IsisCB Explore

Article ID: CBB001211482

Diagrammatic Reasoning in Frege's Begriffsschrift (2012)

Synthese
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

Outside Links

WorldCat

Google Scholar

JSTOR

Academia.edu

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.

...More

Included in

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

Citation URI

http://data.isiscb.org/isis/citation/CBB001211482/

Citations Indexes

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/)

Book Künne, Wolfgang; (2010)
Die Philosophische Logik Gottlob Freges: ein Kommentar; mit den Texten des Vorworts zu Grundgesetze der Arithmetik und der Logischen Untersuchungen I--IV (/isis/citation/CBB001210615/)

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 Textora, Mark; (2013)
“Thereby We Have Broken with the Old Logical Dualism”---Reinach on Negative Judgement and Negation (/isis/citation/CBB001211948/)

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/)