[^14] This has frequently been referred to as just ‘Hume’s Principle’...

[^14] This has frequently been referred to as just ‘Hume’s Principle’; but this does not do justice to Georg Cantor’s role in the story of the use of this principle. Cf. Reck and Beaney 2005, p. [^1]: [^15] In Levine’s account, these are formulated slightly differently, as (Num1) and (Num2); cf. p. [10] below.

[^16] Admittedly, in the Grundlagen (1884), Frege went on to raise some doubts about the use of contextual definition, but his subsequent introduction in the Grundgesetze (1893) of Axiom V, which asserts an analogous equivalence, did not indicate any change in his underlying view of the status of such equivalences, and hence of his conception of numbers as objects.

[^17] Levine notes that Russell introduced logicist definitions of numbers in the spring of 1901, but as late as May 1902 was still hesitant about identifying numbers with equivalence classes (see pp. [12, 15] below).

[^18] See especially Griffin 1991 and Hylton 1990, [^2005]: [^19] It is based on a paper I gave at a conference on the common sources of the two traditions in Memphis in 2001, and which was subsequently published as Beaney [^2002]: I have substantially shortened it for the present volume.

I also drew on this paper in my entry on analysis for the Stanford Encyclopedia of Philosophy (Beaney 2003a), where further details can be found, as well as an extensive bibliography on conceptions of analysis in the history of philosophy. [^20] Cf. Beaney 2003b; Urmson [^1956]: [^21] See, e.g., Baker [^1988]: [^22] See, e.g., Hylton [^2001]: [^23] See, e.g., Moran 2000, ch.

[^6]: [^24] See, e.g., the debate between Thomasson 2003 and Brandl [^2003]: [^25] See Russell 1912, [^1913]: [^26] See, e.g., Baker 2004, chs. 8-[^10]: [^27] Collingwood 1933, [^1940]: Cf. Beaney 2001, 2005. [^28] I am grateful to the contributors to this volume, and especially Peter Hacker and Erich Reck, for comments on the first draft of this introduction.…