- See Blackwell K. The importance to philosophers of the Bertrand Russell Archive Dialogue 1969 7 608 615 The Archives were initially called ‘Archive’, which was changed to ‘Archives’ on Russell's insistence.
- See A detailed catalogue of the archives of Bertrand Russell Feinberg B. London 1967 61 61
- See my Materials for the history of mathematics in the Institut Mittag-Leffler Isis 1971 62 363 374 (p. 368)
- One of them was presented as a little centennial tribute in my Bertand Russell on his paradox and the multiplicative axiom: … J. Phil. Logic 1973 1 103 110 An annotated edition of the full correspondence is asymptotically approaching completion under the title Dear Russell—Dear Jourdain.
- Russell to G. Frege May 1903 24 (original in the Sammlung Darmstaedter, Stiftung Preussischer Kulturbesitz, Berlin; photocopy in the Russell Archives; to be published in the forthcoming edition of Frege's Wissenschaftlicher Briefwechsel).
- Russell to E. Halevy July 1903 19 (original in possession of the Halevy family; photocopy in the Russell Archives).
- Russell to G. Murray, 28 December 1902 (original in Bodleian Library, Oxford; photocopy in the Russell Archives; part—including this phrase—published in The autobiography of Bertrand Russell London 1967 163 163 1872–1914
- Russell , B. 1903 . The principles of mathematics , 1st ed. Cambridge 2nd ed., 1937, London. See esp. ch. 10.
- Russell , B. 1906 . On some difficulties in the theory of transfinite numbers and order types . Proc. London Math. Soc. , 4 ( 2 ) : 29 – 53 . (p. 53). Reprinted in his Essays in analysis (ed. D. Lackey), 1973, London, 135–164 (p. 164). (My paper was written before the publication of Essays.)
- See Russell B. On some difficulties in the theory of transfinite numbers and order types Proc. London Math. Soc. 1906 4 2 45 47 and ‘Les paradoxes de la logique’, Rev. méta. morale, 1906, 14, 627–650 (pp. 636–638). Also respectively in Essays (footnote 9), 154–156 and 200–204 (in the English original for the latter paper).
- Russell , B. 1908 . Mathematical logic as based on the theory of types . Amer. J. Maths. , 30 : 222 – 262 . (pp. 238–239). Reprinted in his Logic and Knowledge (ed. R. C. Marsh), 1956, London, 59–102 (p. 77); and J. van Heijenoort, From Frege to Gödel …, 1967, Cambridge, Mass., 150–182 (pp. 164–165).
- Russell , B. On the substitutional theory of classes and relations . Essays , 165 – 189 . published in (footnote 9) All future citations are from the published version.
- Russell , B. On the substitutional theory of classes and relations . Essays , 169 – 170 . published in (footnote 9)
- Compare Russell's remark in ‘On some difficulties’ Russell B. On some difficulties in the theory of transfinite numbers and order types Proc. London Math. Soc. 1906 45 2 29 53 Essays (footnote 9), 155
- Russell , B. 1905 . On denoting . Mind , 14 : 479 – 493 . n.s. Reprinted (amongst other places) in Essays (footnote 9), 103–119; Logic (footnote 11), 41–56.
- Lackey , D. , ed. 1906 . Essays in analysis 135 – 164 . London
- Lackey , D. , ed. 1906 . Essays in analysis 170 – 170 . London 174, 176–177.
- Lackey , D. , ed. 1906 . Essays in analysis 173 – 174 . London
- Lackey , D. , ed. 1906 . Essays in analysis 168 – 168 . London see also the manuscript ‘On substitution’ (22 December 1905), f.7.
- Lackey , D. , ed. 1906 . Essays in analysis 168 – 169 . London
- The substitutional interpretation of quantification was initiated in papers such as Marcus R.B. Interpreting quantifiers Inquiry 1962 5 252 259 Discussion of this interpretation would form too extensive a digression here, but critical points are made in, for example, W. V. O. Quine, Philosophy of Logic, 1970, Englewood Cliffs, N.J., 91–94.
