# Understanding Frege's Project

In Thomas G. Ricketts & Michael Potter (eds.), The Cambridge companion to Frege. Cambridge: Cambridge University Press. pp. 32-62 (2010)

 Authors Joan Weiner Indiana University, Bloomington Abstract Frege begins Die Grundlagen der Arithmetik, the work that introduces the project which was to occupy him for most of his professional career, with the question, 'What is the number one?' It is a question to which even mathematicians, he says, have no satisfactory answer. And given this scandalous situation, he adds, there is small hope that we shall be able to say what number is. Frege intends to rectify the situation by providing definitions of the number one and the concept of number. But what, exactly, is required of a definition? Surely it will not do to stipulate that the number one is Julius Caesar - that would change the subject. It seems reasonable to suppose that an acceptable definition must be a true statement containing a description that picks out the object to which the numeral '1' already refers. And, similarly, that an acceptable definition of the concept of number must contain a description that picks out precisely those objects that are numbers - those objects to which our numerals refer. Yet, while Frege writes a great deal about what criteria his definitions must satisfy, the above criteria are not among those he mentions. Nor does he attempt to convince us that his definitions of '1' and the other numerals are correct by arguing that these definitions pick out objects to which these numerals have always referred. Yet, while Frege writes a great deal about what criteria his definitions must satisfy, the above criteria are not among those he mentions. Nor does he attempt to convince us that his definitions of ‘1’ and the other numerals are correct by arguing that these definitions pick out objects to which these numerals have always referred. There is, as we shall see shortly, a great deal of evidence that Frege’s definitions are not intended to pick out objects to which our numerals already refer. But if this is so, how can these definitions teach us anything about our science of arithmetic? And what criteria must these definitions satisfy? To answer these questions, we need to understand what it is that Frege thinks we need to learn about the science of arithmetic. Keywords No keywords specified (fix it) Categories (categorize this paper) Buy the book Find it on Amazon.com Options Mark as duplicate Export citation Request removal from index

PhilArchive copy

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 69,257

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)

## References found in this work BETA

No references found.

## Citations of this work BETA

Carnapian Frameworks.Gabriel L. Broughton - 2021 - Synthese 199 (1-2):4097-4126.
Frege on the Generality of Logical Laws.Jim Hutchinson - 2020 - European Journal of Philosophy (2):1-18.
From Lagrange to Frege: Functions and Expressions.Gabriel Sandu, Marco Panza & Hourya Benis-Sinaceur - 2015 - In Gabriel Sandu, Marco Panza & Hourya Benis-Sinaceur (eds.), Functions and Generality of Logic. Springer Verlag.
Why Did Frege Reject the Theory of Types?Wim Vanrie - 2021 - British Journal for the History of Philosophy 29 (3):517-536.

## Similar books and articles

Putting Frege in Perspective.Joan Carol Weiner - 1982 - Dissertation, Harvard University
Frege's Definition of Number: No Ontological Agenda?Edward Kanterian - 2010 - Hungarian Philosophical Review 54 (4):76-92.
Frege.Joan Carol Weiner - 1999 - Oxford, England: Oxford University Press.
Frege on the Foundation of Geometry in Intuition.Jeremy Shipley - 2015 - Journal for the History of Analytical Philosophy 3 (6).
Frege on Definitions.Sanford Shieh - 2008 - Philosophy Compass 3 (5):992-1012.