What makes certain definitions fruitful? And how can definitions play an explanatory role? The purpose of this paper is to examine these questions via an investigation of Frege’s treatment of definitions. Specifically, I pursue this issue via an examination of Frege’s views about the scientific unification of logic and arithmetic. In my view, what interpreters have failed to appreciate is that logicism is a project of unification, not reduction. For Frege, unification involves two separate steps: (1) an account of the content expressed by arithmetical claims and (2) the justification of that content. The distinction between these steps allows us to see that there are two notions of definition at play in Frege’s logicist work, viz., one concerned with conceptual analysis, the other concerned with the construction of gap-free proof. I then use this discussion to explain how Frege employs his definitions to defend an epistemological thesis about arithmetic, and to clarify Grundlagen’s fruitfulness condition of definitions, and thereby address two interpretive puzzles from the recent literature.
...More
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/)
Book
Weiner, Joan;
(2004)
Frege Explained: From Arithmetic to Analytic Philosophy
(/isis/citation/CBB000772767/)
Chapter
Goldfarb, Warren;
(2010)
Frege's Conception of Logic
(/isis/citation/CBB001211649/)
Article
Schirn, Matthias;
(1994)
Frege y los nombres de cursos de valores
(/isis/citation/CBB000048691/)
Article
Babbitt, Donald;
Goodstein, Judith;
(2011)
Federigo Enriques's Quest to Prove the “Completeness Theorem”
(/isis/citation/CBB001211747/)
Article
Centrone, Stefania;
(2012)
Das Problem der apagogischen Beweise in Bolzanos Beyträgen und seiner Wissenschaftslehre
(/isis/citation/CBB001210996/)
Article
Centrone, Stefania;
(2012)
Strenge Beweise und das Verbot der metábasis eis állo génos
(/isis/citation/CBB001210991/)
Article
Anellis, Irving;
(2012)
Jean van Heijenoort's Contributions to Proof Theory and Its History
(/isis/citation/CBB001214119/)
Article
Bellissima, Fabio;
(2002)
Il sistema assiomatico-deduttivo degli Elementi armonici di Aristosseno
(/isis/citation/CBB000411050/)
Book
Yrjönsuuri, Mikko;
(2001)
Medieval Formal Logic: Obligations, Insolubles and Consequences
(/isis/citation/CBB000102010/)
Article
Hunter, David A.;
(1996)
Definition in Frege's Foundations of arithmetic
(/isis/citation/CBB000072012/)
Book
Frege, Gottlob;
(1999)
Zwei Schriften zur Arithmetik: Funktion und Begriff; Ueber die Zahlen des Herrn H. Schubert. Hrsg. von Kienzler, Wolfgang
(/isis/citation/CBB000082256/)
Article
Tappenden, Jamie;
(1995)
Geometry and generality in Frege's philosophy of arithmetic
(/isis/citation/CBB000062899/)
Article
Blanchette, Patricia A.;
(1994)
Frege's reduction
(/isis/citation/CBB000059170/)
Chapter
Diamond, Cora;
(2010)
Inheriting from Frege: The Work of Reception, as Wittgenstein Did It
(/isis/citation/CBB001211660/)
Article
Kessler, Glenn;
(1980)
Frege, Mill, and the foundations of arithmetic
(/isis/citation/CBB000006426/)
Article
Ruffino, Marco Antonio;
(1991)
Context principle, fruitfulness of logic, and the cognitive value of arithmetic in Frege
(/isis/citation/CBB000041078/)
Article
Dick, Stephanie;
(2011)
AfterMath: The Work of Proof in the Age of Human--Machine Collaboration
(/isis/citation/CBB001220009/)
Article
Abeles, Francine F.;
(2012)
Toward A Visual Proof System: Lewis Carroll's Method of Trees
(/isis/citation/CBB001214122/)
Be the first to comment!