Why did Frege reject the theory of types?

  title={Why did Frege reject the theory of types?},
  author={Wim Vanrie},
  journal={British Journal for the History of Philosophy},
  pages={517 - 536}
  • Wim Vanrie
  • Published 2020
  • Philosophy
  • British Journal for the History of Philosophy
ABSTRACT I investigate why Frege rejected the theory of types, as Russell presented it to him in their correspondence. Frege claims that it commits one to violations of the law of excluded middle, but this complaint seems to rest on a dogmatic refusal to take Russell’s proposal seriously on its own terms. What is at stake is not so much the truth of a law of logic, but the structure of the hierarchy of the logical categories, something Frege seems to neglect. To come to a better understanding… Expand
1 Citations
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  • The Rise of Modern Logic: From Leibniz to Frege
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