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Frege’s Ontological Diagram Completed

Abstract

In a letter of 1891, Frege drew a diagram to illustrate his logical ontology. We observe that it omits features that play an important role in his thought on the matter, propose an extension of the diagram to include them, and compare with a diagram of the ontology of current first-order logic.

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Notes

  1. Letter to Husserl 24.5.1891, extract translated by Hans Kaal in McGuinness et al. 1980 pp. 63–64, reproduced in Beaney 1997 pp. 149–150. In some other English translations of Frege’s work, Bedeutung is translated as “reference” or as “meaning” (the latter perhaps rather misleadingly, cf. the discussion in Simons 1992 p. 758 note 15), while “proposition” and “concept word” in the top row of Fig. 1 are sometimes rendered as “sentence” and “predicate” respectively.

  2. Comments on Sense and Meaning, ms of 1892–1895, translated in Beaney 1997 pp. 172–180 with the passage quoted on p. 180. Also in Hermes et al. 1979 pp. 118–125 with the passage quoted on pp. 124–125 and where “Bedeutung” is translated as “meaning”.

  3. Logic, ms of 1897, translated in Beaney 1997 pp. 227–252 with the passage quoted on p. 229. Also in Hermes et al. 1979 pp. 126–151 with the passage quoted on p. 129.

  4. Introduction to Logic, ms of 1906, translated in Beaney 1997 pp. 293–298 with the passage quoted on p. 293. Also in Hermes et al. 1979 pp. 185–196 with the passage quoted on p. 191 and where “Bedeutung” is translated as “meaning”.

  5. Logic in Mathematics, ms of 1914, translated in Hermes et al. 1979 pp. 203–250 with the passage quoted on p. 233.

  6. Thomas Le Myésier Breviculum, cited by Even–Ezra 2021 with Latin original on p. 208 note 52 and an English translation on p. 47. Thomas was a disciple of Ramón Lull. We have taken the liberty of editing Even–Ezra’s translation a little for fluidity.

  7. See e.g. Frege 1903 p. 253. Indeed, he came to think that the introduction of extensions of concepts is, at least in part, responsible for the contradiction in his attempted reconstruction of mathematics. For example, in a letter of 1912 to Jourdain he writes: “And now we know that when classes are introduced, a difficulty, (Russell contradiction) arises ... Only with difficulty did I resolve to introduce classes (or extents of concepts) because the matter did not appear to me to be quite secure–and rightly so as it turned out.” This letter is translated in McGuinness 1980 p. 191 and is quoted in Hill 1995 p. 159.

References

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Acknowledgements

Thanks to Alexei Muravitsky, Peter Simons, Werner Stelzner and two anonymous reviewers for helpful comments and suggestions.

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Correspondence to David Makinson.

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Makinson, D. Frege’s Ontological Diagram Completed. Log. Univers. (2022). https://doi.org/10.1007/s11787-022-00308-6

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  • DOI: https://doi.org/10.1007/s11787-022-00308-6

Keywords

  • Frege
  • Ontological
  • Diagram
  • extensional

Mathematics Subject Classification

  • Primary: 0303
  • Secondary: 03A05
  • 03B10