Skip to main content
SpringerLink
Log in

Proof and Dialogue in Aristotle

  • Published:
Argumentation Aims and scope Submit manuscript

A Commentary to this article was published on 17 December 2015

Abstract

Jan Łukasiewicz’s analysis of Aristotle’s syllogism drew attention to the nature of syllogisms as conditionals rather than premise-conclusion arguments. His further idea that syllogisms should be understood as theorems of an axiom system seems a step too far for many logicians. But there is evidence to suggest that Aristotle’s syllogism was to regularise some of the steps made in ‘dialogue games.’ This way of seeing the syllogism is explored in the framework of modern formal dialogue systems. A modern formal syllogistic game, DLSyll, is set out and analysed in use.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Notes

  1. Łukasiewicz (1957).

  2. This is typical of most modern textbooks in which there is a section devoted to syllogistic. e.g. Delong (1971).

  3. Shenefeldt and White (2013).

  4. Op. cit. page 20.

  5. Ibid. page 21.

  6. And also in the few sites on the internet that acknowledge that Aristotle formulated syllogisms in conditional form. Most internet sites present what Łukasiewicz calls “traditional syllogistic” and not what he calls “Aristotle’s syllogistic”.

  7. e.g. Striker (2009), Jenkinson (1998), Tredennick (1973).

  8. The term “interpreted” carries a fairly narrow connotation, especially in modern metalogic. Our reading is carries a broader connotation which includes explanation. “Interpretational explanation” is quite a mouthful, and we continue to use “interpreted” on the understanding that it is to be read in a broader sense.

  9. Hamblin (1970).

  10. Mackenzie (1990).

  11. Walton and Krabbe (1995).

  12. Church, A. Introduction to Mathematical Logic, Volume 1, Princeton University Press, New Jersey, 1956.

  13. Providing a modern axiomatic model of Aristotle’s syllogistic as it appears in the Prior Analytics would be a formidable task. The main difficulty would be in preventing the system from proving far more than the 24 syllogisms without arbitrary restrictions on the system’s account of theses.

  14. One easy fix is not only to define the domain of quantification as a non-empty set but also to define predicate sets as non-empty so that (∃x)Px becomes necessarily true for every P. Unfortunately, this will not deliver a classical Predicate Logic.

  15. Smith (2012).

  16. Prior Analytics Book 1, 1.

  17. This flies in the face of Shenefelt and White’s assertions about Aristotle and validity.

  18. Prior Analytics 24 a 10–13.

  19. We will use “statement” where others might prefer “proposition” or even “sentence”. But it makes no practical difference to this paper which term is used.

  20. Book 1, 1.

  21. This issue will be the same for traditional syllogistic. There will have to be two assumptions or a conjunction of two assumptions, or even an assumption of a conjunction of two premises.

  22. Prior Analytics 24 a 27.

  23. Prior Analytics 24 b 15.

  24. Op. cit.

  25. Op. cit.

  26. Marion (2013).

  27. There is a variation of translations for the Greek phrase underlying the word “question” here. Tredennick translates to “[the premiss of dialectic] is an answer to the question which of two contradictory statements is to be accepted”; Jenkinson to “the dialectical premiss depends on the adversary’s choice between two contradictories”. Aristotle also says in the Topics (Book 1, 4) that there are two kinds of questions. When a questioner asks, “Are not platypus mammals?” then a proposition is formed. If the answer given is “Yes” then the answerer is taken to be taken as agreeing with the proposition that “Platypus are mammals.” When a questioner asks, “Are platypus mammals or not?” then a problem is formed. For our purposes no such distinction need be drawn because both are subsumed under true–false questions.

  28. Op. cit.

  29. Mates (1961).

  30. see Hunter (1971), pp 72 ff, especially p. 75.

  31. Especially Chapter 8. in Hamblin (1970).

  32. See Van Eemeren et al. (1996).

  33. The reasons conditional is part of what is called a “justification sequence” in many dialogue logics.

  34. The DL3 system can be found in Girle, Roderic A. “Commands in Dialogue Logic”, in Gabbay, Dov M and Olbach, H.J. Eds. Practical Reasoning, International Conference on Formal and Applied Practical Reasoning, FAPR’96, Bonn, Germany, June 3–7, 1996, Springer, pp. 246-260.

  35. Girle (2002).

  36. The translations of the Topics used herein are Forster, E.S., (in the Loeb edition, 391) Harvard University Press, 1976and Pickard-Cambridge, W.A. in British Enclassica Magic Mouse Multimedia, 1998.

  37. Girle and McKeown-Green (2012), July–September.

  38. This formula is one way of expressing what Jackson calls the “uncontested principle” in Jackson (1987), pp 4–5.

  39. Hamblin (1970), Walton and Krabbe (1995).

  40. Girle (1997).

  41. There is a deeper issue here about intentions in discourse, but we have no space to deal with it here. See Girle (1986), pp 123–135.

  42. “AGM” comes from the names of the authors: Alchourrón et al. (1985), AGM theory is set out in more accessible form in: Gärdenfors (1988).

  43. Logical consistency can apply not only to statements but also to commands and questions.

  44. The Hamblin-Mackenzie systems use this terminology in an attempt to avoid the difficulties of speech act theory. Nonetheless, the emphasis is on illocutionary content not on language.

  45. The pragma-dialectic school describe a dialogue in this way. But a look at their examples show that they, also, focus on the illocutionary content of speech acts.

  46. In conversation with Mackenzie he insisted that intentions should be derived from locutions, and not seen as embedded in locutions. This issue raises questions in the Philosophy of Language not dealt with here.

