The Discrete, the Continuous, and the Approximate Number System

This paper explores the value of skepticism towards the Approximate Number System (ANS). I sketch some of the main arguments levied against ANS-based interpretations of numerical cognition data and argue that there are empirical and conceptual reasons to reject wholesale replacement of the ANS with an Analog Magnitude System (AMS). To simplify the discussion, I focus for the most part on a recent critical review representative of this new wave of revisionist skepticism (Leibovich, T., Katzin, N., Harel, M., & Henik, A., 2017). I start with a brief review of some of the reasons offered to deny that experiments studying our numerical abilities reveal the presence of a system dedicated to representing quantities of discrete objects, before turning briefly to empirical responses to these worries. I then offer a few reflections on why even if the empirical rebuttal were to fail, there are conceptual reasons to doubt that we are only equipped with an AMS. While some of these reasons involve methodological implications of AMS-based theories, other conceptual reasons to doubt AMS skepticism revolve around how ANS-skepticism seems to go against the history of the relation between the continuous and the discrete, and how one cannot be derived from the other. I then end with a potential reply to my worries involving an appeal to the Object-File System (OFS) as a source of discrete content in our numerical abilities and find it wanting