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The Discursive Functioning Of Knowledge Claims In Research Studies On Children’S Conceptual Knowledge Of Number, Patrick D. Byers Sep 2016

The Discursive Functioning Of Knowledge Claims In Research Studies On Children’S Conceptual Knowledge Of Number, Patrick D. Byers

All Dissertations, Theses, and Capstone Projects

Researchers interested in the development of conceptual knowledge of number have studied children’s behavior in various tasks or other contexts in order to draw conclusions about what they know. The guiding assumption of this work is that the presence or absence of a given form of knowledge is typically reflected in the ability/inability to perform certain types of behavior. Researchers complicate this assumption when they claim that (1) the ability to perform a given behavior may also reflect simple imitation or rote learning in the absence of understanding, and/or (2) that the inability to perform a certain ...


Toward A Kripkean Concept Of Number, Oliver R. Marshall Feb 2016

Toward A Kripkean Concept Of Number, Oliver R. Marshall

All Dissertations, Theses, and Capstone Projects

Saul Kripke once remarked to me that natural numbers cannot be posits inferred from their indispensability to science, since we’ve always had them. This left me wondering whether numbers are objects of Russellian acquaintance, or accessible by analysis, being implied by known general principles about how to reason correctly, or both. To answer this question, I discuss some recent (and not so recent) work on our concepts of number and of particular numbers, by leading psychologists and philosophers. Special attention is paid to Kripke’s theory that numbers possess structural features of the numerical systems that stand for them ...