Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-22T00:23:37.548Z Has data issue: false hasContentIssue false
  • English
  • Français

The Syllogism's Final Solution

Published online by Cambridge University Press:  15 January 2014

I. Susan Russinoff
I. Susan Russinoff*
Affiliation:
Department of Philosophy, Tufts University Medford, Massachusetts 02155-7068, USAE-mail:[email protected]
Get access Rights & Permissions [Opens in a new window]

Extract

In 1883, while a student of C. S. Peirce at Johns Hopkins University, Christine Ladd-Franklin published a paper titled On the Algebra of Logic, in which she develops an elegant and powerful test for the validity of syllogisms that constitutes the most significant advance in syllogistic logic in two thousand years. Sadly, her work has been all but forgotten by logicians and historians of logic. Ladd-Franklin's achievement has been overlooked, partly because it has been overshadowed by the work of other logicians of the nineteenth century renaissance in logic, but probably also because she was a woman. Though neglected, the significance of her contribution to the field of symbolic logic has not been diminished by subsequent achievements of others.

In this paper, I bring to light the important work of Ladd-Franklin so that she is justly credited with having solved a problem over two millennia old. First, I give a brief survey of the history of syllogistic logic. In the second section, I discuss the logical systems called “algebras of logic”. I then outline Ladd-Franklin's algebra of logic, discussing how it differs from others, and explain her test for the validity of the syllogism, both in her symbolic language and the more familiar language of modern logic. Finally I present a rigorous proof of her theorem. Ladd-Franklin developed her algebra of logic before the methods necessary for a rigorous proof were available to her. Thus, I do now what she could not have done then.

Type
Research Article
Information
Bulletin of Symbolic Logic , Volume 5 , Issue 4 , December 1999 , pp. 451 - 469
Copyright
Copyright © Association for Symbolic Logic 1999

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.)

References

REFERENCES

[1] Aristotle, , Posterior and prior analytics (Ross, W. D., editor), Oxford, 1949.Google Scholar
[2] Baldwin, J.M., Dictionary of philosophy and psychology, Macmillan, New York, 1901–1905, three volumes.Google Scholar
[3] Boole, G., Studies in logic and probability (Rhees, R., editor), Watts and Co., London, 1952.Google Scholar
[4] Cohen, M. and Nagel, E., An introduction to logic and scientific method, Harcourt, Brace, New York, 1934.Google Scholar
[5] de Morgan, A., Formal logic or the calculus of inference .Google Scholar
[6] Dotterer, R. H., A generalization of the antilogism, this Journal, vol. 6 (1941), pp. 90–95.Google Scholar
[7] Dotterer, R. H., A supplementary note on the rule of the antilogism, this Journal, vol. 8 (1943).Google Scholar
[8] Edwards, J. T. (editor), Christine Ladd-Franklin, Notable American women: A biographical dictionary 1607–1950, vol. II, Belknap Press of Harvard University Press, Cambridge, MA, 1971.Google Scholar
[9] Gardner, M., Logic machines, diagrams and Boolean algebra, Dover, New York, 1968.Google Scholar
[10] Hodges, W., Elementary predicate logic, Handbook of philosophical logic (Gabbay, G. and Guenthner, F., editors), vol. I, Reidel, 1983, pp. 1–131.Google Scholar
[11] Kneale, W. and Kneale, M., The development of logic, Clarendon, Oxford, 1962.Google Scholar
[12] Kretzman, and Stump, E. (editors), The Cambridge translations of medieval philosophical texts, vol. I, Cambridge University Press, Cambridge, 1988.Google Scholar
[13] Ladd-Franklin, C., On the algebra of logic, Studies in logic by the members of the Johns Hopkins University (C. S. Peirce, editor), Little, Brown, Boston, 1883, pp. 17–71.Google Scholar
[14] Ladd-Franklin, C., The antilogism, Mind, Vol. 37 1928, pp. 532–534.Google Scholar
[15] Lear, J., Aristotle and logical theory, Cambridge, 1980.Google Scholar
[16] Lewis, C. I., A survey of symbolic logic, Dover, New York, 1960.Google Scholar
[17] Łukasiewicz, J., Aristotle's syllogistic from the standpoint of modern formal logic, Oxford, 1957.Google Scholar
[18] Peirce, C. S., Studies in logic by the members of the Johns Hopkins University, Little, Brown, Boston, 1883.Google Scholar
[19] Quine, W. V., Methods of logic, 3rd ed., Holt Rinehart and Winston, New York, 1972.Google Scholar
[20] Sabre, R. M., Extending the antilogism, Logique et Analyse, vol. 30 (1987), pp. 103–111.Google Scholar
[21] Shen, E., The Ladd-Franklin formula in logic: The antilogism, Mind, vol. 36 (1927), pp. 54–60.Google Scholar
[22] van Heijenoort, J. (editor), From Frege to Gödel: A source book in mathematical logic, 1879–1931, Harvard University Press, Cambridge, 1967.Google Scholar