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Axiomathes

pp 1–12 | Cite as

Extensions, Numbers and Frege’s Project of Logic as Universal Language

  • Nora GrigoreEmail author
Original Paper
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Abstract

Frege’s famous definition of number (in)famously uses the concept of “extension”. Extensions, in the Fregean framework, are susceptible to bringing many difficulties, and, some say, even paradoxes. Therefore, neo-logicist programs want to avoid the problems and to replace the classical Fregean definition of number with Hume’s Principle (where Frege does not use extensions). I argue that this move, even if it makes sense from a computational point of view, is at odds with Frege’s larger philosophical project. For Frege, I claim, extensions were an important part of his philosophical program of logic-as-an-universal-language. This is why Frege places his project in line with Leibniz’ philosophical project of finding a lingua characterica universalis.

Keywords

Extensions Frege Language Logic Numbers 

Notes

References

  1. Beaney M (1996) Frege: making sense. Duckworth, LondonGoogle Scholar
  2. Beaney M (2005) Sinn, Bedeutung and the paradox of analysis. In: Beaney and Reck IV, pp 288–310Google Scholar
  3. Boolos G (1987) The consistency of Frege’s foundations of arithmetic. In: Thomson JJ (ed) On being and saying: essays for Richard Cartwright. MIT Press, Cambridge, pp 211–233Google Scholar
  4. Demopoulos W (1998) The philosophical basis of our knowledge of number. Noûs 32(4):81–503CrossRefGoogle Scholar
  5. Demopoulos W (2003) On the philosophical interest of Frege arithmetic. In: Hale B, Wright C (eds) Book symposium: the reason’s proper study Essays towards a Neo-Fregean philosophy of mathematics. Blackwell, OxfordGoogle Scholar
  6. Dummett M (1991) Frege: philosophy of mathematics. Harvard University Press, HarvardGoogle Scholar
  7. Dummett M (1998) Neo-Fregeans: In bad company? In: Schirn M (ed) The philosophy of mathematics today. Clarendon Press, OxfordGoogle Scholar
  8. Frege G (1880/81) Boole’s logical calculus and the concept-script. In: Hermes, Kambaratel, Kaulbach (eds) and Long P, White R (trans) Posthumous writings. University of Chicago Press, 1979Google Scholar
  9. Frege G (1884) Foundations of arithmetic. A logic-mathematical inquiry into the concept of number. Austin J L (ed and translated) Blackwell, 1950Google Scholar
  10. Heck R K (1998) The Julius Caesar objection. In: Language, thought, and logic: essays in honour of Michael Dummett, pp 273–308Google Scholar
  11. Ruffino M (2003) Why Frege would not be a Neo-Fregean. Mind 112:51–78CrossRefGoogle Scholar
  12. Schirn M (2017) Frege on the foundations of mathematics. In: Otávio B (ed) Synthese library series studies in epistemology, logic, methodology, and philosophy of science. Springer, LondonGoogle Scholar
  13. Sluga H (1999) Gottlob Frege. Routledge, LondonGoogle Scholar
  14. van Heijenoort J (1967) Logic as calculus and logic as language. Synthese 17:324–330CrossRefGoogle Scholar
  15. Weiner J (1999) Frege. Oxford University Press, OxfordGoogle Scholar
  16. Wright C (1983) Frege’s conception of numbers as objects. Aberdeen University Press, AberdeenGoogle Scholar
  17. Wright C (1998a) On the harmless impredicativity of N= (‘Hume’s principle’). In: Schirn M (ed) The philosophy of mathematics today. Clarendon Press, OxfordGoogle Scholar
  18. Wright C (1998b) Response to Dummett. In: Schirn M (ed) The philosophy of mathematics today. Clarendon Press, OxfordGoogle Scholar
  19. Wright C (2001) Is Hume’s principle analytic? In The reason’s proper study. Oxford University Press, OxfordGoogle Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.BucharestRomania

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