Dual Axiomatics

Reinhard Kahle

doi:10.1007/978-3-030-16673-1_35

Dual Axiomatics

Reinhard Kahle

CMA - Centro de Matemática e Aplicações

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Abstract

Mario Bunge forcefully argues for Dual Axiomatics, i.e., an axiomatic method applied to natural sciences which explicitly takes into account semantic aspects of the concepts involved in an axiomatization. In this paper we will discuss how dual axiomatics is equally important in mathematics; both historically in Hilbert and Bernays’s conception as well as today in a set-theoretical environment.

Original language	English
Title of host publication	Mario Bunge: A Centenary Festschrift
Editors	M. R. Matthews
Place of Publication	Cham
Publisher	Springer
Pages	633-642
ISBN (Electronic)	978-3-030-16673-1
ISBN (Print)	978-3-030-16672-4
DOIs	https://doi.org/10.1007/978-3-030-16673-1_35
Publication status	Published - 2019

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title = "Dual Axiomatics",

abstract = "Mario Bunge forcefully argues for Dual Axiomatics, i.e., an axiomatic method applied to natural sciences which explicitly takes into account semantic aspects of the concepts involved in an axiomatization. In this paper we will discuss how dual axiomatics is equally important in mathematics; both historically in Hilbert and Bernays{\textquoteright}s conception as well as today in a set-theoretical environment.",

author = "Reinhard Kahle",

note = "This work is partially supported by the Portuguese Science Foundation, FCT, through the projects UID/MAT/00297/2019 (Centro de Matem{\'a}tica e Aplica{\c c}{\~o}es) and PTDC/MHC-FIL/2583/2014 (Hilbert{\textquoteright}s 24th Problem), and by the Udo Keller Foundation.",

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AB - Mario Bunge forcefully argues for Dual Axiomatics, i.e., an axiomatic method applied to natural sciences which explicitly takes into account semantic aspects of the concepts involved in an axiomatization. In this paper we will discuss how dual axiomatics is equally important in mathematics; both historically in Hilbert and Bernays’s conception as well as today in a set-theoretical environment.

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