Diagrammatic reasoning in Frege's Begriffsschrift
Document Type
Journal Article
Role
Author
Standard Number
1573-0964
Journal Title
Synthese
Volume
186
Issue
1
First Page
289
Last Page
314
Publication Date
2012
Abstract
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. --author-supplied description
Repository Citation
Macbeth, Danielle. “Diagrammatic Reasoning in Frege’s Begriffsschrift”, Synthese 186: 289-314. Special issue: Diagrams in Mathematics: History and Philosophy. 2012.