aleksander Gemel Paula Quinon THE APPROXIMATE NUMBERS SYSTEM AND THE TREATMENT OF VAGUENESS IN CONCEPTUAL SPACES 1 1. Introduction The theory of conceptual spaces is intended to provide a framework for models of both symbolic and non-symbolic representations of knowledge and information (Gärdenfors 2000). As such, it seems to us to be very clearly suit- ed to modeling pre-verbal representations belonging to a so-called core cogni- tion, whose existence is postulated by cognitive developmental psychologists (Feigenson et al., 2004; Carey, 2009). In this paper we propose a treatment of representations of quantity that embraces both symbol-based and pre-verbal nu- merical concepts. The representations we aim to study are related to the Approximate Num- ber System (ANS). Cognitive psychologists claim that humans share with an- imals an abstract sense of quantity: they have a so-called “number sense”. To “number sense” amounts two core systems of representations, which get activat- ed by different core mechanisms: the ANS is one of these mechanisms (Dehaene 1997, 2008; Gallistel 1993; Feigenson et al., 2004; Carey, Sarnecka, 2006). The ANS is a core system in the sense that it is present in human apprehen- sion of quantities before verbal conceptual these of quantities appears. But, it is 1 The core idea of this paper was frst formulated in a private conversation of the second author (the authors’ names are listed in alphabetical order) with Jakub Szymanik in the summer 2010. The research of the second author has been supported by the IEF FP7 Marie Curie Fellow- ship “Numbers” (PIEF-GA-2011-301470). We wish to express our gratitude to Peter Gärden- fors for comments on an earlier version of this paper. http://dx.doi.org/10.18778/7969-759-5.06