Chapter ID: CBB001211648

Understanding Frege's Project (2010)

unapi

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.

...More
Included in

Book Ricketts, Tom; Potter, Michael D. (2010) The Cambridge Companion to Frege. unapi

Citation URI
https://data.isiscb.org/isis/citation/CBB001211648/

Similar Citations

Chapter Thiel, Christian; (2009)
Gottlob Frege and the Interplay between Logic and Mathematics (/isis/citation/CBB001210345/)

Book Heijenoort, Jean van; (2002)
From Frege to Gödel: A Source Book in Mathematical Logic, 1879-1931 (/isis/citation/CBB000201415/)

Book Ricketts, Tom; Potter, Michael D.; (2010)
The Cambridge Companion to Frege (/isis/citation/CBB001211647/)

Chapter Goldfarb, Warren; (2010)
Frege's Conception of Logic (/isis/citation/CBB001211649/)

Article Schirn, Matthias; (2010)
On Translating Frege's Die Grundlagen der Arithmetik (/isis/citation/CBB001210971/)

Chapter Wilson, Mark; (2010)
Frege's Mathematical Setting (/isis/citation/CBB001211656/)

Article de Rouilhan, Philippe; (2012)
In Defense of Logical Universalism: Taking Issue with Jean van Heijenoort (/isis/citation/CBB001214124/)

Article Reck, Erich H.; (2013)
Frege, Dedekind, and the Origins of Logicism (/isis/citation/CBB001212886/)

Article Korte, Tapio; (2010)
Frege's Begriffsschrift as a lingua characteristica (/isis/citation/CBB001211456/)

Book Frege, Gottlob; (1999)
Idéographie (/isis/citation/CBB000631020/)

Article Mark Textor; (2021)
Saying Something about a Concept: Frege on Statements of Number (/isis/citation/CBB227044624/)

Thesis Rohloff, Waldemar; (2007)
Kant and Frege on the a priori Applicability of Mathematics (/isis/citation/CBB001561363/)

Article Macbeth, Danielle; (2012)
Diagrammatic Reasoning in Frege's Begriffsschrift (/isis/citation/CBB001211482/)

Book Macbeth, Danielle; (2005)
Frege's Logic (/isis/citation/CBB001211035/)

Chapter Haaparanta, Leila; (2009)
The Relations between Logic and Philosophy, 1874--1931 (/isis/citation/CBB001210347/)

Chapter Peckhaus, Volker; (2009)
The Mathematical Origins of Nineteenth-Century Algebra of Logic (/isis/citation/CBB001210344/)

Article Eder, Günther; (2013)
Remarks on Independence Proofs and Indirect Reference (/isis/citation/CBB001212142/)

Article Weltya, Ivan; (2011)
Frege on Indirect Proof (/isis/citation/CBB001210988/)

Article Käufer, Stephan; (2005)
Hegel to Frege: Concepts and Conceptual Content in Nineteenth-Century Logic (/isis/citation/CBB000670376/)

Authors & Contributors
Macbeth, Danielle
Wilson, Mark D.
Weltya, Ivan
Thiel, Christian
Textor, Mark
Schirn, Matthias
Concepts
Logic
Philosophy
Philosophy of mathematics
Mathematics
Proof
Signs and symbols
Time Periods
19th century
20th century, early
20th century
18th century
Places
Germany
Great Britain
Comments

Be the first to comment!

{{ comment.created_by.username }} on {{ comment.created_on | date:'medium' }}

Log in or register to comment