Russell: The Journal of Bertrand Russell Archives

I. INTRODUCTION "ON DENOTING" AGAINST DENOTING GREGORY LANDINI Philosophy 1University of Iowa Iowa City, IA 52242, USA E-mail: LANDINI@BLUE.WEEG.UIOWA.EDU I n his article "On Denoting", Russell infamously announced that the whole theory ofmeaning and denotation is enveloped in an "inextricable tangle" and has to be abandoned. The "tangle", however, has yet to be recovered from its expression in the obscure "Gray's Elegy argument" of the work-but not for lack oftrying. Indeed, there are so many different interpretations ofthe argument now in the literature that we do well to ask by what criteria shall any account of the argument be assessed. Is there any way that the real Gray's Elegy argument could be recognized? Years ago Geach (I958) suggested an answer. The argument is best understood if targeted at the theory of denoting of Russell's 1903 Principles ofMathematics. Cassin (I970) agreed, and attempted to set out the argument within the historical context of the Principles. It is no longer possible to doubt the correctness of this approach; Russell himself unequivocally authenticates it a June 1905 manuscript entided "On Fundamentals". Russell even scrawled on the first leaf that pages ISf[ contain the reasons for the new theory of denoting. The manuscript arrives at the "inextricable tangle" which, for the most part, would be presented in "On Denoting"; and the working notes proceed wholly independently of Frege, by working though difficulties with the Principles 'theory ofdenoting. The Gray's Elegy argument has proved to be resistant, however. It is a siren song which lives up to the Odyssey in bringing to ruin all who hope n.s. 18 (summer 1998): 43-80 \IssN 0036-01631 russell: the Journal ofthe Benrand Russell Archives McMaster University Library Press 44 GREGORY LANDINI to probe its pages. The manuscripts Russell left unpublished! are as obscure and involuted as ever they could be; and new possibilities for reading his many animadversions grow exponentially. One must stay the course, holding onto what Russell regarded as fundamental principles. But what principles were fundamental? Sooner or later the interpreter is seduced by one or another of the songs and, impelled by its blissful soporific, dashed on the rocky crags. This paper takes the lead of Odysseus, navigating past the sirens by being firmly lashed to the mast of the Principles. The firm lashing was generated by my work on Russell's so-called "substitutional theory of classes and relations" which he revamped in December 1905 under the auspices of the theory of definite and indefinite descriptions. Russell regarded this theory as the natural ally of the Principles, adhering, as he put it, with "drastic pedantry", to the fundamental doctrine ofthe Principles that "whatever is, is one" ([STCR], p. 189). With the historical development and mechariics of the substitutional theory understood, and the security ofRussell's explicit view that it adheres to the Principles' fundamentals, we can resist the siren songs ofRussell's manuscripts. In a letter to Jourdain of 14 March 1906, Russell recounted the road to substitution . He wrote: About June 1904, I tried hard to construct a substitutional theory more or less like my present theory. But I failed for want ofthe theory ofdenoting: also I did not distinguish between substitution ofa constant for a constant and determination ofa variable as this or that constant.... Then, last autumn, as a consequence ofthe new theory ofdenoting, I found at last that substitution would work, and all went swimmingly.2 The substitutional theory emerged from Russell's attempt (in the Principles ) to use denoting concepts and the notion of the substitution of entities (including denoting concepts themselves) in the explanation of the constituents ofpropositions named by formulas involving the use of single letters as variables. The problem of the logical form of the propositions in question is thrust to the fore; and, as we shall see, this reveals I These include "Poims about Denoting", "On the Meaning and Denotation of Phrases", "On Meaning and Denotation", and "On Fundamentals." 2. Grattan-Guinness, I977, p. 79-80. "On Denoting" against Denoting 45 the sound argument Russell had against denoting concepts. 2. FORMAL IMPLICATION The introduction of variables into a symbolic calculus for Logic was...