Logica Universalis

, Volume 6, Issue 3–4, pp 477–483 | Cite as

Frege’s Ancestral and Its Circularities

  • Ignacio Angelelli


After presenting the ordinary and the Fregean formulations of the ancestral, I raise the question of what is their relationship, the natural candidate being that the Fregean version is an analysans intended to improve upon, and replace, the common notion of ancestral (the analysandum). Next, two types of circles that arise in connection with the Fregean ancestral are presented, and it is claimed that one of the circles makes it impossible to maintain the just described (“replacement”) interpretation. A reference is made to Kerry, who was the first to point out a circularity in Frege’s ancestral. Some of Frege’s remarks are examined in order to tentatively sketch, an answer to the issue of the relationship between ordinary and Fregean ancestral; the latter, if not as an analysans replacing the common notion, can still be seen as a profound enrichment of the former.

Mathematics Subject Classification



Ancestral analysans analysandum Frege Kerry 


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  1. 1.
    Angelelli I.: Studies on Gottlob Frege and Traditional Philosophy. Reidel, Dordrecht (1967)zbMATHGoogle Scholar
  2. 2.
    Carnap R.: The Logical Syntax of Language. Kegan Paul Trench, Trubner & Co., London (1937)Google Scholar
  3. 3.
    Chisholm R.M., Potter R.C.: The paradox of analysis: a solution. Metaphilosophy 12, 1–6 (1981)CrossRefGoogle Scholar
  4. 4.
    Frege, G.: Begriffsschrift, eine der arithmetischen nachgebildete Formelsprache des reinen Denkens. L. Nebert, Halle (1879)Google Scholar
  5. 5.
    Frege G.: Die Grundlagen der Arithmetik. Wilhelm Koebner, Breslau (1884)Google Scholar
  6. 6.
    Kant, I.: Critique of Pure Reason, English translation by N. Kemp Smith. St Martin’s Press, New York (1965)Google Scholar
  7. 7.
    Kerry B.: Ueber Anschauung und ihre psychische Verarbeitung. Vierter Artikel, Vierteljahrsschrift für wissenschaftliche Philosophie 11, 249–307 (1887)Google Scholar
  8. 8.
    Kolata, G.: Math archive in disarray. Science (New Series) 219(4587), 940 (1983)Google Scholar
  9. 9.
    Linsky, B.: Russell’s notes on Frege for Appendix A of “The Principles of Mathematics”. Russell J. Bertrand Russell Stud. 24, 133–172 (2004–2005)Google Scholar
  10. 10.
    Russell B.: The Principles of Mathematics, 2nd edn. Allen and Unwin, London (1956)Google Scholar

Copyright information

© Springer Basel AG 2012

Authors and Affiliations

  1. 1.Philosophy DepartmentThe University of Texas at AustinAustinUSA

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