Necessary Propositions and the Square of Opposition

NECESSARY PROPOSITIONS AND THE SQUARE OF OPPOSITION MARK ROBERTS University of Rhode Island Kingston, Rhode Island IT IS COMMONPLACE to define contradictory, contrary, and subcontrary propositions in the following way: contradictory propositions cannot both be true and cannot both be false; contrary propositions cannot both be true but can both be false; and subcontrary propositions can both be true but cannot both be false. In his Introduction to Logic 1 Irving Copi raises a problem with two of these definitions which he believes forces him to limit the range of propositions which can be used in the square of opposition. Since contrary propositions can both be false, but the falsity of a necessarily true proposition is not possible , a necessarily true proposition has no contrary. Therefore, only contingent propositions can be contraries. Subcontrary propositions can both be true, but the truth of a necessarily false proposition is not possible.2 This problem is rarely raised in other logic texts, but, it is interesting to note, it is mentioned by a number of neoscholastic philosophers, for example, P. Nicholas Russo,3 Rev. H. Grenier,4 1 Irving M. Copi, Introduction to Logic (New York: Macmillan, 1986), pp. 178-179. Copi first introduced this problem in the fifth edition of his work on the basis of an article by David H. Sanford entitled " Contraries and Subcontraries ,'' Nous 2 (1968) : 95-96. Sanford argues that the most reasonable way to resolve the problem of necessary propositions is to assume that contingent propositions comprise the square of opposition. 2 Copi, pp. 178-179. 8 Nicholas Russo, Summa Philosophica (Boston: Apud Marlier et Socios, 1[;85), p. 23. 4 Henri Grenier, Thomistic Philosophy, Vol. I (Charlottetown, Canada: St. Dunstan's University, 1950), p. 69. 427 428 MARK ROBERTS G. Sanseverino,5 Jacques Maritain,6 F.-X. Maquart,7 P. Coffey,8 and others.9 (It is also mentioned by Bishop Whately.10 ) Each of these philosophers makes necessarily true or false propositions an exception to the definition of contrary and subcontrary propositions . The reason is they and Copi interpret the definitions of contrary and subcontrary propositions to mean that the falsity of each contrary proposition is possible and the truth of each subcontrary proposition is possible. It should be mentioned, however, that the position of the philosophers cited above is not entirely the same as Copi's. Copi reasons that these definitions imply that necessary propositions have no contrary or subcontrary. The other philosophers believe that necessary propositions can be contraries and subcontraries. Thus, in the case of necessary propositions contrary and subcontrary propositions are, instead, defined merely in terms of their quantity and quality, not by whether or not they can both be false or can both be true. In fact, Coffey and some of the other philosophers cited above assert that, when the propositions composing the square are necessary , one can infer the truth of the universal from the truth of 5 Gaietano Sanseverino, Philosophia Christiana, Vol. II (Neapoli: Vincentii Manfredi, 1862), pp. DCCXXXVIII ff. 6 J. Maritain, An Introduction to Logic (London: Sheed & Ward, 1937), p. 135, notes 1 & 2. 7 F.-X. Maquart, Elementa Philosophiae, Vol. I (Parisiis: Andreas Blot, 1937)' p. 126 ff. 8 P. Coffey, The Science of Logic, Vol. 1 (New York: Longmans, Green & Co., 1918), p. 225, 226. 9 Joseph Gredt, Elementa Philosophiae, Vol. I (Friburgi: Herder, 1929), p. 46, notes 1 & 2; Sylvester J. Hartman, A Textbook of Logic (New York: American Book Co., 1936), p. 162 ff; Roland Houde and Jerome J. Fischer, Handbook of Logic (Dubuque, Iowa: Wm. C. Brown Co., 1954), p. 61; Eduard Hugon, Cursus Philosophiae Thomisticae, Vol. I (Parisiis: P. Lethielleux n.d), p. 155; Dennis C. Kane, Logic: The Art of Predication and Inference (Providence: Providence College Press, 1978), p. 98 ff; Francis P. Siegfried, Essentialia Philosophiae (Philadelphia: Dolphin Press, 1927), p. 25; Francis Varvello, Minor Logic, trans. and supplemented Arthur D. Fearon (San Francisco: Univ. of San Francisco Press, 1933), p. 73 ff. 10 Richard Whately, Elements of Logic (Boston: James Munroe & Co., 1854), p. 77 ff. PROPOSITIONS AND THE SQUARE OF OPPOSITION 429 the particular and the falsity of the particular from the falsity of the universal.11 Maritain maintains that in the case...