Categories, Structures, and the Frege-Hilbert Controversy: The Status of Meta-mathematics

@article{Shapiro2005CategoriesSA,
  title={Categories, Structures, and the Frege-Hilbert Controversy: The Status of Meta-mathematics},
  author={S. Shapiro},
  journal={Philosophia Mathematica},
  year={2005},
  volume={13},
  pages={61-77}
}
  • S. Shapiro
  • Published 2005
  • Mathematics
  • Philosophia Mathematica
There is a parallel between the debate between Gottlob Frege and David Hilbert at the turn of the twentieth century and at least some aspects of the current controversy over whether category theory provides the proper framework for structuralism in the philosophy of mathematics. The main issue, I think, concerns the place and interpretation of metamathematics in an algebraic or structuralist approach to mathematics. Can meta-mathematics itself be understood in algebraic or structural terms? Or… Expand
48 Citations
Structuralism and Meta-Mathematics
Structuralism and MetaMathematics
Reconstructing Hilbert to Construct Category Theoretic Structuralism
How to be a structuralist all the way down
On three arguments against categorical structuralism
  • M. Pedroso
  • Philosophy, Computer Science
  • Synthese
  • 2008
The common foundation of neo-logicism and the Frege-Hilbert controversy
Anti-Foundational Categorical Structuralism
Sets , Categories and Structuralism ∗
Curves in Gödel-Space: Towards a Structuralist Ontology of Mathematical Signs
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 39 REFERENCES
...
1
2
3
4
...