- Lackey , D. , ed. 1906 . Essays in analysis 172 – 172 . London
- Lackey , D. , ed. 1906 . Essays in analysis 169 – 169 . London In ‘On substitution’ (footnote 20), f. 6, the names of the defined properties were different. ‘ex’ was ‘out’ while ‘ind’ was ‘ex’. Another property was defined as ‘ind’, namely: a ind b. = .a out b.b out a Df.
- Lackey , D. , ed. 1906 . Essays in analysis 173 – 174 . London
- Lackey , D. , ed. 1906 . Essays in analysis 168 – 168 . London
- For a quotation of one of these criticisms see Lackey D. The Whitehead correspondence Russell 1972 5 14 16 spring
- Lackey , D. , ed. 1906 . Essays in analysis 173 – 173 . London (footnote)
- Lackey , D. , ed. 1906 . Essays in analysis 176 – 176 . London
- Compare Essays in analysis Lackey D. London 1906 175 175
- Compare Essays in analysis Lackey D. London 1906 175 175
- Russell . 1906 . On substitution . Proc. London Math. Soc. , 4 ( 2 ) : 4 – 4 .
- Lackey , D. , ed. 1906 . Essays in analysis 169 – 169 . London
- Russell . 1906 . On some difficulties . Proc. London Math. Soc. , 4 ( 2 ) : 46 – 46 . Essays (footnote 9), 155.
- Lackey , D. , ed. 1906 . Essays in analysis 176 – 176 . London
- Lackey , D. , ed. 1906 . Essays in analysis 176 – 176 . London
- Lackey , D. , ed. 1906 . Essays in analysis 177 – 177 . London
- Lackey , D. , ed. 1906 . Essays in analysis 178 – 178 . London
- This fact should have been indicated editorially in Essays in analysis Lackey D. London 1906 180 180 at the paragraph beginning ‘The difficulties as regards ….’.
- Lackey , D. , ed. 1906 . Essays in analysis 180 – 183 . London
- Compare Russell's Mathematical logic Amer. J. Maths. 1908 30 222 262 art. 10; and Russell and Whitehead's Principia Mathematica, 1st ed. 1910–13; 2nd ed. 1925–27, Cambridge, *265.
- On this question see, for example Quine W.V.O. Whitehead and the rise of modern logic The philosophy of Alfred North Whitehead , 2nd ed. Schilpp P.A. New York 1951 125 163 (reprinted in Quine's Selected logic papers, 1966, New York, 3–36); K. Gödel, ‘Russell's mathematical logic’, P. A. Schlipp (ed.,), The philosophy of Bertrand Russell, 1944, New York, 123–153 (reprinted in D. F. Pears, Bertrand Russell, 1972, New York, 192–226); C. S. Chihara, ‘Russell's theory of types’, Pears (ibid.), 245–289 (reprinted with revisions in Chihara's Ontology and the vicious circle principle, 1973, Ithaca and London, ch. 1); J. Vuillemin, Leçons sur la première philosophie de Russell, 1968, Paris, passim; and also my edition of the Russell-Jourdain correspondence in preparation (footnote 4).
- Russell . 1967 . The Autobiography of Bertrand Russell 1872–1914 183 – 183 . London
- See ff. 94–95 of his ‘On substitution’ (May–June 1906; not the same manuscript as that cited in Russell B. On some difficulties in the theory of transfinite numbers and order types Proc. London Math. Soc. 1906 4 2 29 53 and also f. 76 of ‘The paradox of the liar’ (September 1906).
- Lackey , D. , ed. 1906 . Essays in analysis 168 – 168 . London
- Russell , B. 1918 . The philosophy of logical atomism [part 1] . The Monist , 28 : 495 – 527 . (p. 507); reprinted in Logic (footnote 11), 178–203 (p. 187).
- Lackey , D. , ed. 1906 . Essays in analysis 188 – 188 . London
- Russell . 1903 . The principles of mathematics , 1st ed. 527 – 527 . Cambridge
- Russell , B. April–May 1906 . Logic in which propositions are not entities April–May , In the context of truth, see also the manuscript ‘What is truth?’ (June 1905). Note also ‘Fundamentals’ (1907), f.6: ‘A value of an apparent variable must be something, and thus the no-classes theory won't work. It worked while we had propositions because then they became apparent variables …’.
