Journal ArticleDOI
Mental Magnitudes and Increments of Mental Magnitudes
TLDR
It is argued that learning the number words and the counting routine may allow one to mark in memory the number of increments that composed to form a magnitude, thereby creating a precise representation of cardinality.Abstract:
There is at present a lively debate in cognitive psychology concerning the origin of natural number concepts. At the center of this debate is the system of mental magnitudes, an innately given cognitive mechanism that represents cardinality and that performs a variety of arithmetical operations. Most participants in the debate argue that this system cannot be the sole source of natural number concepts, because they take it to represent cardinality approximately while natural number concepts are precise. In this paper, I argue that the claim that mental magnitudes represent cardinality approximately overlooks the distinction between a magnitude and the increments that compose to form that magnitude. While magnitudes do indeed represent cardinality approximately, they are composed of a precise number of increments. I argue further that learning the number words and the counting routine may allow one to mark in memory the number of increments that composed to form a magnitude, thereby creating a precise representation of cardinality.read more
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Analog representations and their users
TL;DR: This paper argues that the analog–digital distinction does not apply to representational schemes but only to representsational systems, and that whether a representational system is analog or non-analog depends on facts about that user.
References
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Book
Word and Object
TL;DR: This edition offers a new preface by Quine's student and colleague Dagfinn Follesdal that describes the never-realized plans for a second edition of Word and Object, in which Quine would offer a more unified treatment of the public nature of meaning, modalities, and propositional attitudes.
Journal ArticleDOI
Core systems of number
TL;DR: This work reviews recent behavioral and neuropsychological evidence that these ontogenetically and phylogenetically shared abilities rest on two core systems for representing number, and identifies one system for representing large, approximate numerical magnitudes, and a second system for the precise representation of small numbers of individual objects.
Book
The Origin of Concepts
TL;DR: Carey argues that the key to understanding cognitive development lies in recognizing conceptual discontinuities in which new representational systems emerge that have more expressive power than core cognition and are also incommensurate with core cognition as mentioned in this paper.