## Notre Dame Journal of Formal Logic

### Is There a Modal Syllogistic?

#### Abstract

Aristotle's modal syllogistic has been described as "incoherent," "a failure," "a realm of darkness." Even the gentler critics claim that it is inconsistent. I offer an interpretation according to which validity in the modal syllogistic is always obtained by substituting modal terms in the nonmodal syllogistic, and restricting the principles of modal conversion. In this paper I discuss the apodeictic syllogistic, showing that the restrictions I propose are powerful enough to do all the work Aristotle requires and, in fact, are supported by a close analysis of Aristotle's text. The upshot of this is that there is for Aristotle no separate modal syllogistic.

#### Article information

Source
Notre Dame J. Formal Logic Volume 39, Number 4 (1998), 554-572.

Dates
First available in Project Euclid: 5 December 2002

http://projecteuclid.org/euclid.ndjfl/1039118870

Mathematical Reviews number (MathSciNet)
MR1776227

Digital Object Identifier
doi:10.1305/ndjfl/1039118870

Zentralblatt MATH identifier
0971.03002

#### Citation

Rini, Adriane A. Is There a Modal Syllogistic?. Notre Dame Journal of Formal Logic 39 (1998), no. 4, 554--572. doi:10.1305/ndjfl/1039118870. http://projecteuclid.org/euclid.ndjfl/1039118870.

#### References

• [1] Becker, A., Die Aristotelische Theorie der Möglichkeitsschlüsse, Junker, Berlin,1933. Reprinted Wissenschaftliche Buchgesellschaft, Darmstadt, 1968.
• [2] Johnson, F., Models for modal syllogisms," Notre Dame Journal of Formal Logic, vol. 30 (1989), pp. 271--84.
• [3] Kneale, W., and M. Kneale, The Development of Logic, Clarendon Press, Oxford, 1962.
• [4] Ł ukasiewicz, J., Aristotle's Syllogistic from the Standpoint of Modern Formal Logic, 2d edition, Clarendon Press, Oxford, 1957.
• [5] McCall, S., Aristotle's Modal Syllogisms, North-Holland, Amsterdam, 1963.
• [6] Patterson, R., Aristotle's Modal Logic: Essence and Entailment in the Organon, Cambridge University Press, Cambridge, 1995.
• [7] Patzig, G., Aristotle's Theory of the Syllogism, translated by J. Barnes, Reidel, Dordrecht, 1968.
• [8] Rini, A. A., The Aristotelicity of Thomason's semantics," Logique et Analyse, No. 155--56 (1996), pp. 255--70.
• [9] Ross, W. D., Aristotle's Prior and Posterior Analytics. A Revised Text with Introduction and Commentary, Clarendon Press, Oxford, 1949.
• [10] Smith, R., Aristotle: Prior Analytics, translated with introduction, notes, and commentary, Hackett Publishing Company, Indianapolis, 1989.
• [11] Striker, G., Modal vs. Assertoric Syllogistic," Ancient Philosophy, vol. 14 (1994), pp. 39--51.
• [12] Thom, P., The Logic of Essentialism: An Interpretation of Aristotle's Modal Syllogistic, Kluwer Academic Publishers, Dordrecht, 1996.
• [13] Thomason, S. K., Semantic analysis of the modal syllogistic," Journal of Philosophical Logic, vol. 22 (1993), pp. 111--28.
• [14] van Rijen, J., Aspects of Aristotle's Logic of Modalities, Reidel, Dordrecht, 1989.