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Gentzen’s Approach to Logic

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Rethinking Logic: Logic in Relation to Mathematics, Evolution, and Method

Part of the book series: Logic, Argumentation & Reasoning ((LARI,volume 1))

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Abstract

In Chapter 10 it has been argued that Frege’s analysis of deduction does not achieve his ideal of atomizing deduction. A better approximation to this ideal is provided by Gentzen’s analysis of deduction. In order to describe it, we need to fix some terminology and notation about first-order languages.

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Notes

  1. 1.

    Gentzen sequent calculus rules give an analysis of deducibility rather than deduction.

  2. 2.

    See Gentzen (1969, 77).

  3. 3.

    Ibid., 80.

  4. 4.

    Ibid., 81.

  5. 5.

    Prawitz (1971, 247).

  6. 6.

    Ibid.

  7. 7.

    Ibid., 246.

  8. 8.

    Ibid., 247.

  9. 9.

    Ibid.

  10. 10.

    Ibid., 259.

  11. 11.

    Prawitz (2011, 393).

  12. 12.

    Ibid., 387.

  13. 13.

    Prawitz (1971, 248).

  14. 14.

    See Prawitz (2006, 35–38); Prawitz (1971, 252–253).

  15. 15.

    See Prawitz (2006, 51); Prawitz (1971, 253).

  16. 16.

    See Prawitz (2006, 50–51).

  17. 17.

    Prawitz (1971, 259).

  18. 18.

    See Prawitz (2006, 53).

  19. 19.

    Gentzen (1969, 69).

  20. 20.

    Ibid., 149.

  21. 21.

    Ibid., 154.

  22. 22.

    Ibid., 153.

  23. 23.

    Prawitz (2006, 35).

  24. 24.

    Ibid., 39–41.

  25. 25.

    Gentzen (1969, 68).

  26. 26.

    Ibid., 79.

  27. 27.

    Ibid., 255.

  28. 28.

    See Shoesmith and Smiley (1978); Ungar (1992).

  29. 29.

    Gentzen (1969, 255).

  30. 30.

    See Cellucci (1992).

  31. 31.

    Zimmermann (2002, 562).

  32. 32.

    Prawitz (2011, 394, footnote 6).

  33. 33.

    See Read (2010); Wansing (2006).

  34. 34.

    Prawitz (2011, 395).

  35. 35.

    Belnap (1962, 1932).

References

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Authors and Affiliations

  1. Sapienza University of Rome, Rome, Italy

    Carlo Cellucci

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  1. Carlo Cellucci
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Cellucci, C. (2013). Gentzen’s Approach to Logic. In: Rethinking Logic: Logic in Relation to Mathematics, Evolution, and Method. Logic, Argumentation & Reasoning, vol 1. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-6091-2_11

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