RT Journal Article
T1 Function and argument in Begriffsschrift
A1 Badesa, Calixto
A1 Bertran-San-Millán, Joan
AB It is well known that the formal system developed by Frege in Begriffsschrift is based upon the distinction between function and argument—as opposed to the traditional distinction between subject and predicate. Almost all of the modern commentaries on Frege's work suggest a semantic interpretation of this distinction, and identify it with the ontological structure of function and object, upon which Grundgesetze is based. Those commentaries agree that the system proposed by Frege in Begriffsschrift has some gaps, but it is taken as an essentially correct formal system for second-order logic: the first one in the history of logic. However, there is strong textual evidence that such an interpretation should be rejected. This evidence shows that the nature of the distinction between function and argument is stated by Frege in a significantly different way: it applies only to expressions and not to entities. The formal system based on this distinction is tremendously flexible and is suitable for making explicit the logical structure of contents as well as of deductive chains. We put forward a new reconstruction of the function-argument scheme and the quantification theory in Begriffsschrift. After that, we discuss the usual semantic interpretation of Begriffsschrift and show its inconsistencies with a rigorous reading of the text.
PB Taylor & Francis
SN 0144-5340
YR 2017
FD 2017
LK https://hdl.handle.net/20.500.14352/132640
UL https://hdl.handle.net/20.500.14352/132640
LA eng
NO Badesa, C. y Bertran-San-Millán, J. (2017) «Function and Argument in Begriffsschrift», History and Philosophy of Logic, 38(4), pp. 316-341. Disponible en: https://doi.org/10.1080/01445340.2017.1354173.
NO Earlier versions of this paper were presented at the APA/ASL 2014 Spring Meeting in San Diego, at the ECAP8 2014 in Bucharest and at the meeting of the Philosophy of Logic group, Department of Philosophy, University of Barcelona.Received 12 May 2016 ; Accepted 08 Jul 2017 ; Published online: 02 Aug 2017.
NO Ministerio de Economía y Competitividad  (España)
NO Universidad de Barcelona
DS Docta Complutense
RD 19 mar 2026