Russell’s Modal Logic?

Abstract

Reviews 165 RUSSELrs MODAL LOGIC? GARY OSTERTAG Philosophy I New York U. New York, NY 10003, USA G02@NYU.EDU Jan Dejnofka, Bertrand Russell on Modality and Logical Relevance. Aldershot, U.K.: Ashgate, 1999. Pp. ix, 241. £37.50; US$65.95 (cloth). Russell's discussions of modality hardly form a centrepiece of his philosophical logic. He published no articles on this topic,I nor do any of his books devote even a single chapter to. it. Nonetheless, remarks on modality appear-although with no great frequency-scattered throughout his writings, spanning the entire period in which he was seriously engaged in logical matters. I "Non-Euclidean Geometry" (Papers 4: 482-5), first published in 19°4, is arguably an exception. r66 Reviews In a 1905 manuscript only recently published, he argues that modal predicates are correctly applied not to propositions bur to propositional functions.2 Moreover , in a roughly coeval review of Meinong, serialized in Mind, he expresses scepticism towards the view that "it is possible to distinguish, among true propositions , some which are necessary from others which are mere facts" (Papers 4: 435). His views on modality receive further clarification in his 1913 Aristotelian Society lecture, "On the Notion of Cause"; but a more fully developed picture does not emerge until 1918-19. Two writings of that period, "The Philosophy of Logical Atomism" and Introduction to Mathematical Philosophy, state Russell's most considered thoughts on this topic. Even here, Russell does not devote an extensive amount of space to the subject. But their individual brevity notwithstanding , Russell's remarks, collectively, form a view of modality that is worth considering in detail, since it not only sheds light on his conceptions of logic and logical truth, but also provides an interesting, if incomplete, reworking of the traditional approach. Jan Dejnoika's new book attempts to provide an interpretation ofthese remarks. While Dejnofka is not the first Russell scholar to address them, his book is by far the most comprehensive discussion yet published ) Moreover, his interpretation of Russell, if correct, would require a radical reconception of the logic of Principia Mathematica. As I shall argue, Dejnoika's book falls far short ofestablishing anything so revolutionary. As early as 1905, Russell has settled into what becomes his official view, that "there is no such comparative and superlative of truth as is implied by the notions ofcontingency and necessity" (Papers 4: 520). Later, in "On the Notion of Cause", he considers the doctrine that "That is necessary which is not only true, but would be true under all circumstances."4 His response is definitive: A proposition is simply true or false, and that ends the matter: there can be no question of "circumstances." "Charles I's head was cut off' is just as true in summer as in winter, on Sundays as on Mondays. (Papers 6: 194) The notions of necessity, possibility, etc., are therefore correctly applied to propositional functions, not to propositions. In particular, a propositional function f(x) is necessary just in case it determines a true proposition for each value of x, possible just in case it determines a true proposition for at least one value of x, and impossible just in case there is no value of x for which it determines a true proposition. Brief reflection will reveal that the property of being 1 "Necessity and Possibility" (Papers 4: 5°7-20). The suggestion also occurs in Russell's review of Meinong; see Papers 4: 436, 450, . 3 Which is not to imply that there are not striking omissions; see note 8. 4 Taken from Baldwin's Dictionary ofPhilosophy and Psychology. Reviews r67 necessary, understood in the above sense, is precisely what the universal quantifier expresses, whereas the property of being possible is what existential quantification expresses. (Being impossible is expressed by the existential quantifier prefixed by the negation sign.) Most readers pause, however briefly, at these definitions..What recommends the use of "possible" as applying to a function that is, in Russell's words, "sometimes true"? One suspects that Russell is using the expression in a way that deviates from its standard use in philosophy . The suspicion is confirmed in "The Philosophy ofLogical Atomism": When I...