, Volume 131, Issue 3, pp 371–388 | Cite as

Is Hintikka's Logic First-Order?

  • Matti Eklund
  • Daniel Kolak


Jaakko Hintikka has argued that ordinary first-order logic should be replaced byindependence-friendly first-order logic, where essentially branching quantificationcan be represented. One recurring criticism of Hintikka has been that Hintikka'ssupposedly new logic is equivalent to a system of second-order logic, and henceis neither novel nor first-order. A standard reply to this criticism by Hintikka andhis defenders has been to show that given game-theoretic semantics, Hintikka'sbranching quantifiers receive the exact same treatment as the regular first-orderones. We develop a different reply, based around considerations concerning thenature of logic. In particular, we argue that Hintikka's logic is the logic that bestrepresents the language fragment standard first-order logic is meantto represent. Therefore it earns its keep, and is also properly regarded as first-order.


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  1. Barwise, J.: 1979, 'On Branching Quantifiers in English', Journal of Philosophical Logic 8, 47–80.Google Scholar
  2. Boolos, G.: 1984, 'To Be is to Be a Value of a Variable (or to Be Some Values of Some Variables', Journal of Philosophy81, 430–449.Google Scholar
  3. Boolos, G.: 1985, 'Nominalist Platonism', Philosophical Review 94, 327–344.Google Scholar
  4. Enderton, H. B.: 1970, 'Finite Partially-Ordered Quantifiers', Zeitschrift fur mathematisehe Logik und Grundlagen der Mathematik 16, 393–397.Google Scholar
  5. Fauconnier, G.: 1975, 'Do Quantifiers Branch?', Linguistic Inquiry 6, 555–567.Google Scholar
  6. Hand, M.: 1993, 'A Defense of Branching Quantification', Synthese 95, 115–129.Google Scholar
  7. Hintikka, J.: 1974, 'Quantifiers vs. Quantification Theory', Linguistics and Philosophy 5, 153–177.Google Scholar
  8. Hintikka, J.: 1979, 'Quantifiers in Natural Language: Some Logical Problems', in Esa Saarinen (ed.), Game-Theoretical Semantics, Reidel, Dordrecht, pp. 81–117.Google Scholar
  9. Hintikka, J.: 1996, The Principles of Mathematics Revisited, Cambridge University Press, Cambridge.Google Scholar
  10. Hintikka, J.: 1997, 'No Scope for Scope?', Linguistics and Philosophy 20, 515–544.Google Scholar
  11. Hintikka, J.: 2000, 'Game-Theoretical Semantics as a Challenge to Proof Theory', Nordic Journal of Philosophical Logic 4, 127–141.Google Scholar
  12. Hintikka, J.: forthcoming, 'Independence-Friendly Logic of Which Order?'.Google Scholar
  13. Kolak, D.: 2001, On Hintikka, Wadsworth, Belmont.Google Scholar
  14. Quine, W. v. O.: 1960, 'Variables Explained Away', Proceedings of the American Philosophical Society 104, 343–347.Google Scholar
  15. Rayo, A. and S. Yablo: 2001, 'Nominalism Through De-Nominalization', Noûs 35, 74–92.Google Scholar
  16. Restall, G. and J. C. Beall: 2000, 'Logical Pluralism', Australasian Journal of Philosophy 78, 475–493.Google Scholar
  17. Varzi, A.: forthcoming, 'Words and Objects', in A. Bottani, M. Carrara and D. Giaretta (eds), Individuals, Essence and Identity: Themes of Analytic Metaphysics, Kluwer Academic Publishers, Dordrecht, Boston and London.Google Scholar
  18. Velleman, J. D.: 1999, 'Review of Jaakko Hintikka, The Principles of Mathematics Revisited', Mind 108, 170–179.Google Scholar
  19. Walkoe, W: 1970, 'Finite Partially-Ordered Quantification', Journal of Symbolic Logic 35, 535–555.Google Scholar

Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Matti Eklund
    • 1
  • Daniel Kolak
    • 2
  1. 1.HugvísindastofnunUniversity of IcelandReykjavikIceland
  2. 2.Department of PhilosophyWilliam Paterson UniversityWayne

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