Advertisement

The Completion of the Emergence of Modern Logic from Boole’s The Mathematical Analysis of Logic to Frege’s Begriffsschrift

  • Priyedarshi Jetli
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6521)

Abstract

Modern logic begins with Boole’s The Mathematical Analysis of Logic when the algebra of logic was developed so that classical logic syllogisms were proven as algebraic equations and the turn from the logic of classes to propositional logic was suggested. The emergence was incomplete as Boole algebraised classical logic. Frege in Begriffsschrift replaced Aristotelian subject–predicate propositions by function and argument and displaced syllogisms with an axiomatic propositional calculus using conditionals, modus ponens and the law of substitution. Further Frege provided the breakthrough to lay down the groundwork for the development of quantified logic as well as the logic of relations. He achieved all of this through his innovative formal notations which have remained underrated. Frege hence completed the emergence of modern logic. Both Boole and Frege mathematised logic, but Frege’s goal was to logicise mathematics. However the emergence of modern logic in Frege should be detached from his logicism.

Keywords

Boole Frege conditional modus ponens propositional calculus quantifiers function and argument axioms 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Boole, G.: The mathematical analysis of logic: being an essay towards a calculus of deductive reasoning. Macmillan, Barclay and Macmillan, Cambridge (1847)Google Scholar
  2. 2.
    Frege, G.: Begriffsschrift, Eine der arithmetischen nachgebildete Formelsprache des reinen Denkens. Verlag von Louis Nebert, Halle (1879)Google Scholar
  3. 3.
    Frege, G.: Begriffsschrift, a formula language, modeled upon that of arithmetic, for pure thought (translated by Stefan Bauer-Mengelberg). In: van Heijenoort, J. (ed.) From Frege to Gödel: a source book in mathematical logic, 1879–1931, pp. 1–82 (1879). Excel Press, New York (1967)Google Scholar
  4. 4.
    Jetli, P.: The emergence of modern logic. Paper presented at the Third Indian School of Logic and its Applications, University of Hyderabad, India (January 18, 2010), http://ali.cmi.ac.in/isla2010/slides/jetli-lec.pdf
  5. 5.
    Whitehead, A.N., Russell, B.: Principia Mathematica, vol. I. Cambridge University Press, Cambridge (1910)zbMATHGoogle Scholar
  6. 6.
    Couturat, L.: La logique de Leibniz d’après des documents inédits. Felix Alcan, Paris (1901)Google Scholar
  7. 7.
    Peacock, G.: A treatise on algebra. J. and J. J. Deighton, Cambridge (1830)Google Scholar
  8. 8.
    Boole, G.: An investigation of the laws of thought on which are founded the mathematical theories of logic and probabilities. Walton and Maberly, London (1854)Google Scholar
  9. 9.
    Kneale, W., Kneale, M.: The development of logic. Clarendon Press, Oxford (1962)Google Scholar
  10. 10.
    van Heijenoort, J.: Historical development of modern logic. The Review of Modern Logic 2(3), 242–255 (1992)MathSciNetzbMATHGoogle Scholar
  11. 11.
    Haaparanta, L.: Introduction. In: Haaparanta, L. (ed.) The development of modern logic, pp. 3–10. Oxford University Press, Oxford (2009)CrossRefGoogle Scholar
  12. 12.
    Thiel, C.: Gottlob Frege and the interplay between logic and mathematics. In: Haaparanta, L. (ed.) The development of modern logic, pp. 196–202. Oxford University Press, Oxford (2009)CrossRefGoogle Scholar
  13. 13.
    Cavaliere, F.: L’opera di Hugh MacColl alle origini delle logiche non-classiche. The Review of Modern Logic 6(4), 373–402 (1995)Google Scholar
  14. 14.
    Euclid: The thirteen books of Euclid’s Elements. Translated by Sir Thomas L. Heath, vol. I. Dover, New York (1956)zbMATHGoogle Scholar
  15. 15.
    Church, A.: Introduction to mathematical logic. Princeton University Press, Princeton (1956)zbMATHGoogle Scholar
  16. 16.
    Imai, Y., Iséki, K.: On axiom systems of propositional calculi. Proceedings of the Japan Academy 42(1), 19–22 (1966)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Mendelson, E.: Introduction to mathematical logic, 4th edn, 1997. Chapman & Hall, New York (1964)zbMATHGoogle Scholar
  18. 18.
    Lewis, C.I.: A survey of symbolic logic. University of California Press, Berkeley (1918)Google Scholar
  19. 19.
    Jourdain, P.E.B.: Preface. In: Couterat, L. (ed.) The algebra of logic (translated by Lydia Gilingham Robinson), pp. iii–x. The Open Court Publishing Company, Chicago (1914)Google Scholar
  20. 20.
    Green, J.: The algebra of logic: what Boole really started. The Review of Modern Logic 4(1), 48–62 (1994)MathSciNetzbMATHGoogle Scholar
  21. 21.
    Sullivan, P.M.: Frege’s logic. In: Gabbay, D.M., Woods, J. (eds.) Handbook of the history of logic. The rise of modern logic: from Leibniz to Frege, vol. 3, pp. 659–750. Elsevier, London (2004)Google Scholar
  22. 22.
    Houser, N.: Peirce’s logic today: (a report on the logic program of the Peirce Sesquicentennial Congress). The Review of Modern Logic 1(1), 92–101 (1990)MathSciNetGoogle Scholar
  23. 23.
    Ferreiros, J.: The road to modern logic: an interpretation. The Bulletin of Symbolic Logic 7(4), 441–484 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Adamson, R.: A brief history of logic. William Blackwood and Sons, London (1911)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Priyedarshi Jetli
    • 1
  1. 1.Department of PhilosophyUniversity of MumbaiMumbaiIndia

Personalised recommendations