Article ID: CBB001211482

Diagrammatic Reasoning in Frege's Begriffsschrift (2012)


Macbeth, Danielle (Author)

Volume: 186, no. 1
Issue: 1
Pages: 289-314

Publication Date: 2012
Edition Details: Part of a special issue, “Diagrams in Mathematics: History and Philosophy”
Language: English

In Part III of his 1879 logic Frege proves a theorem in the theory of sequences on the basis of four definitions. He claims in Grundlagen that this proof, despite being strictly deductive, constitutes a real extension of our knowledge, that it is ampliative rather than merely explicative. Frege furthermore connects this idea of ampliative deductive proof to what he thinks of as a fruitful definition, one that draws new lines. My aim is to show that we can make good sense of these claims if we read Frege's notation diagrammatically, in particular, if we take that notation to have been designed to enable one to exhibit the (inferentially articulated) contents of concepts in a way that allows one to reason deductively on the basis of those contents.

Included in

Article Mumma, John; Panza, Marco (2012) Diagrams in Mathematics: History and Philosophy. Synthese (pp. 1-5). unapi

Citation URI

Similar Citations

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

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 Weiner, Joan; (2010)
Understanding Frege's Project (/isis/citation/CBB001211648/)

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

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

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

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/)

Chapter Korte, Tapio; Maunu, Ari; Aho, Tuomo; (2009)
Modal Logic from Kant to Possible World Semantics (/isis/citation/CBB001210352/)

Article Centrone, Stefania; (2010)
Functions in Frege, Bolzano and Husserl (/isis/citation/CBB001210980/)

Thesis David E. Dunning; (2020)
Writing the Rules of Reason: Notations in Mathematical Logic, 1847–1937 (/isis/citation/CBB517005733/)

Chapter Heck, Richard; (2010)
Frege and Semantics (/isis/citation/CBB001211655/)

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

Article Günther Eder; (2021)
Frege on intuition and objecthood in projective geometry (/isis/citation/CBB221284966/)

Article Bellucci, Francesco; (2013)
Diagrammatic Reasoning: Some Notes on Charles S. Peirce and Friedrich A. Lange (/isis/citation/CBB001213915/)

Book Weiner, Joan; (2004)
Frege Explained: From Arithmetic to Analytic Philosophy (/isis/citation/CBB000772767/)

Authors & Contributors
Weiner, Joan
Eder, Günther
Heijenoort, Jean van
Käufer, Stephan
Thiel, Christian
Haaparanta, Leila
History and Philosophy of Logic
History of Philosophy Quarterly
British Journal for the History of Philosophy
Harvard University Press
Open Court
Vittorio Klostermann
Cambridge University Press
Princeton University
Philosophy of mathematics
Frege, Gottlob
Peirce, Charles Sanders
Husserl, Edmund
Gödel, Kurt
Hegel, Georg Wilhelm Friedrich
Wolff, Christian von
Time Periods
19th century
20th century, early
20th century
North America

Be the first to comment!

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

Log in or register to comment