  47. The Pickard-Cambridge translation of the Topics.

  48. Girle (2002).

  49. This rule treats questions in a quite restricted way. But it will suffice for the moment.

  50. Walton and Krabbe (1995).

  51. Mackenzie (1984).

  52. Prior Analytics 1, 4 (Jenkinson tr. and Tredennick tr.).

  53. Ibid.

  54. Prior Analytics, I, 4.

  55. Tredennick’s commentry pg. 184.

  56. Tredennick’s translation in both cases.

  57. Topics 8, 1.

  58. Op.cit. p. 66.

  59. Carroll (1977), pg 160 ff.

  60. tr. Forster Topics 156 a 15.

  61. Girle and McKeown-Green (2012).

References

  • Alchourrón, C.E., P. Gärdenfors, and D. Makinson. 1985. On the logic of theory change: Partial meet functions for contraction and revision. Journal of Symbolic Logic 50: 510–530.

    Article  Google Scholar 

  • Aristotle. Prior Analytics. Trans. A. J. Jenkinson, 1998 in British Enclassica, Magic Mouse Multimedia, on CD.

  • Aristotle. Prior Analytics. Trans. H. Tredennick, 1973 (in the Loeb edition: 325). Cambridge: Harvard University Press.

  • Aristotle. Topics. Trans. E. S. Forster, 1976 (in the Loeb edition, 391) Cambridge: Harvard University Press.

  • Aristotle. Topics. Trans. W. A. Pickard-Cambridge, 1998 in British Enclassica, Magic Mouse Multimedia, on CD.

  • Carroll, Lewis. 1977. Symbolic logic. In Lewis Carroll’s Symbolic Logic, ed. W.W. Bartley III. New York: Harvester Press.

    Google Scholar 

  • Delong, H. 1971. A Profile of Mathematical Logic. Reading: Addison Wesley.

    Google Scholar 

  • Gärdenfors, P. 1988. Knowledge in Flux: Modeling the Dynamics of Epistemic States. Cambridge, Mass: The MIT Press.

    Google Scholar 

  • Girle, R. A. 1986. Dialogue and discourse. In Bishop, G. and van Lint, W. eds., In Proceedings of the Fourth Annual Computer Assisted Learning in Tertiary Education Conference (CALITE), Adelaide.

  • Girle, R. A. 1994. Knowledge organized and disorganized. In Proceedings of the Seventh Florida Artificial Intelligence Research Symposium, Pensacola Beach, Florida, April 27–29, 1–5.

  • Girle, Roderic A. 1996. Commands in dialogue logic. Practical Reasoning, Lecture Notes in Computer Science Volume 1085, pp 246–260.

  • Girle, R. A. 1997. Belief sets and commitment stores. OSSA 2, Argumentation and Rhetoric, Brock University, May 1997, http://scholar.uwindsor.ca/ossaarchive/OSSA2/papersandcommentaries/39/.

  • Girle, Roderic A. 2002. Positive agnosticism in belief revision. In Logic and Multi-agent Systems Workshop, University of Otago, http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.108.2626&rep=rep1&type=pdf.

  • Girle, R.A., and J. McKeown-Green. 2012. Methodological issues in the logic of questions and commands. International Journal of Cognitive Information and Natural Intelligence 6(3): 1–16.

    Article  Google Scholar 

  • Hamblin, C.L. 1970. Fallacies. London: Methuen.

    Google Scholar 

  • Hunter, G.G.B. 1971. Metalogic. London: Macmillan.

    Book  Google Scholar 

  • Jackson, F. 1987. Conditionals. Oxford: Blackwell.

    Google Scholar 

  • Łukasiewicz, Jan. 1957. Aristotle’s Syllogistic, 2nd ed. Oxford: Clarendon Press.

    Google Scholar 

  • Mackenzie, J. D. 1984. Begging the question in dialogue. Australasian Journal of Philosophy 62(2): 174–181.

  • Mackenzie, J. 1990. Four dialogue systems. Studia Logica 49(4): 567–583.

  • Mates, Benson. 1961. Stoic Logic. Berkeley: University of California Press.

    Google Scholar 

  • Marion, Mathieu 2013. Some remarks on Syllogistic, dialectic and the study of their History. http://almukhatabatjournal.unblog.fr/files/2013/06/mathieu-marion1.pdf.

  • Shenefeldt, M., and H. White. 2013. If A then B: How the World Discovered Logic. New York: Columbia University Press.

    Google Scholar 

  • Smith, Robin, 2012. Aristotle’s logic. In The Stanford Encyclopedia of Philosophy. Spring 2012 Edition, ed. Edward N. Zalta, http://plato.stanford.edu/archives/spr2012/entries/aristotle-logic/.

  • Striker, G. 2009. Aristotle Prior Analytics Book 1. Oxford: Clarendon Press.

    Google Scholar 

  • van Eemeren, F.H., et al. 1996. Fundamentals of Argumentation Theory. New Jersey: Lawrence Erlbaum.

    Google Scholar 

  • Walton, D.N., and E.C.W. Krabbe. 1995. Commitment in Dialogue. Albany: State University of New York Press.

    Google Scholar 

Download references

Acknowledgments

I would like to thank the anonymous reviewers who have contributed an enormous amount of help, guidance, correction and disputation in the producing of this paper.

Author information

Authors and Affiliations

  1. Philosophy Department, University of Queensland, Brisbane, Australia

    Roderic A. Girle

Authors
  1. Roderic A. Girle
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Roderic A. Girle.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Girle, R.A. Proof and Dialogue in Aristotle. Argumentation 30, 289–316 (2016). https://doi.org/10.1007/s10503-015-9382-2

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10503-015-9382-2

Keywords

Search

Navigation