Jean-Charles Pelland

Saul Kripke’s (1982) sceptical take on Wittgenstein’s rule-following paradox challenges us to find facts that can justify one interpretation of a symbol’s past use over another. While Ruth Millikan (1990) has answered this challenge by appealing to biological purposes, her answer has been criticized for failing to account for the normativity of rules like addition, which require explicit representations. In this paper, I offer a defense of Millikan. I claim that we can explain how we build intentions to add from the content of core cognition modules like the approximate number system, and argue that Millikan’s answer is better equipped to explain the origins of rules than communitarian approaches like that endorsed by Kusch (2006). I then explore the worth of pluralism about rules and try to find common ground between expressed and unexpressed rules in terms of expectations of how the world is supposed to behave.

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.

This paper presents a challenge to enactivist approaches to cognition (e.g. Ward, D., Silverman, D. & Villalobos, M. 2017) that is based on the theoretical commitments behind forms of looking time studies that have been extensively used to probe into the cognitive abilities of infants and nonhuman animals. I briefly summarize the Violation of Expectation (VoE) paradigm (Ginnobili & Olmos 2021) to illustrate why such methods might pose a problem for enactivists and their conception of cognition as a largely representation-free dynamic coupling between organism and environment. I argue that despite the lack of clarity regarding how the notion of expectation should be applied to the minds of neonates and nonhuman animals, there is an inherently representational aspect to expectation, given that it embodies satisfaction conditions. The challenge is, then: given that many forms of enactivism seem to reject the notion of representationas it is used in the VoE literature, how can enactivists make sense of data and results obtained using such research methods?

One of the most important questions in the young field of numerical cognition studies is how humans bridge the gap between the quantity-related content produced by our evolutionarily ancient brains and the precise numerical content associated with numeration systems like Indo-Arabic numerals. This gap problem is the main focus of this paper. The aim here is to evaluate the extent to which cultural factors can help explain how we come to think about numbers beyond the subitizing range. To do this, I summarize Clark’s notion of a difference maker in explaining complex causation that criss-crosses between mind and world and apply it to Menary’s Open MIND. MIND Group, Frankfurt, 2015a) discussion of mathematical cognition as a case of enculturation. I argue that while Menary’s views on enculturation can help explain what makes the difference between numerate and anumerate cultures, it cannot help specify what makes the difference between numerate and anumerate individuals. I argue that features of enculturation do not provide an account of innovation capable of explaining how individuals manage to improve and modify the practices of their cultural niche. This is because Menary’s construal of the role of enculturation in the development of mathematical cognition focuses mostly on the inheritance and transmission of practices, not on their origins, which involve individual-level understanding, rather than population-level practices and pressures. The upshot is that culture provides the necessary background conditions against which individuals can innovate. This role is crucial in the development of numerical abilities—crucial, but explanatorily limited.