¹ On Moore's contribution to analytic philosophy, see T. Baldwin, G.E. Moore (London: Routledge, 1990) and ‘G.E. Moore and the Cambridge School of Analysis’ in The Oxford Handbook of the History of Analytic Philosophy (ed.) M. Beaney (Oxford University Press, 2013), 430–50.

² For an account of Wittgenstein's influence, see P.M.S. Hacker, Wittgenstein's Place in Twentieth-Century Analytic Philosophy (Oxford: Blackwell, 1996).

³ In fact, Frege only introduced a notation for the universal quantifier, relying on the equivalence between ‘Something is F’ and ‘It is not the case that everything is not F’ to represent the existential quantifier. For an account of Frege's logical notation, see App. 2 of The Frege Reader (ed.) M. Beaney (Oxford: Blackwell, 1997).

⁴ To make clear that there are two different relations here, between object and concept and between first-level and second-level concept, Frege distinguishes between falling under (subsumption) and falling within. But the two relations are analogous. See Frege, ‘Über Begriff und Gegenstand’, Vierteljahrsschrift für wissenschaftliche Philosophie 16 (1892), 192–205Google Scholar; tr. as ‘On Concept and Object’ in The Frege Reader, 181–93, 189. Both relations are different from subordination (as explained in the previous section), which is a relation between concepts of the same level.

⁵ As Frege himself makes clear (Die Grundlagen der Arithmetik, (Breslau: W. Koebner, 1884), §53/The Frege Reader, 103), his analysis of existential statements also offers a diagnosis of what is wrong with the traditional ontological argument for the existence of God. In its most succinct form, this may be set out as follows: (1) God has every perfection; (2) existence is a perfection; therefore (3) God exists. In (1) we are taking ‘perfections’ to be first-level properties, but on Frege's view, ‘existence’ is not to be understood as a first-level property, so the argument fails.

⁶ For fuller discussion of conceptions of analysis in the history of philosophy, and of the interpretive conception, which is what I think especially characterizes analytic philosophy, see M. Beaney, ‘Analysis’ (2009) in The Stanford Encyclopedia of Philosophy, online at: plato.stanford.edu/entries/analysis.

⁷ Frege does not, in fact, provide a logical analysis of precisely this example, and I also use here modern notation; but the analysis is in the spirit of his account in the Foundations.

⁸ I give a fuller sketch in Beaney Frege: Making Sense (London: Duckworth, 1996), chs. 3–4; and in comparing Frege's and Russell's logicist projects, in Beaney ‘Russell and Frege’, in The Cambridge Companion to Bertrand Russell (ed.) N. Griffin (Cambridge: Cambridge University Press, 2003), 128–70; Beaney ‘Frege, Russell and Logicism’ in (eds) M. Beaney and E.H. Reck Gottlob Frege: Critical Assessments (London: Routledge).

⁹ For a detailed account of this, see Griffin Russell’s Idealist Apprenticeship (Oxford: Clarendon Press, 1991); Griffin ‘Russell and Moore’s Revolt against British Idealism’, in The Oxford Handbook of the History of Analytic Philosophy (ed.) M. Beaney (Oxford: Oxford University Press, 2013), 383–406.

¹⁰ There has been a huge amount written both on the theory of descriptions itself and on its history, and I can do no justice to any of this here. A full understanding would have to recognize, for example, how the theory improved on Russell's own earlier theory of denoting (as presented in The Principles of Mathematics of 1903). For discussion, see e.g. Hylton Russell, Idealism, and the Emergence of Analytic Philosophy (Oxford: Clarendon Press, 1990); Hylton, ‘The Theory of Descriptions’, in The Cambridge Companion to Bertrand Russell (ed.) Griffin, N. (Cambridge: Cambridge University Press, 2003); Linsky ‘Russell’s Theory of Descriptions and the Idea of Logical Construction’, in The Oxford Handbook of the History of Analytic Philosophy (ed.) M. Beaney (Oxford: Oxford University Press, 2013).

¹¹ Russell had first tried to answer these questions in his earlier theory of denoting (see the previous note). But for various reasons which we cannot address here, he soon became dissatisfied with his answer.

¹² Very roughly, it could be read as saying that were it to seem as if two objects fell under the concept King of France, then they would actually be one and the same.

¹³ Russell, ‘On Denoting', 488; My Philosophical Development (London: George Allen and Unwin, 1959), 64.

¹⁴ Die Grundlagen der Arithmetik, §57.

¹⁵ For details, see Beaney Frege: Making Sense (London: Duckworth, 1996), ch. 5; Beaney ‘Sinn, Bedeutung and the Paradox of Analysis’ in Gottlob Frege: Critical Assessments (eds) M. Beaney and E.H. Reck (London: Routledge, 2005).

¹⁶ I discuss the issue in Beaney Frege: Making Sense (London: Duckworth, 1996), ch. 8.

¹⁷ I offer an account of the different – but related – conceptions and practices of analysis in the history of philosophy in Beaney ‘Analysis’, in The Stanford Encyclopedia of Philosophy (2009), online at: plato.stanford.edu/entries/analysis.