The Approximate Numbers System and the treatment of vagueness in conceptual spaces

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 suited to modeling pre-verbal representations belonging to a so-called core cognition, 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 numerical concepts. The representations we aim to study are related to the Approximate Number System (ANS). Cognitive psychologists claim that humans share with animals an abstract sense of quantity: they have a so-called “number sense”. To “number sense” amounts two core systems of representations, which get activated 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 apprehension of quantities before verbal conceptual these of quantities appears. But, it is