The Nature and Contents of Number Concepts

Description of the Project

This is a project being done in collaboration with Richard Samuels and Stewart Shapiro. Very broadly, the project is concerned with numerical talk and thought. What are the meanings of numerical expressions, and what, if anything, can these tell us about traditional questions within philosophy of mathematics? What is the nature of our numerical thoughts and the numerical concepts featuring in them? How do we acquire those concepts, and how might this shed light on arithmetic knowledge? Thus, we conceive of the project as largely interdisciplinary in nature, bringing issues from linguistics, cognitive science and developmental psychology, and the philosophy of mathematics to bear on each other. In addition to the publications listed below, we have two monographs currently under contract related to the project. The first, contracted with Cambridge University Press, is short and is centrally concerned with theories of number concepts. The second, contracted with Oxford University Press, is longer and concerns the interplay of the various questions posed above. 

Research Relevant to the Project

There are several publications of potential relevance to the project. These include:

• Number Concepts: An Interdisciplinary Inquiry

• Semantics and the Ontology of Number

• Computability, Notation, and de re Knowledge of Numbers

• Unwarranted Philosophical Assumptions in Research on ANS 

• Resolving Frege's Other Puzzle

• Hofweber's Nominalist Naturalism

• Hale's Argument from Transitive Counting

• Neologicism, Frege's Constraint, and the Frege-Heck Condition

• Numbers and Cardinalities: What's Really Wrong with the Easy Argument for Numbers?

• Cardinals, Ordinals, and the Prospects for a Neo-Fregean Foundations

• Frege on the Real Numbers