Armstrong and the Problem of Converse Relations

• Published in: Erkenntnis Vol. 56; no. 2; pp. 215 - 227
• Main Author: Cross, Charles B.
• Format: Journal Article
• Language: English
• Published: Dordrecht Kluwer Academic Publishers and Felix Meiner 01.01.2002; Springer; Springer Nature B.V
• Subjects: Binary relations; Concept of being; Counterexamples; Fregean content; Logical postulates; Metaphysics; Philosophical logics. Philosophy of language; Philosophy; Referents; Relational properties; Supervenience; Verbs; Armstrong (D. M.); Russell (B.); Frege (G.); Supervenience; Metaphysics; States of Affairs; Postulate; Direction; Property; Symmetry
• ISSN: 0165-0106; 1572-8420
• DOI: 10.1023/A:1015650310608

In "A World of States of Affairs" (Cambridge University Press, 1997) David Armstrong offers a comprehensive metaphysics based on the thesis that the world consists of states of affairs. Among the entities postulated by Armstrong's theory are relations, including non-symmetrical relations, and while Armstrong does not agree with Russell that all relations have a direction or definite order among their places, he does explicitly acknowledge that the slots of a non-symmetrical relation have a definite order or direction. I first show that non-symmetrical relations pose a problem for Armstrong's theory by raising "The Problem of Converse Relations." I then argue that the best resolution of this problem in the context of Armstrong's theory involves adopting an analysis of the order or direction of a relation that differs from the analysis that Russell assumes. I conclude by discussing a further problem facing Armstrong's ontology: "The Problem of Converse Relational Properties."