- Russell , B. 1906–07 . On the nature of truth . Proc. Arist. Soc. , 7 : 28 – 49 . (esp. p. 49).
- Russell , B. 1910 . Philosophical Essays , 1st ed. London ch. 7
- Russell , B. 1912 . The problems of philosophy London see esp. chs. 5 and 12.
- 1908 . Principia Mathematica , 2nd ed. Vol. 1 , 41 – 43 . and 62 respectively; see also pp. 128–129.
- On the other hand, he was a pioneer in even recognising the problem. The manuscript ‘On the paradox of the liar’ (1906) is relevant in places, one of which is quoted by Lackey Essays in analysis Lackey D. London 1906 134 134 Lackey's judgement that Russell ‘was certainly not confused’ about the problem is surely over-optimistic, for having made such insights Russell would then discard them.
- See Russell The Principles of mathematics , 1st ed. Cambridge 1903 ch. 2. I have discovered new documentary information on Peano's influence on Russell, which will be presented in a paper dealing with Norbert Wiener's unpublished Ph.D. thesis.
- See Russell The Principles of mathematics , 1st ed. Cambridge 1903 see esp. ch. 7. Quine has criticised this view of Russell, in connection with first and higher order quantification, in various places; see for example, his ‘Whitehead’ (footnote 42), art. 5.
- Compare Russell's account of the problem in his later Introduction to mathematical philosophy London 1919 chs. 15 and 17.
- The manuscript is now published in Essays in analysis Lackey D. London 1906 295 306
- Peano , G. 1895 . Riv. di mat. , 1 : 122 – 128 . [Review of G. Frege, Grundgesetze der Arithmetik …, vol. 1, 1893, Jena] Reprinted in Peano's Opere scelte, vol. 2, 1958, Rome, 189–195.
- Russell , B. 1956 . Portraits from memory 25 – 25 . London
- Wittgenstein , L. 1922 . Tractatus logico-philosophicus London see esp. props. 301 and 303.
- Russell , B. 1911 . Sur les axiomes de l'infini et du transfini . C.R. Soc. Math. France , : 22 – 35 . (p. 23). An English translation of this extremely little-known paper will appear in my edition of the Russell-Jourdain correspondence (footnote 4).
- This assumption is made in Principia Mathematica, though never in a prominent place. In vol. 1 (2nd ed.) see pp. 162, 208, 216, 225–226 and 335. Compare also Russell Introduction to mathematical philosophy London 1919 203 203
- Russell also asserted the opposite view ‘In pure mathematics as such, we do not consider objects existing in the actual world’. ‘Non-Euclidean geometry’ The Athenaeum 1904 4018 592 593
- Russell . 1919 . Introduction to mathematical philosophy 131 – 133 . London
- See especially Russell's The axiom of infinity Hibbert J. 1903–04 2 809 812 (reprinted in Essays, 256–259); and compare The principles (footnote 8), art. 292.
- Russell . 1908 . Mathematical logic . Amer. J. Maths. , 30 : 258 – 258 . (Logic (footnote 11), 97; van Heijenoort (footnote 11), 179).
- 1910–13 . Principia Mathematica , 2nd ed. Vol. 2 , vii – xxxi . see also *126.
- 1910–13 . Principia Mathematica , 2nd ed. Vol. 2 , xvii – xvii .
- 1910–13 . Principia Mathematica , 2nd ed. Vol. 2 , xxii – xxiii .
- See The philosophy of Alfred North Whitehead , 2nd ed. Schilpp P.A. New York 1951 749 749
- Wiener's relationship with Russell at this time is discussed in my paper in preparation Russell The Principles , 1st ed. Cambridge 1903
- This paragraph has been published in Pitt J. With Russell at the Archives Russell 1971 2 3 7 summer (p. 6).
Annals of Science
Volume 31, 1974 - Issue 5