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Two roads to the successor axiom

Synthese 197 (3):1241-1261 (2020)

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  1. Re-establishing the distinction between numerosity, numerousness, and number in numerical cognition.César Frederico Dos Santos - 2022 - Philosophical Psychology 35 (8):1152-1180.
    In 1939, the influential psychophysicist S. S. Stevens proposed definitional distinctions between the terms ‘number,’ ‘numerosity,’ and ‘numerousness.’ Although the definitions he proposed were adopted by syeveral psychophysicists and experimental psychologists in the 1940s and 1950s, they were almost forgotten in the subsequent decades, making room for what has been described as a “terminological chaos” in the field of numerical cognition. In this paper, I review Stevens’s distinctions to help bring order to this alleged chaos and to shed light on (...)
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  • Building blocks for a cognitive science-led epistemology of arithmetic.Stefan Buijsman - 2021 - Philosophical Studies 179 (5):1-18.
    In recent years philosophers have used results from cognitive science to formulate epistemologies of arithmetic :5–18, 2001). Such epistemologies have, however, been criticised, e.g. by Azzouni, for interpreting the capacities found by cognitive science in an overly numerical way. I offer an alternative framework for the way these psychological processes can be combined, forming the basis for an epistemology for arithmetic. The resulting framework avoids assigning numerical content to the Approximate Number System and Object Tracking System, two systems that have (...)
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  • Building blocks for a cognitive science-led epistemology of arithmetic.Stefan Buijsman - 2021 - Philosophical Studies 179 (5):1777-1794.
    In recent years philosophers have used results from cognitive science to formulate epistemologies of arithmetic :5–18, 2001). Such epistemologies have, however, been criticised, e.g. by Azzouni, for interpreting the capacities found by cognitive science in an overly numerical way. I offer an alternative framework for the way these psychological processes can be combined, forming the basis for an epistemology for arithmetic. The resulting framework avoids assigning numerical content to the Approximate Number System and Object Tracking System, two systems that have (...)
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