Advertisement

Hugh MacColl and George Boole on Hypotheticals

  • Shahid Rahman
Chapter
Part of the Synthese Library book series (SYLI, volume 291)

Abstract

Hugh MacColl (1837–1909), the father of formal non-classical logic, reported that he had developed his early formal system—published as papers in the journals Educational Times, Proceedings of the London Mathematical Society and Mind between 1877 and 1893—without having even read the work of George Boole.1Later on, however, MacColl felt it necessary to publish further papers in order to clarify the basic lines of his concept of logic as opposed to that of Boole. MacColl’s main criticism of Boole may be summarised as follows:
  • Pure logic was devised as an aid for practical uses in argumentation. For MacColl this practical character is due to its abstract nature, which in turn makes generalisations possible. Since pure logic is abstract, its categorical symbols do not stand for numbers or for classes of objects or temporal states, but more generally for statements or propositions. Boole’s logic, in which propositional operations are translated into class operations, is basically not general enough and should be replaced by a Calculus of Equivalent Statements in which propositional connectives occur instead of Boole’s equations.2

  • It could well be that for some sciences the existing argumentation demands a type of logic which is not applicable in others. When constructing a symbolic system for a particular type of logic, the corresponding expressions in use should therefore be taken into careful consideration. In MacColl’s opinion, for example, Boole’s logic coincides neither with the propositions in the theory of probability nor with those in use in natural language, since both the theory of probability and natural language require a strongly connected if-then.3

