When Three Is Not Some: On the Pragmatics of Numerals Einat Shetreet 1,2 , Gennaro Chierchia 2 , and Nadine Gaab 1,3,4 Abstract ■ Both numerals and quantifiers (like some) have more than one possible interpretation (i.e., weak and strong interpreta- tions). Some studies have found similar behavior for numerals and quantifiers, whereas others have shown critical differences. It is, therefore, debated whether they are processed in the same way. A previous fMRI investigation showed that the left inferior frontal gyrus is linked to the computation of the strong inter- pretation of quantifiers (derived by a scalar implicature) and that the left middle frontal gyrus and the medial frontal gyrus are linked to processing the mismatch between the strong interpretation of quantifiers and the context in which they are presented. In the current study, we attempted to characterize the similarities and differences between numbers and quan- tifiers by examining brain activation patterns related to the processing of numerals in these brain regions. When numbers were presented in a mismatch context (i.e., where their strong interpretation did not match the context), they elicited brain activations similar to those previously observed with quantifiers in the same context type. Conversely, in a match context (i.e., where both interpretations of the scalar item matched the con- text), numbers elicited a different activation pattern than the one observed with quantifiers: Left inferior frontal gyrus activa- tions in response to the match condition showed decrease for numbers (but not for quantifiers). Our results support previous findings suggesting that, although they share some features, numbers and quantifiers are processed differently. We discuss our results in light of various theoretical approaches linked to the representation of numerals. ■ INTRODUCTION The comprehension of scalar expressions has been exten- sively studied in logic, linguistics, and psycholinguistics (e.g., Shetreet, Chierchia, & Gaab, in press; Huang & Snedeker, 2009a, 2009b; Chierchia, Fox, & Spector, 2008; Chierchia, 2004; Noveck, 2001; Grice, 1975; Horn, 1972). These studies usually focus on the interpretation of weak scalar expressions. Scalar expressions form ordered scales with other scalar expressions of the same type 1 (e.g., hsome, many, most, every/alli; hor, andi; hmay, musti; and hwarm, hot, boilingi). Weak scalar expressions, such as some, which is positioned at the lower end of the scale, have two possible interpretations, illustrated in Exam- ples (1) and (2). Under the lexical (logical) meaning, the weak scalar expression is compatible with the strong mem- ber of the same scale (e.g., some is compatible with every/ all, or in other words, its logical meaning is at least some, as shown in Example (2)). However, the interpretation of the weak scalar is often strengthened to exclude the strong member (e.g., some but not all, as can be seen in Example (1)). (1) Some dogs in this neighborhood bark at night. (2) If some dogs in this neighborhood bark at night, we wonʼt get enough sleep. (3) Every dog in this neighborhood barks at night. Although it is controversial what linguistic component drives the interpretation strengthening of weak scalar expressions (e.g., grammatical or pragmatic, for more details, see Chierchia, 2004; Noveck & Sperber, 2007), there is a general agreement regarding the computation process that generates the strong interpretation. This computation occurs through a scalar implicature by con- sidering the alternatives of the weak scalar expression like the quantifier some. When encountering this quanti- fier, language users consider the other members of the quantifier scale as alternatives for what they have en- countered (e.g., Example (3) as an alternative for Exam- ple (1)). Using the weak scalar and assuming that the speaker is cooperative and knowledgeable indicates to the listener that the strong alternative (i.e., Example (3)) does not hold. Thus, the listener interprets some using the strong (pragmatic) interpretation of “some but not all.” Like quantifiers, numerals are also ordered on a scale (hone, two, three…i). They also have more than one interpretation as shown in Examples (4) and (5). In Ex- ample (4), the numeral three has the strong interpreta- tion of three and not more (or in other words exactly three), which corresponds to the strong interpretation of quantifiers (i.e., some and not all ). In Example (5), three has the weak interpretation of at least three, which corresponds to the weak interpretation of quantifiers (i.e., some and possibly all ). It has therefore been argued by the classical neo-Gricean approach that the same computa- tion process applies to quantifiers and numerals (e.g., van Rooij & Schulz, 2006; Horn, 1972): A scalar implica- ture is computed with a weak scalar by considering its 1 Boston Childrenʼs Hospital, 2 Harvard University, 3 Harvard Medical School, 4 Harvard Graduate School of Education © 2013 Massachusetts Institute of Technology Journal of Cognitive Neuroscience X:Y, pp. 1–10 doi:10.1162/jocn_a_00514