In his 1903 Principles of Mathematics, Russell holds that “it is a characteristic of the terms of a proposition”—that is, its “logical subjects”—“that any one of them may be replaced by any other entity without our ceasing to have a proposition”. Hence, in PoM, Russell holds that from the proposition ‘Socrates is human’, we can obtain the propositions ‘Humanity is human’ and ‘The class of humans is human’, replacing Socrates by the property of humanity and the class of humans, respectively. (...) Hence also, in PoM, Russell accepts the doctrine of the unrestricted variable: if we replace a logical subject of a proposition by a variable to yield a propositional function, the range of that variable includes absolutely every entity. For absolutely any entity can be taken as a value of that variable to yield a proposition, true or false. The doctrine of the unrestricted variable is thus incompatible with any type-theoretic metaphysics, according to which only entities of a certain restricted type can replace a logical subject of a given proposition so as to yield another proposition. (shrink)
Michael Dummett has long argued that Frege is committed to recognizing a distinction between two sorts of analysis of propositional contents: 'analysis', which reveals the entities that one must grasp in order to apprehend a given propositional content; and 'decomposition', which is used in recognizing the validity of certain inferences. Whereas any propositional content admits of a unique ultimate 'analysis' into simple constituents, it also admits of distinct 'decompositions', no one of which is ultimately privileged over the others. I argue (...) that although Russell accepts this distinction between analysis and decomposition, Frege does not. In particular, I consider claims which Dummett makes regarding how 'analysis' and 'decomposition' are related to two different models Frege at least suggests in discussing the composition of thoughts, the part/whole model and the function/argument model; and I argue that in each case, while Russell accepts views which Dummett attributes to Frege, Frege does not. (shrink)
In his recent book, "The Metaphysicians of Meaning" (2000), Gideon Makin argues that in the so-called "Gray's Elegy" argument (the GEA) in "On Denoting", Russell provides decisive arguments against not only his own theory of denoting concepts but also Frege's theory of sense. I argue that by failing to recognize fundamental differences between the two theories, Makin fails to recognize that the GEA has less force against Frege's theory than against Russell's own earlier theory. While I agree with many aspects (...) of Makin's interpretation of the GEA, I differ with him regarding some significant details and present an interpretation according to which the GEA emerges as simpler, stronger, and more integrated. (shrink)
In a recent article, Michael Kremer revisits Russell's "Gray's Elegy" argument—the argument in "On Denoting" in which Russell rejects "the whole distinction of meaning and denotation". Kremer argues that the Gray's Elegy argument is directed not at Frege's distinction between Sinn and Bedeutung but rather at Russell's own theory of "denoting concepts" in his earlier Principles of Mathematics. Furthermore, and more originally, Kremer argues that Russell's views of acquaintance play a central role in the argument. For Kremer, it is because (...) Frege does not share Russell's views of acquaintance that the Gray's Elegy argument succeeds against Russell's own earlier theory but not against Frege's position. (shrink)
In a recent article, Michael Kremer revisits Russell's "Gray's Elegy" argument—the argument in "On Denoting" in which Russell rejects "the whole distinction of meaning and denotation". Kremer argues that the Gray's Elegy argument is directed not at Frege's distinction between Sinn and Bedeutung but rather at Russell's own theory of "denoting concepts" in his earlier Principles of Mathematics. Furthermore, and more originally, Kremer argues that Russell's views of acquaintance play a central role in the argument. For Kremer, it is because (...) Frege does not share Russell's views of acquaintance that the Gray's Elegy argument succeeds against Russell's own earlier theory but not against Frege's position. (shrink)
I distinguish three periods in Russell’s philosophical development: the Moorean period, following his break with Idealism around 1899 through his attending the Paris conference in August 1900 at which he saw Peano; the period following the Paris conference through his prison stay in 1918; and his post-prison period, in which he becomes concerned with the nature of language as such. I argue that while the topic of vagueness becomes an explicit theme in his post-1918 writings, his view that ordinary language (...) is vague plays a central role in his post-Peano practice and characterization of analysis. On the Moorean view, analysis is intended to make explicit what is already “present to the mind” of anyone who understands the relevant sentence prior to analysis; post-Peano and pre-prison, Russell presents analysis as making precise what was previously vague; post-prison, he denies that any language is precise, so that analysis involves a transition only from the more to the less vague. I argue that the failure to recognize the character of Russell’s post-Peano conception of analysis reflects a broader misunderstanding of the character of Russell’s philosophy and of his place in the history of analytic philosophy. (shrink)
