Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-25T02:30:37.528Z Has data issue: false hasContentIssue false
  • English
  • Français

INDIRECT PROOF AND INVERSIONS OF SYLLOGISMS

Published online by Cambridge University Press:  25 July 2019

ROY DYCKHOFF
ROY DYCKHOFF*
Affiliation:
UNIVERSITY OF ST ANDREWS ST ANDREWS KY16 9AJ, UK
Get access Rights & Permissions [Opens in a new window]

Abstract

By considering the new notion of the inverses of syllogisms such as Barbara and Celarent, we show how the rule of Indirect Proof, in the form (no multiple or vacuous discharges) used by Aristotle, may be dispensed with, in a system comprising four basic rules of subalternation or conversion and six basic syllogisms.

Keywords

03F99deductionsyllogismindirect proof
Type
Communications
Information
Bulletin of Symbolic Logic , Volume 25 , Issue 2 , June 2019 , pp. 196 - 207
Copyright
Copyright © The Association for Symbolic Logic 2019 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

*

Roy Dyckhoff passed away on August 23, 2018.

References

REFERENCES

Bobzien, S., Stoic syllogistic, Oxford Studies in Ancient Philosophy, vol. 14, Oxford University Press, 1996, pp. 133–192.Google Scholar
Bobzien, S. and Dyckhoff, R., Analyticity, balance and non-admissibility of cut in stoic logic. Studia Logica (2018).Google Scholar
Corcoran, J., Completeness of an ancient logic. Journal of Symbolic Logic, vol. 37 (1972), pp. 696–702.10.2307/2272415CrossRefGoogle Scholar
Corcoran, J., A mathematical model of Aristotle’s syllogistic. Archiv für Geschichte der Philosophie, vol. 55 (1973), pp. 191–219.10.1515/agph.1973.55.2.191CrossRefGoogle Scholar
Joray, P., The principle of contradiction and ecthesis in Aristotle’s syllogistic. History and Philosophy of Logic, vol. 35 (2014), pp. 219–236.10.1080/01445340.2014.907976CrossRefGoogle Scholar
Joray, P., A completed system for Robin Smith’s incomplete ecthetic syllogistic. Notre Dame Journal of Formal Logic, vol. 58 (2017), pp. 329–342.10.1215/00294527-3882234CrossRefGoogle Scholar
Smiley, T. J., What is a syllogism? Journal of Philosophical Logic, vol. 2 (1973), pp. 136–154.10.1007/BF02115614CrossRefGoogle Scholar
Smith, R., Completeness of an ecthetic syllogistic. Notre Dame Journal of Formal Logic, vol. 24 (1983), pp. 224–232.10.1305/ndjfl/1093870312CrossRefGoogle Scholar
Tennant, N., Aristotle’s syllogistic and core logic. History and Philosophy of Logic, vol. 35 (2014), pp. 120–147.10.1080/01445340.2013.867144CrossRefGoogle Scholar
Troelstra, A. S. and Schwichtenberg, H., Basic Proof Theory, Cambridge University Press, Cambridge, 1996 and 2001.Google Scholar
von Plato, J., Element of Logical Reasoning, Cambridge University Press, Cambridge, 2013.10.1017/CBO9781139567862CrossRefGoogle Scholar
von Plato, J., Aristotle’s deductive logic: A proof-theoretical study, Concepts of Proof in Mathematics, Philosophy and Computer Science (Probst, D. and Schuster, P., editors), De Gruyter, Berlin, 2016, pp. 323–346.Google Scholar
von Plato, J., The Great Formal Machinery Works: Theories of Deduction and Computation at the Origins of the Digital Age, Princeton University Press, Princeton, NJ, 2017.Google Scholar