On Analogy

ON ANALOGY 1. INTRODUCTORY. The present paper is an attempt to clear up some of the problems involved in the traditional theory of analogy as presented by the Thomistic school. The two main ideas behind the formal developments offered here are: (1) analogy is an important discovery, worthy of a thorough examination and further development, (2) contemporary mathematical logic supplies excellent tools for such work. This paper is, as far as the author knows, the first of its kind; 1 it deals with a difficult subject in a sketchy way; what it contains is, therefore, not meant to be definitive truths, but rather proposals for discussion. The approach to the problems of analogy used here is the semantic one. This is not the only method, but it would seem to be both the most convenient and the most traditional. As a matter of fact, it is difficult to see how equivocity, which is and must be treated as a relation of the same type as analogy, can be considered except by the semantic method. Also, St. Thomas Aquinas examined analogy in his question concerning divine names and the title of Cajetan's classical work is "De Nominum Analogia." It will be taken for granted that the reader has a good knowledge of classical texts of St. Thomas and Cajetan, and of the content of the Principia Mathematica; 2 no reference 1 The author is, however, indebted to the late Fr. Jan Salamucha and to J. Fr. Drewnowski who were the first to apply recent Formal Logic to Thomistic problems. The present paper may be considered as an attempt to formalize some of the opinions expressed by them. Cf. Mysl katolicka wobec Logiki wsp6lczesnej (Polish = The Catholic Thought and Contemporary Logic), Poznan 1937 (with French abstracts) and J. Fr. Drewnowski, Zarys programu filozoficznego (Polish= A sketch of a Philosophic Programme), Przeglad Filozoficzny, 37, 1943, 3-38, 150-181, 262-292, especially pp. 95-98. (There is a French account of this important work in Studia Philosophica (Lwow) I, 1935, 4ii1-454. • A. N. Whitehead and B. Russell, Principia Mathematica, e ·S (b, l, g, y) [by (5) and "p = qra · => ·p =>.r," dropping the quantifier]. We enumerate now the five hypotheses of the syllogism in Barbara with analogical middle terms, explained according to the alternative theory: H1. H2. H3. H4. H5. II+m1+a1eT IT+ b1 +m2e T Anp (m1, m2, l, P-1> p.2, x, y) Un (al> a2, l, a1, a2, z, t) Un (b1, b2, l, {31, f32, u, v). The proof of " II +b2 +a2 e T " runs as follows: (1) (3 h) S(m1o l, [p.2 U h], x) by H3 and 15. 1 (!2) S(al> l, al> z) by IJ4 and 5. 7 (3) (3 h) · [P-2 U h] C a1 by (1), (!2), H1 and 14. 2 (4) S(b1, l, f11o u) by H5 and 5. 7 (5) S (m2, l, p.2, y) by H3 and 15. 2 (6) {31 c /J-2 by (4), (5), H2 and 14.1 (7) {31 C P-2 · (3 h) · [P-2 U h] C a1 by (6) and (3) (8) (3 h) ·{31 C P.2 · [P-2 U h] C a1 by (7) and *10. 35 PM (9) (3 h) · {31 C a1 by (8)' "f c g. [g uh] c j . => .f c j" and *10. 28 PM (10) {31 C a1 by (9) (11) S(b2, l, /31, u) byH5 and 5.8 (12) S(a2 , l, a1o z) by H4 and 5.8 (13) II + b2 + a2 e T · =·{31 C a1 by (11), (12) and 14.1 (14) II+ b2+ a2 e T by (10) and (13) Q.E.D. 16. CRITICISM OF THE ALTERNATIVE THEORY. Jt has been shown that a syllogism in Barbara with analogical middle terms, defined according to the alternative theory, is a formally ON ANALOGY 441 valid formula. This is, however, the only advantage of this theory. Not even all requirements of Theology and Metaphysics in regard to the syllogism can be met by means of it. For a syllogism of these sciences has not only analogical middle terms, but...