In lieu of an abstract, here is a brief excerpt of the content:February 19, 2011 (11:48 am) E:\CPBR\RUSSJOUR\TYPE3002\russell 30,2 040 red.wpd Reviews 161 7 In, respectively, PaciWsm in Britain and Semi-Detached Idealists: the British Peace Movement and International Relations (Oxford: Oxford U. P., 2000). 8 See Monk 2: Chap. 13. FUNCTIONS OR PROPOSITIONAL FUNCTIONS? Alexander Paul Bozzo Philosophy / Marquette U. Milwaukee, wi 53233, usa [email protected] Michael Potter and Tom Ricketts, eds. The Cambridge Companion to Frege. Cambridge, uk: Cambridge U. (...) P., 2010. Pp. vii, 630. isbn 978-0-521-62479-4 (pb). £57.00; £21.99 (pb). us$38.99 (pb). February 19, 2011 (11:48 am) E:\CPBR\RUSSJOUR\TYPE3002\russell 30,2 040 red.wpd 162 Reviews 1 Frege: Philosophy of Mathematics (Cambridge, ma: Harvard U. P., 1991), p. 111. The paragraph contains an expression of Frege’s Context Principle and the need for Hume’s Principle as a criterion of identity in the deWnition of number. 2 There are in fact Wve stated goals. The others are: (iii) to serve as a reference work for students and non-specialists, (iv) to provide a route into the study of Frege historically and to any relevant contemporary concerns in the philosophies of logic, language, mathematics, and mind, and (v) to provide, for new readers, the most convenient detailed guide to Frege currently available. Gottlob Frege is widely recognized as one of the chief progenitors of mathematical logic and philosophy of languagez—zindeed, the importance attributed to Frege’s innovations is such that Michael Dummett, when reXecting on§62 of Frege’s Die Grundlagen der Arithmetik, feels compelled to remark that the paragraph therein is “arguably the most pregnant philosophical paragraph ever written.”1 Whether or not one agrees with Dummett on this point, the magnitude of Frege’s inXuence on the current philosophical landscape is incontestable. Frege revolutionized the then dominant Aristotelian conception of logic, introducing a formal language now recognized as the predicate calculus. Central to this end were Frege’s insights on quantiWcation, the notation that expressed it, the logicist project, and the extension of mathematical notions like function and argument to natural language. The long-awaited Cambridge Companion to Frege is a compendium of Fregean scholarship that rigorously explores these and similar topics; editors Thomas Ricketts and Michael Potter have compiled a comprehensive collection of fourteen essays that individually provide focused appraisals of a number of Frege’s most substantial insights. On the advice of this journal’s editor, I have limited my review to the connections (or rather dissimilarities ) that exist between Frege and Russell, relying exclusively on Peter Hylton ’s contribution to the collection, “Frege and Russell”. Following a brief consideration of the volume as a whole, I move immediately into a detailed explication of Hylton’s analysis. The volume includes among its goals the following two aims: (i) to provide, for advanced students and specialists, a conspectus of recent interpretation of Frege, and (ii) to dispel the intimidation felt by readers who confront a diUcult thinker.2 I single out these ambitions because they most clearly represent the volume’s strengths and shortcomings. Enthusiasts of Frege will not be disappointed by the multitude of rigorously and technically written essays, essays that contribute substantially and originally to the collective understanding of Frege and his work. For instance, Thomas Ricketts provides a thoughtful and thorough analysis—an analysis that moves well beyond mere explication—of Frege’s concept/object distinction, in particular its relevance for Frege’s Context Principle and logicism more generally. Similarly, Richard Heck addresses a number of central yet largely unexplored issues pertaining to the overall signiWcance of February 19, 2011 (11:48 am) E:\CPBR\RUSSJOUR\TYPE3002\russell 30,2 040 red.wpd Reviews 163 3 I strongly encourage that non-specialists augment The Cambridge Companion to Frege with Joan Weiner’s Frege Explained: from Arithmetic to Analytic Philosophy (Chicago : Open Court, 2004), one of the best available introductory texts on Frege. 4 The essay in fact was available as early as 2005 in Hylton’s Propositions, Functions, and Analysis: Selected Essays on Russell’s Philosophy (New York, ny: Oxford U. P., 2005). The editors of The Cambridge Companion to Frege partially... (shrink)

Alex Oliver; XI*—A Few More Remarks on Logical Form, Proceedings of the Aristotelian Society, Volume 99, Issue 1, 1 June 1999, Pages 247–272, https://doi.org/10.

This is the introductory essay to a collection commemorating the 100th anniversary of the publication in Mind of Bertrand Russell’s paper ‘On Denoting’.

Russell had two theories of definite descriptions: one for singular descriptions, another for plural descriptions. We chart its development, in which ‘On Denoting’ plays a part but not the part one might expect, before explaining why it eventually fails. We go on to consider many-valued functions, since they too bring in plural terms—terms such as ‘4’ or the descriptive ‘the inhabitants of London’ which, like plain plural descriptions, stand for more than one thing. Logicians need to take plural reference seriously (...) if only because mathematicians take many-valued functions seriously. We assess the objection (by Russell, Frege and others) that many-valued functions are illegitimate because the corresponding terms are ambiguous. We also assess the various methods proposed for getting rid of them. Finding the objection ill-founded and the methods ineffective, we introduce a logical framework that admits plural reference, and use it to answer some earlier questions and to raise some more. (shrink)

We present a plural logic that is as expressively strong as it can be without sacrificing axiomatisability, axiomatise it, and use it to chart the expressive limits set by axiomatisability. To the standard apparatus of quantification using singular variables our object-language adds plural variables, a predicate expressing inclusion (is/are/is one of/are among), and a plural definite description operator. Axiomatisability demands that plural variables only occur free, but they have a surprisingly important role. Plural description is not eliminable in favour of (...) quantification; on the contrary, quantification is definable in terms of it. Predicates and functors (function signs) can take plural as well as singular terms as arguments, and both many-valued and single-valued functions are expressible. The system accommodates collective as well as distributive predicates, and the condition for a predicate to be distributive is definable within it; similarly for functors. An essential part of the project is to demonstrate the soundness and completeness of the calculus with respect to a semantics that does without set-theoretic domains and in which the use of settheoretic extensions of predicates and functors is replaced by the sui generis relations and functions for which the extensions were at best artificial surrogates. Our metalanguage is designed to solve the difficulties involved in talking plurally about individuals and about the semantic values of plural items. (shrink)