Keywords

Propositional Variable Problematic Modality Syllogistic Reasoning Material Implication Free Logic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aristotle. 1963. The works of Aristotle translated into English. Vol. I. Oxford: Oxford University Press.Google Scholar
  2. Astroh, M. 1993. Der Begriff der Implikation in einigen frühen Schriften von Hugh McColl. In Stelzner (1993a), 128–44.Google Scholar
  3. Astroh, M. 1995. Subjekt, Prädikat und Modalität. Ein Beitrag zur logischen Rekonstruktion einer kategorischen Syllogistik. Typescript.Google Scholar
  4. Astroh, M. 1996. Präsupposition und Implikatur. In Dascal et al. (1992–96), Vol. II, 1391–1407.Google Scholar
  5. Bain, A. 1870. Logic. 2 vols. London: Longmans, Green and Reader.Google Scholar
  6. Bochenski, I.M. 1956. Formale Logik. Freiburg/München: Alber.Google Scholar
  7. Boethius, A.M.S. 1969. De hypotheticis syllogismes. Edited, commented and translated by Luca Libertello. Brescia: Paideia.Google Scholar
  8. Boole, G. [1847] 1965. The mathematical analysis of logic, being an essay towards a calculus of deductive reasoning. Reprint, Oxford: Basil Blackwell.Google Scholar
  9. Boole, G. [1854] 1958. An investigation of the laws of thought on which are founded the mathematical theories of logic and probabilities. Reprint, New York: Dover.Google Scholar
  10. Dascal, M., D. Gerhardus, K. Lorenz, and G. Meggle, eds. 1992–96. Sprachphilosophie, Philosophy of Language, La philosophie du langage, Vol. I (1992), Vol. II (1996), Berlin: Walter de Gruyter.Google Scholar
  11. Grover, D., J.L. Camp, and N.D. Belnap. 1975. A prosentential theory of truth. Philosophical Studies 27: 73–125.CrossRefGoogle Scholar
  12. Hamilton, W. [1861] 1966. Lectures on logic. In Lectures on metaphysics and logic, edited by H.L. Mansel and J. Veitch. Edinburgh: W. Blackwood. Reprint, Stuttgart: Frommann-Holzboog.Google Scholar
  13. Jevons, W.S. 1864. Pure logic or the logic of quality apart from quantity. In Jevons (1890), 1–79.Google Scholar
  14. Jevons, W.S. [1890] 1971. Pure logic and other minor works. Reprint, New York: Burt Franklin.Google Scholar
  15. Kant, I. 1800. Immanuel Kants Logik, ein Handbuch zu Vorlesungen. In Kant (1983, vol. 5, 421–582).Google Scholar
  16. Kant, I. 1983. Kant. Werke. 10 vols. Darmstadt: Wissenschaftliche Buchgesellschaft.Google Scholar
  17. Kneale, W., and M. Kneale. 1962. The development of logic. Oxford: Clarendon Press.Google Scholar
  18. Lambert, J. [1781] 1965. Logische und Philosophische Abhandlungen, edited by J. Bernoulli. Leipzig: Wendler. Reprint, Hildesheim: Olms.Google Scholar
  19. Lorenz, K. 1996. Artikulation und Prädikation. In Dascal, Gerhardus, Lorenz, and Meggle (1992–96), vol. 2, 1098–1122.Google Scholar
  20. Lukasiewicz, J. 1951. Aristotle’s syllogistic from the standpoint of modern formal logic. Oxford: Clarendon Press.Google Scholar
  21. MacColl, H. 1877a. Symbolical or abbreviated language, with an application to mathematical probability. The Educational Times and Journal of the College of Preceptors 29: 91–2.Google Scholar
  22. MacColl, H. 1877b. The calculus of equivalent statements and integration limits. Proceedings of the London Mathematical Society 9: 9–20.Google Scholar
  23. MacColl, H. 1878. The calculus of equivalent statements (II). Proceedings of the London Mathematical Society 9: 177–86.Google Scholar
  24. MacColl, H. 1880. Symbolical reasoning (I). Mind 5: 45–60.CrossRefGoogle Scholar
  25. MacColl, H. 1882. On the growth and use of a symbolical language. Memoirs of the Manchester Literary and Philosophical Society 7: 225–48.Google Scholar
  26. MacColl, H. 1897. Symbolic reasoning (II). Mind 6: 493–510.CrossRefGoogle Scholar
  27. MacColl, H. 1900. Symbolic reasoning (III). Mind 9: 75–84.CrossRefGoogle Scholar
  28. MacColl, H. 1902. Symbolic reasoning (IV). Mind 11: 352–68.CrossRefGoogle Scholar
  29. MacColl, H. 1905. Symbolic reasoning (VI). Mind 14: 74–81.CrossRefGoogle Scholar
  30. MacColl, H. 1906. Symbolic logic and its applications. London: Longmans, Green.Google Scholar
  31. MacColl, H. 1908. If and imply. Mind 17: 453–5.CrossRefGoogle Scholar
  32. McCall, S. 1963. Aristotle’s modal syllogisms. Amsterdam: North-Holland.Google Scholar
  33. McCall, S. 1964. A new variety of implication. Journal of Symbolic Logic 29: 151–2.Google Scholar
  34. McCall, S. 1966. Connexive implication. Journal of Symbolic Logic 31: 415–32.CrossRefGoogle Scholar
  35. McCall, S. 1967a. Connexive implication and the syllogism. Mind 76: 346–56.CrossRefGoogle Scholar
  36. McCall, S. 1967b. MacColl. In The Encyclopedia of Philosophy, edited by P. Edwards. London: Macmillan. 4: 545–6.Google Scholar
  37. Patzig, G. 1969. Die aristotelische Syllogistik. Logisch-philologische Untersuchungen über das Buch A der „ Ersten Analytiken “. 3rd ed. Göttingen: Vandenhoeck & Ruprecht.Google Scholar
  38. Ploucquet, G. [1776] 1970. Sammlung der Schriften, welche den logischen Kalkül des Herrn Prof. Ploucquet betreffen. Frankfurt: A.F. Bök. Reprint, Stuttgart: Frommann-Holzboog.Google Scholar
  39. Prior, A.N. 1949. Categoricals and hypotheticals in George Boole and his successors. Australasian Journal of Philosophy 27: 171–96.CrossRefGoogle Scholar
  40. Rahman, S. 1997a. Hugh MacColl—eine bibliographische Erschließung seiner Hauptwerke und Notizen zu ihrer Rezeptionsgeschichte. History and Philosophy of Logic 18: 165–83.CrossRefGoogle Scholar
  41. Rahman, S. 1997b. Die Logik der zusammenhängenden Behauptungen im frühen Werk von Hugh MacColl. Basel: Birkhäuser, forthcoming.Google Scholar
  42. Rahman, S. 1999. Ways of understanding Hugh MacColl’s concept of symbolic existence. Nordic Journal of Philosophical Logic 3: 35–58.Google Scholar
  43. Rahman, S., and H. Rückert. 1998. Die Logik der Zusammenhängenden Aussagen: ein dialogischen Ansatz zur konnexen Logik. Fachrichtung 5.1 — Philosophie, Universität des Saarlandes, Memo no 28, September 1999.Google Scholar
  44. Rahman, S., H. Rückert, and M. Fishmann. 2000. On dialogues and ontology. The dialogical approach to free logic. Logique et Analyse, forthcoming.Google Scholar
  45. Sextus Empiricus. 1976. Sextus Empiricus, with an English translation by R.G. Bury. Vol. 1. Loeb Classical Library. Cambridge Mass.: Harvard University Press.Google Scholar
  46. Stelzner, W. 1993a. Philosophie und Logik, Frege-Kolloquien Jena 1989/1991. Berlin: Walter de Gruyter.Google Scholar
  47. Stelzner, W. 1993b. Hugh MacColl—Ein Klassiker der nicht-klassischen Logik. In Stelzner (1993a), 145–54.Google Scholar
  48. Strawson, P. 1950. Truth II. In Truth, edited by George Pitcher. Englewood Cliffs: Prentice-Hall. Venn, J. [1881] 1971. Symbolic logic. Reprint, New York: Chelsea (unaltered reprint of the 2nd ed. of 1894).Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2000

Authors and Affiliations

  • Shahid Rahman
    • 1
  1. 1.Fachrichtung 5.1. — PhilosophieUniversität des SaarlandesSaarbrückenGermany

Personalised recommendations