May 2023 Spiritus Asper versus Lambda: On the Nature of Functional Abstraction
Ansten Klev
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Notre Dame J. Formal Logic 64(2): 205-223 (May 2023). DOI: 10.1215/00294527-10670089

Abstract

The spiritus asper as used by Frege in a letter to Russell from 1904 bears resemblance to Church’s lambda. It is natural to ask how they relate to each other. An alternative approach to functional abstraction developed by Per Martin-Löf some thirty years ago allows us to describe the relationship precisely. Frege’s spiritus asper provides a way of restructuring a unary function name in Frege’s sense such that the argument place indicator occurs all the way to the right. Martin-Löf’s alternative approach shows that this is only half of what lambda does. The other half is the deletion of the argument place indicator, resulting in what Frege would have called an isolated function name.

Citation

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Ansten Klev. "Spiritus Asper versus Lambda: On the Nature of Functional Abstraction." Notre Dame J. Formal Logic 64 (2) 205 - 223, May 2023. https://doi.org/10.1215/00294527-10670089

Information

Received: 9 June 2022; Accepted: 12 March 2023; Published: May 2023
First available in Project Euclid: 27 June 2023

MathSciNet: MR4609005
zbMATH: 07720263
Digital Object Identifier: 10.1215/00294527-10670089

Subjects:
Primary: 00A30 , 03A05
Secondary: 03B38 , 03B40

Keywords: functional abstraction , Gottlob Frege , typed lambda calculus

Rights: Copyright © 2023 University of Notre Dame

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Vol.64 • No. 2 • May 2023
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