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

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