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In his review of my anthology Logicism and the Philosophy of Language: Selections from Frege and Russell, Kevin Klement raises some fair criticisms. For example, he points out that the anthology does not contain nearly enough philosophy of mathematics to give beginners grounds for informed conclusions about the logicist thesis. (p.41) I agree, and I did struggle with this point (see p. 9 of my Preface). Given the constraints I was working under, including budget restrictions, I chose to cover the philosophy of language as well as possible, rather than to cover some philo-sophy of language and some philosophy of mathematics. The main aim of this note is to briefly discuss two of Klement’s criticisms of my Introduction: [1] “It ... oddly claims that Russell, contra Kant, wanted to restore the ‘analyticity’ of arithmetical claims, whereas Russell actually claimed that both logic and mathematics were synthetic a priori” (pp. 42-3); and [2] “The editor ... insinuates that Russell never fully engaged with dualistic theories of meaning ... which is easily shown to be false by a study of his 1903-1905 manuscripts.” (p. 43) [1] Klement is right that Russell (1903, p. 457) claims that both mathematics and logic are synthetic a priori. However, by 1919, Russell’s view had evolved considerably: “It is clear that the definition of ‘logic’ or ‘mathematics’ must be sought by trying to give a new definition of the old notion of ‘analytic’ propositions.” (Sullivan, p. 296) To get to the bottom of this would require extensive investigation of such matters as precisely what Russell means by ‘synthetic’ in 1903, precisely what he means by ‘analytic’ in 1919, and precisely which factors lead to this change of doctrine. In any case, in this short note, I respond to this charge of uttering a falsehood by pleading guilty to the lesser charge of oversimplifying this complex issue. The reason why I stress connections between logicism and analyticity in my Introduction is that I have found these connections to be helpful for illuminating and clarifying various things. For instance, Russell’s rejection of an idealist philosophy was one of the crucial factors that lead him to the logicist thesis, and, on many questions concerning logic, mathematics, and their relation, Russell sides with Frege contra Kant. Frege, of course, explicitly argues for the analyticity of the truths of arithmetic - that substantive “conclusions ... are contained in the definitions, but as plants are contained in their seeds, not as beams are contained in a house”(1884, p. 101). I see much in this germane metaphor with which Russell would agree, both in 1903 and in 1919. My focus in the Introduction is on this crux of agreement and its relations to what would become the philosophy of language. [2] It is true that Russell spent much time and effort from 1903 to 1905 working on theories that distinguish between two semantic notions, such as meaning and denotation. However, this per se is not negatively relevant to my claim (p. 81) that the arguments in ‘On Denoting’ that Russell directs at Frege’s theory do not succeed in engaging with Frege’s brand of semantic dualism. Following Coffa (1991, p. 79), I define semantic dualism as the view that the content of what we say is distinct from the objects, events, and states of affairs that we say it about. A semantic dualist, in this sense, holds that every significant linguistic expression is systematically correlated with two different sorts of entity – something like Frege’s senses (i.e., the content of what we say) and references (i.e., what we say it about). Each term expresses a sense, and a sense is a way of representing, or pointing to, a reference. The arguments in ‘On Denoting’ do not engage with this type of semantic dualism, in my opinion, because the arguments rely on some assumptions that this dualism explicitly rejects - for instance, that co-referential words make exactly the same contribution to propositional content, or that if a term does not refer to anything actual, then sentences in which it occurs must express nonsense. Indeed, concerning the relevant notion of semantic dualism, Russell made his position perfectly clear in the famous “Mont Blanc” letter to Frege: “I believe that in spite of all its snowfields Mont Blanc is itself a component of what is actually asserted in the proposition ‘Mont Blanc is more than 4000 meters high’. ... If we do not admit this, then we get the conclusion that we know nothing at all about Mont Blanc” (Frege 1980, p. 169). So, clearly, in the 1903-1905 manuscripts, Russell engages with several views that deserve to be called ‘semantic dualism’, in some sense or other. However, by 1905 Russell considers the view that I, following Coffa, call ‘semantic dualism’ to be a total non-starter - on the questionable grounds that if what we say does not literally consist of what we say it about, then we are cognitively cut off from the worldly referents of our thought and talk. My claim is that no arguments in ‘On Denoting’ engage with this notion of dualism, I do not see how this claim could be refuted by that anything one might point to in the 1903-1905 manuscripts.
Coffa, J. Alberto. 1991. The Semantic Tradition from Kant to Carnap. Cambridge: Cambridge University Press. Frege, Gottlob. 1884. The Foundations of Arithmetic. J.L. Austin, trans. Oxford: Blackwell, 1950. Frege, Gottlob. 1980. Philosophical and Mathematical Correspondence. H. Kaal, trans. Oxford: Blackwell. Klement, Kevin C. 2003. Review of Sullivan, ed. (2003). Bertrand Russell Society Quarterly 120, 39-43. Russell, Bertrand. 1903. Principles of Mathematics. London: Allen and Unwin. Sullivan, Arthur, ed. 2003. Logicism and the Philosophy of Lan-guage: Selections from Frege and Russell. Peterborough, Ontario: Broadview Press. |