Samuels R. Number Concepts. An Interdisciplinary Inquiry 2024

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Samuels R. Number Concepts. An Interdisciplinary Inquiry 2024

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Textbook in PDF format This Element aims to review and critically assess research on number-concepts within developmental psychology and cognitive science, in a manner that is helpful to researchers within both philosophy and the relevant sciences. It outlines i) commonplace theoretical commitments underlying most mainstream number cognition research, such as representationalism, the existence of certain number-specific cognitive systems, e.g. the Approximate Number System and the Small Number System, and a trajectory of key developmental milestones specific to number concept possession; ii) a taxonomy of existing views within mainstream number cognition research, including influential formulations of those views, along with significant challenges they face; and iii) various philosophical assumptions often adopted by number cognition researchers, concerning e.g. the relationship between foundational mathematics and developmental psychology, and what natural numbers are like. The Element also distinguishes and motivates different versions of conceptual pluralism about number concepts. Introduction Why Care about Philosophy of Mathematics? Why Care about Number Cognition Research? Ambitions and Scope of the Present Element The Mainstream Representationalism Representationalism about Concepts The Core Systems Hypothesis Approximate Number System The Small Number System The Developmental Sequence Some Explanatory Targets The Acquisition Problem A Taxonomy of Developmental Hypotheses ANS-Dominant Models The Representation Requirement The Feasibility Requirement Nativist Models Hybrid Models Spelke’s Hybrid View Troubles for Spelke SNS-Dominant Models Conceptual Continuity and Quinean Bootstrapping Bootstrapping the Count List Troubles for Carey Assessing the Mainstream Psychology and Foundational Mathematics Metaphysics of Natural Number Cultural Constructionism Term Formalism The Frege–Russell Characterization Conceptual Pluralism Synchronic Pluralism The Complex Transition Thesis Diachronic Pluralism Conclusion References