, Volume 170, Issue 3, pp 371–391 | Cite as

Bad company tamed

  • Øystein LinneboEmail author


The neo-Fregean project of basing mathematics on abstraction principles faces “the bad company problem,” namely that a great variety of unacceptable abstraction principles are mixed in among the acceptable ones. In this paper I propose a new solution to the problem, based on the idea that individuation must take the form of a well-founded process. A surprising aspect of this solution is that every form of abstraction on concepts is permissible and that paradox is instead avoided by restricting what concepts there are.


Abstraction Frege Logicism Neo-Fregeanism Paradox 


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  1. Boolos, G. (1987). The consistency of Frege’s foundations of arithmetic. In J. Thomson (Ed.), On beings and sayings: Essays in honor of Richard Cartwright (pp. 3–20). Cambridge: MIT Press, Reprinted in Boolos [1998].Google Scholar
  2. Boolos, G. (1990). The standard of equality of numbers. In G. Boolos (Ed.), Meaning and method: Essays in honor of Hilary Putnam. Cambridge: Harvard University Press, Reprinted in Boolos [1998].Google Scholar
  3. Boolos, G. (1997). Is Hume’s principle analytic? In R. Heck (Ed.), Logic, language, and thought. Oxford: Oxford University Press, Reprinted in Boolos [1998].Google Scholar
  4. Boolos G. (1998). Logic, logic, and logic. Cambridge, Harvard University PressGoogle Scholar
  5. Burgess J.P. (2005). Fixing Frege. Princeton, Princeton University PressGoogle Scholar
  6. Cook R., Ebert P. (2005). Abstraction and identity. Dialectica 59(2): 121–139CrossRefGoogle Scholar
  7. Eklund, M. (2008). Bad company and neo-Fregean philosophy. Synthese, doi:  10.1007/s11229-007-9262-x.
  8. Fine K. (2002). The limits of abstraction. Oxford, Oxford University PressGoogle Scholar
  9. Fine K. (2005a). Class and membership. Journal of Philosophy 102(11): 547–572Google Scholar
  10. Fine K. (2005b). Our knowledge of mathematical objects. In: Gendler T.S., Hawthorne J. (eds). Oxford studies in epistemology (Vol. 1). Oxford, Oxford University Press, pp. 89–109Google Scholar
  11. Frege G. (1953). Foundations of arithmetic (trans.: Austin, J. L.). Oxford, BlackwellGoogle Scholar
  12. Frege G. (1964). Basic laws of arithmetic (Ed. and trans.: Montgomery Furth). University of California Press, Berkeley and Los AngelesGoogle Scholar
  13. Hale B., Wright C. (2001). Reason’s proper study. Oxford, ClarendonCrossRefGoogle Scholar
  14. Heck R.G. (1996). The consistency of predicative fragments of Frege’s Grundgesetze der Arithmetik. History and Philosophy of Logic 17, 209–220CrossRefGoogle Scholar
  15. Hodes H. (1984). On modal logics which enrich first-order S5. Journal of Philosophical Logic 13, 423–454Google Scholar
  16. Leitgeb H. (2005). What truth depends on. Journal of Philosophical Logic 34, 155–192CrossRefGoogle Scholar
  17. Linnebo Ø. (2004). Frege’s proof of referentiality. Notre Dame Journal of Formal Logic 45(2): 73–98CrossRefGoogle Scholar
  18. Linnebo Ø. (2006). Sets, properties, and unrestricted quantification. In Rayo A., Uzquiano G. (eds). Absolute generality. Oxford, Oxford University Press, pp. 149–178Google Scholar
  19. Linnebo, Ø. (2008). Introduction. Synthese, doi:  10.1007/s11229-007-9267-5.
  20. Parsons, C. (1983). Sets and modality. Mathematics in philosophy (pp. 298–341). Cornell: Cornell University Press.Google Scholar
  21. Shapiro S. (2000). Frege meets Dedekind: A neologicist treatment of real analysis. Notre Dame Journal of Formal Logic 41(4): 335–364CrossRefGoogle Scholar
  22. Uzquiano, G. (2008). Bad company generalized. Synthese, doi:  10.1007/s11229-007-9266-6.
  23. Wright C. (1999). Is Hume’s principle analytic?. Notre Dame Journal of Formal Logic 40(1): 6–30 Reprinted in Hale and Wright [2001]CrossRefGoogle Scholar

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© Springer Science+Business Media B.V. 2007

Authors and Affiliations

  1. 1.Department of PhilosophyUniversity of BristolBristolUK

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