Axiomatics Without Foundations. On the Model-theoretical Viewpoint In Modern Axiomatics
Résumé
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.
Notes de l’auteur
My standpoint and arguments are based on common work with Michael Otte [Lenhard and Otte 2002]. I acknowledge the helpful comments given at PILM.
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Référence papier
Johannes Lenhard, « Axiomatics Without Foundations. On the Model-theoretical Viewpoint In Modern Axiomatics », Philosophia Scientiæ, 9-2 | 2005, 97-107.
Référence électronique
Johannes Lenhard, « Axiomatics Without Foundations. On the Model-theoretical Viewpoint In Modern Axiomatics », Philosophia Scientiæ [En ligne], 9-2 | 2005, mis en ligne le 15 juin 2011, consulté le 10 octobre 2024. URL : http://journals.openedition.org/philosophiascientiae/526 ; DOI : https://doi.org/10.4000/philosophiascientiae.526
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