Eric Mandelbaum

The idea that there is a “Number Sense” (Dehaene, 1997) or “Core Knowledge” of number ensconced in a modular processing system (Carey, 2009) has gained popularity as the study of numerical cognition has matured. However, these claims are generally made with little, if any, detailed examination of which modular properties are instantiated in numerical processing. In this article, I aim to rectify this situation by detailing the modular properties on display in numerical cognitive processing. In the process, I review literature from across the cognitive sciences and describe how the evidence reported in these works supports the hypothesis that numerical cognitive processing is modular. I outline the properties that would suffice for deeming a certain processing system a modular processing system. Subsequently, I use behavioral, neuropsychological, philosophical, and anthropological evidence to show that the number module is domain specific, informationally encapsulated, neurally localizable, subject to specific pathological breakdowns, mandatory, fast, and inaccessible at the person level; in other words, I use the evidence to demonstrate that some of our numerical capacity is housed in modular casing

The overwhelming majority of those who theorize about implicit biases posit that these biases are caused by some sort of association. However, what exactly this claim amounts to is rarely specified. In this paper, I distinguish between different understandings of association, and I argue that the crucial senses of association for elucidating implicit bias are the cognitive structure and mental process senses. A hypothesis is subsequently derived: if associations really underpin implicit biases, then implicit biases should be modulated by counterconditioning or extinction but should not be modulated by rational argumentation or logical interventions. This hypothesis is false; implicit biases are not predicated on any associative structures or associative processes but instead arise because of unconscious propositionally structured beliefs. I conclude by discussing how the case study of implicit bias illuminates problems with popular dual-process models of cognitive architecture.

Philosophical discussions of Molyneux's problem within contemporary philosophy of mind tend to characterize the problem as primarily concerned with the role innately known principles, amodal spatial concepts, and rational cognitive faculties play in our perceptual lives. Indeed, for broadly similar reasons, rationalists have generally advocated an affirmative answer, while empiricists have generally advocated a negative one, to the question Molyneux posed after presenting his famous thought experiment. This historical characterization of the dialectic, however, somewhat obscures the role Molyneux's problem has played in spawning debates within the empiricist tradition. Fortunately, the differences between various empiricist accounts have been widely recognized and discussed among historians of philosophy working on the topic. The focus of the present essay is to develop an interpretation of John Locke's views on Molyneux's problem that best coheres with his other views on human understanding as well as with the predominant scientific opinion about the nature of perception during the period in which he lived.