We refer to previous neuropsychological investigations of the same problem and suggest extending their experimental setting. Moreover, we give some direct empirical evidence linking computational complexity predictions with cognitive reality.<br>In the empirical study we compare time needed for understanding different types of quantifiers. We show that the computational distinction between quantifiers recognized by finite-automata and push-down automata is psychologically relevant. Our research improves upon hypothesis and (...) explanatory power of recent neuroimaging studies as well as provides<br>evidence. (shrink)

To determine what the speaker in a cooperative dialog meant with his assertion, on top of what he explicitly said, it is crucial that we assume that the assertion he gave was optimal. In determining optimal assertions we assume that dialogs are embedded in decision problems (van Rooij 2003) and use backwards induction for calculating them (Benz 2006). In this paper, we show that in terms of our framework we can account for several types of implicatures in a uniform way, (...) suggesting that there is no need for an independent linguistic theory of generalized implicatures. In the final section, we show how we can embed our theory in the framework of signaling games, and how it relates with other game theoretic analyses of implicatures. (shrink)