On representational content and format in core numerical cognition. (17th February 2017) - Ball, Brian
Abstract: Carey has argued that there is a system of core numerical cognition – the analog magnitude (AM) system – in which (approximate) cardinal numbers are explicitly represented in iconic format. While the existence of this system is beyond doubt, this paper aims to show that its representations cannot have the combination of features attributed to them by Carey. According to the argument from abstractness, the representation of the (approximate) cardinal number of a collection of individuals as such requires the representation of individuals as such, and this in turn requires non-iconic format, from which it is concluded that the explicit representation of the (approximate) cardinal number of some individuals requires non-iconic representational format. In support of the first premise, an account is given of what approximate cardinal numbers might be (namely, quantifiers), and in support of the second, a direct argument is articulated and defended. Finally, in response to an objection, a second argument (from parts) for the central thesis is provided. While the discussion is couched in the terms of Carey's work, the considerations it adduces are perfectly general, and the conclusion should therefore be taken into consideration by all those aiming to characterize the AM system.