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Axiomatics Without Foundations. On the Model-theoretical Viewpoint In Modern Axiomatics

Johannes Lenhard
p. 97-107

Abstract

Two conflicting interpretations of modern axiomatics will be considered. The logico-analytical interpretation goes back to Pasch, while the model-theoretical approach stems from Hilbert. This perspective takes up the distinction between logic as calculus ratiocinator versus lingua characterica that Heijenoort and Hintikka placed emphasis on. It is argued that the Heijenoort-Hintikka distinction can be carried over from logic to mathematical axiomatics. In particular, the model-theoretical viewpoint is deeply connected to a philosophy of mathematics that is not committed to a foundational perspective, but oriented more at applications and at mathematical practice.

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Author’s notes

My standpoint and arguments are based on common work with Michael Otte [Lenhard and Otte 2002]. I acknowledge the helpful comments given at PILM.

References

Bibliographical reference

Johannes Lenhard, Axiomatics Without Foundations. On the Model-theoretical Viewpoint In Modern Axiomatics Philosophia Scientiæ, 9-2 | 2005, 97-107.

Electronic reference

Johannes Lenhard, Axiomatics Without Foundations. On the Model-theoretical Viewpoint In Modern Axiomatics Philosophia Scientiæ [Online], 9-2 | 2005, Online since 15 June 2011, connection on 28 March 2024. URL: http://journals.openedition.org/philosophiascientiae/526; DOI: https://doi.org/10.4000/philosophiascientiae.526

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About the author

Johannes Lenhard

University of Bielefeld (Germany)

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Copyright

The text and other elements (illustrations, imported files) are “All rights reserved”, unless otherwise stated.

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