# Axiomatics without foundations. On the model-theoretical viewpoint in modern axiomatics

Philosophia Scientiae (2005)

- Volume: 9, Issue: 2, page 97-107
- ISSN: 1281-2463

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topLenhard, Johannes. "Axiomatics without foundations. On the model-theoretical viewpoint in modern axiomatics." Philosophia Scientiae 9.2 (2005): 97-107. <http://eudml.org/doc/103763>.

@article{Lenhard2005,

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.},

author = {Lenhard, Johannes},

journal = {Philosophia Scientiae},

language = {eng},

number = {2},

pages = {97-107},

publisher = {Éditions Kimé},

title = {Axiomatics without foundations. On the model-theoretical viewpoint in modern axiomatics},

url = {http://eudml.org/doc/103763},

volume = {9},

year = {2005},

}

TY - JOUR

AU - Lenhard, Johannes

TI - Axiomatics without foundations. On the model-theoretical viewpoint in modern axiomatics

JO - Philosophia Scientiae

PY - 2005

PB - Éditions Kimé

VL - 9

IS - 2

SP - 97

EP - 107

AB - 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.

LA - eng

UR - http://eudml.org/doc/103763

ER -

## References

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- [12] Majer, Ulrich2001.— Hilbert’s Axiomatic Method and the Foundations of Science: Historical Roots of Mathe-matical Physics in Göttingen (1900-1930), in (M. Rédei and M. Stöltzner, eds.) John von Neumann and the Foundations of Quantum Physics, Dordrecht: Kluwer, 11–33. MR2042739
- [13] Pasch, Moritz1882.— Vorlesungen über neuere Geometrie, Berlin: Springer.
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