Samuels R. Number Concepts. An Interdisciplinary Inquiry 2024 torrent

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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