In his 1903 Principles of Mathematics, Russell holds that “it is a characteristic of the terms of a proposition”—that is, its “logical subjects”—“that any one of them may be replaced by any other entity without our ceasing to have a proposition”. Hence, in PoM, Russell holds that from the proposition ‘Socrates is human’, we can obtain the propositions ‘Humanity is human’ and ‘The class of humans is human’, replacing Socrates by the property of humanity and the class of humans, respectively. (...) Hence also, in PoM, Russell accepts the doctrine of the unrestricted variable: if we replace a logical subject of a proposition by a variable to yield a propositional function, the range of that variable includes absolutely every entity. For absolutely any entity can be taken as a value of that variable to yield a proposition, true or false. The doctrine of the unrestricted variable is thus incompatible with any type-theoretic metaphysics, according to which only entities of a certain restricted type can replace a logical subject of a given proposition so as to yield another proposition. (shrink)
Influenced by G. E. Moore, Russell broke with Idealism towards the end of 1898; but in later years he characterized his meeting Peano in August 1900 as ?the most important event? in ?the most important year in my intellectual life?. While Russell discovered his paradox during his post-Peano period, the question arises whether he was already committed, during his pre-Peano Moorean period, to assumptions from which his paradox may be derived. Peter Hylton has argued that the pre-Peano Russell was thus (...) vulnerable to (at least one version of) Russell's paradox and hence that the paradox exposes a pre-existing difficulty in Russell's Moorean philosophy. Contrary to Hylton, I argue that the Moorean Russell adhered to views which insulated him against the paradox. Further, I argue that Russell became vulnerable to his paradox as a result of changes in his Moorean position occasioned, first, by his acceptance of Cantor's theory of the transfinite, and, second, by his correspondence with Frege. I conclude with some general comments regarding Russell's acceptance of naïve set theory. (shrink)
In this review article of Volumes 2 and 3 of _The Collected Papers of Bertrand Russell, I distinguish and attempt to clarify three periods of Russell's early philosophical development: R 'subscript 1', his Hegelian period of 1894-1898; R 'subscript 2', his Moore-influenced period from the end of 1898 to his meeting Peano in August 1900; and R 'subscript 3', the period after he met Peano through the completion of _The Principles of Mathematics. I argue that the position Russell defends in (...) R 'subscript 2' is in conflict with the logicism he develops in R 'subscript 3' and that this conflict within Russell's postidealist philosophy is reflected in the _Principles. (shrink)
As Gideon Makin introduces his book, it may seem that his concerns are primarily historical and negative—namely, to show that when properly understood, Russell’s “On Denoting” and Frege’s “On Sense and Reference” make little, if any, contact with issues in contemporary philosophy of language. First, he claims that these papers are not typically understood in the context of the philosophical development of their authors. Russell’s central argument in “On Denoting”—the so-called “Gray’s Elegy argument”—is directed against the theory of denoting concepts (...) he advocated in The Principles of Mathematics, while Frege begins “On Sense and Reference” by arguing against his Begriffsschrift account of identity. And, for Makin, without a proper understanding of the old theories which are being rejected, and the reasons why they are being rejected, we will lack a full understanding of the new theories which are being advocated. More generally, he claims that when we understand the theoretical context in which Russell and Frege are operating, we will recognize that they are engaged in an “enterprise which is radically different in kind from what current practitioners of the philosophy of language profess to be doing”, an enterprise which arises out of their logicist project, which, in turn, is tied to their “peculiarly metaphysical conception of logic”. (shrink)
This paper presents structural similarities and historical connections between Prior’s rejection of the Barcan formula and his critique of Berkeley’s master argument for idealism in his 1955 paper “Berkeley in Logical Form”. Making use of Mackie’s paper “Self-Refutation—A Formal Analysis”, it concludes with some suggestions concerning what is at stake in the debate between Prior and Berkeley and in structurally similar debates such as whether to accept the Barcan formula.
