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1Instituto de Investigaciones Filosóficas, Universidad Nacional Autónoma de México, Circuito Maestro Mario de la Cueva s/n, Cuidad Universitaria, C. P. 04510, Coyoacán México, D.F., Mexico. OMarshall@gradcenter.cuny.eduhttps://olivermarshall.commons.gc.cuny.edu/.
The Behavioral and Brain Sciences
|December 15, 2021
Summary
This study challenges the empirical basis of Clarke and Beck's theory of numbers, suggesting their "weak sensitivity principle" is questionable. Alternative explanations for numerical perception exist without relying on a direct sensory link to abstract numbers.
Area of Science:
- Philosophy of Mathematics
- Epistemology
- Cognitive Science
Background:
- Clarke and Beck propose numbers are second-order and sensible.
- Their theory relies on the "weak sensitivity principle."
Purpose of the Study:
- To critically evaluate the empirical claims underlying Clarke and Beck's view of numbers.
- To explore alternative explanations for the perception of numerical properties.
Main Methods:
- Analysis of the empirical claims in Clarke and Beck's theory.
- Comparative evaluation of explanatory benefits.
Main Results:
- The empirical claim supporting the "weak sensitivity principle" is found to be dubious.
- The purported explanatory benefits of a sensory relation to numbers can be achieved by considering relations to multitudes of objects.
Conclusions:
- Clarke and Beck's theory faces significant empirical challenges.
- A direct sensory relation to numbers is not necessary to explain numerical perception; relations to object collections suffice.
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