Functional operations in Frege's Begriffsschrift

History and Philosophy of Logic 9 (1):35-42 (1988)
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Abstract

Frege uses Greek letters in two different ways in his Begriffsschrift. One way is the familiar use of bound variables, in conjunction with variable-binding operators, to mark and close argument-places. The other, which is quite unfamiliar, employs letters to mark places for operators to reach into, without thereby closing these places. Frege thereby invents a powerful and compact notation for functional operations which can be recommended even today. His regrettable double use of Greek letters obscured his invention, and this, together with the fact that in the Grundgesetze he no longer has need of function-valued functions, explains why the device was overlooked and has not passed into general use

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Peter Simons
Trinity College, Dublin

Citations of this work

Frege and the rigorization of analysis.William Demopoulos - 1994 - Journal of Philosophical Logic 23 (3):225 - 245.
Spiritus Asper versus Lambda: On the Nature of Functional Abstraction.Ansten Klev - 2023 - Notre Dame Journal of Formal Logic 64 (2):205-223.
Linguistic Complexity and Argumentative Unity: A Lvov-Warsaw School Supplement.Peter Simons - 2014 - Studies in Logic, Grammar and Rhetoric 36 (1):101-119.

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