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Why did Frege reject the theory of types?

Wim Vanrie (UGent)
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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 of Frege’s response, I investigate his conception of the nature of the logical categories, and how it differs from Russell’s. I argue that, for Frege, our grasp of the logical categories cannot be severed from our grasp of the Begriffsschrift notation itself. Russell, on the other hand, attaches no such importance to notation. From Frege’s point of view, Russell has not succeeded in presenting an alternative conception of the logical hierarchy, since such a conception must go together with the development of a notation. Moreover, Frege has good reasons to think that Russell’s proposal does not admit of a suitable notation.
Keywords
Philosophy, Logic, History of philosophy, History of logic, Gottlob Frege, Bertrand Russell, Theory of types, Logical categories, Begriffsschrift

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Citation

Please use this url to cite or link to this publication:

MLA
Vanrie, Wim. “Why Did Frege Reject the Theory of Types?” BRITISH JOURNAL FOR THE HISTORY OF PHILOSOPHY, vol. 29, no. 3, 2021, pp. 517–36, doi:10.1080/09608788.2020.1807908.
APA
Vanrie, W. (2021). Why did Frege reject the theory of types? BRITISH JOURNAL FOR THE HISTORY OF PHILOSOPHY, 29(3), 517–536. https://doi.org/10.1080/09608788.2020.1807908
Chicago author-date
Vanrie, Wim. 2021. “Why Did Frege Reject the Theory of Types?” BRITISH JOURNAL FOR THE HISTORY OF PHILOSOPHY 29 (3): 517–36. https://doi.org/10.1080/09608788.2020.1807908.
Chicago author-date (all authors)
Vanrie, Wim. 2021. “Why Did Frege Reject the Theory of Types?” BRITISH JOURNAL FOR THE HISTORY OF PHILOSOPHY 29 (3): 517–536. doi:10.1080/09608788.2020.1807908.
Vancouver
1.
Vanrie W. Why did Frege reject the theory of types? BRITISH JOURNAL FOR THE HISTORY OF PHILOSOPHY. 2021;29(3):517–36.
IEEE
[1]
W. Vanrie, “Why did Frege reject the theory of types?,” BRITISH JOURNAL FOR THE HISTORY OF PHILOSOPHY, vol. 29, no. 3, pp. 517–536, 2021.
@article{8678214,
  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 of Frege’s response, I investigate his conception of the nature of the logical categories, and how it differs from Russell’s. I argue that, for Frege, our grasp of the logical categories cannot be severed from our grasp of the Begriffsschrift notation itself. Russell, on the other hand, attaches no such importance to notation. From Frege’s point of view, Russell has not succeeded in presenting an alternative conception of the logical hierarchy, since such a conception must go together with the development of a notation. Moreover, Frege has good reasons to think that Russell’s proposal does not admit of a suitable notation.}},
  author       = {{Vanrie, Wim}},
  issn         = {{0960-8788}},
  journal      = {{BRITISH JOURNAL FOR THE HISTORY OF PHILOSOPHY}},
  keywords     = {{Philosophy,Logic,History of philosophy,History of logic,Gottlob Frege,Bertrand Russell,Theory of types,Logical categories,Begriffsschrift}},
  language     = {{eng}},
  number       = {{3}},
  pages        = {{517--536}},
  title        = {{Why did Frege reject the theory of types?}},
  url          = {{http://doi.org/10.1080/09608788.2020.1807908}},
  volume       = {{29}},
  year         = {{2021}},
}

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