Axiomatics Without Foundations. On the Model-theoretical Viewpoint In Modern Axiomatics
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...
Spremljeno u:
| Glavni autor: | |
|---|---|
| Format: | Article ou chapitre numérique |
| Jezik: | Français |
| Izdano: |
2005
|
| Online pristup: | Accès Université d'Orléans et IFPM Accès Université d'Orléans et IFPM |
| Sažetak: | 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. |
|---|