In writings prior to the publication of The Principles of Mathematics (PoM), Russell denies that relations “in the abstract” ever relate and holds instead that only particularized relations, or relational tropes, do so; however, in PoM section 55, he argues against his former view and adopts the view that relations “in the abstract” are capable of a “twofold use” – either as “relations in themselves” or as “actually relating”. I argue that while Russell rightly came to recognize that rejecting his (...) earlier view is necessary for avoiding the Bradleyan view that complex wholes are unanalyzable, his later view can appear as an ad hoc means of avoiding Bradley's argument against “relational thought”. (shrink)
The purpose of this dissertation is to clarify the relationship between two traditions within analytic philosophy: the epistemologically-centered philosophy exemplified by C. I. Lewis and other logical empiricists; and the semantically-generated philosophy which derives from certain views of Frege and Russell and which is exemplified in Wittgenstein's Tractatus. Logical empiricists generate their views by pursuing concerns with justification and evidence; the early Wittgenstein generates his views by pursuing concerns with the nature of language. I argue, however, that although they develop (...) their views by pursuing wholly different, and perhaps apparently unrelated, initial concerns, the early Wittgenstein and logical empiricists arrive at conflicting, and not merely unrelated, philosophical positions. ;In particular, I argue that solely by accepting certain basic views of the nature of language, each of which either Frege or Russell accepts, Wittgenstein is led in his Tractatus to reject certain views--including views of the issue of scepticism and of the nature of sense-experience--which logical empiricists generate through their concerns with justification. In doing so, I seek not only to clarify the Tractatus as well as logical empiricism, but also to show that accepting either of these positions requires rejecting the other. ;I conclude by arguing that understanding the relationship between the Tractatus and logical empiricism helps to clarify the work of Donald Davidson, a recent philosopher who rejects logical empiricism. As opposed to certain other commentators , I argue that Davidson is best understood as rejecting logical empiricism, not because he somehow rejects traditional philosophy altogether, but rather because he pursues the same sorts of philosophical concerns with the nature of language which preoccupy the early Wittgenstein. (shrink)
Recently, there has been a growing awareness that Russell’s post–1918 writings call into question the sort of picture that Rorty presents of the relation of Russell’s philosophy to the views of subsequent figures such as the later Wittgenstein, Quine, and Sellars. As I will argue in this paper, those writings show that by the early 1920’s Russell himself was advocating views—including an anti-foundationalist naturalized epistemology, and a behaviorist–inspired account of what is involved in understanding language—that are more typically associated with (...) philosophers from later decades whom are mistakingly often rpesented as dismantling Russell’s philosophy. (shrink)
Until relatively recently, the main focus of interest in Russell’s philosophy, has been, I think it is fair to say, on his views from his 1905 paper “On Denoting” through his 1918 lectures ”The Philosophy of Logical Atomism”. Such a focus does not involve distinguishing Russell’s early Moore–influenced post–Idealist position from the views he accepted in the wake of the 1900 Paris Congress or considering the interplay between these two aspects of Russell’s development in his 1903 book, The Principles of (...) Mathematics; nor does it involve any consideration of his concerns with “the problems connected with meaning” that are reflected in such post–1918 publications as “On Propositions: What They Are and How They Mean” or The Analysis of Mind. Recently, there has been a growing awareness that Russell’s post–1918 writings call into question the sort of picture that Rorty presents of the relation of Russell’s philosophy to the views of subsequent figures such as the later Wittgenstein, Quine, and Sellars. As I will argue in this paper, those writings show that by the early 1920’s Russell himself was advocating views—including an anti-foundationalist naturalized epistemology, and a behaviorist–inspired account of what is involved in understanding language—that are more typically associated with philosophers from later decades whom are mistakingly often rpesented as dismantling Russell’s philosophy. (shrink)
