Faith, fluxions and impossible numbers in Berkeley's writings of the early 1730S

Modern Schoolman

Volumn 80, Issue 1, 2002, Pages 1-22

  Reid, Jasper ^a  

^a NONE

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EID: 60949666395     PISSN: 00268402     EISSN: None     Source Type: Journal    
DOI: 10.5840/schoolman20028011     Document Type: Article

References (26)

1. G.J. Warnock, Berkeley (Oxford: Blackwell, 1953, 1982 edition). 212.
2. One rare exception, which does take the polemical theological motive seriously, is G.N. Cantor, "Berkeley's The Analyst Revisited," Isis 75(1984)668-683.
3. George Berkeley, Works, A.A. Luce & T.E. Jessop (eds.) (London: Thomas Nelson & Sons, 1948-1957), 2:137.
4. For discussion of Berkeley's theory of meaning, see Anthony Flew, "Was Berkeley a precursor of Wittgenstein?" in David Berman (ed.), George Berkeley: Alciphron or the Minute Philosopher in focus (London & New York: Routledge, 1993), 214-226;
5. Bertil Belfrage, "The clash on semantics in Berkeley's Notebook A," in David Berman (ed.), George Berkeley: Essays and Replies (Dublin: Irish Academic Press, 1986). 117-126;
6. Bertil Belfrage, "Berkeley's Theory of Emotive Meaning (1708)," History of European Ideas, 7 (1986) 643-9.
7. For further discussion, with particular reference to the issue of faith, see David Berman, "Cognitive theology and emotive mysteries in Berkeley's Alciphron" in George Berkeley: Alciphron or the Minute Philosopher in focus, 200-213.
8. Berkeley, "A Sermon preached before the Incorporated Society for the Propagation of the Gospel in Foreign Parts," in his Works, 7:116.
9. Berkeley, De Motu and The Analyst, Douglas M. Jesseph (ed.) (Dordrecht/Boston/London: Kluwer Academic Publishers, 1992), editor's introduction, 130-132.
10. Douglas M. Jesseph, Berkeley's Philosophy of Mathematics (Chicago & London: University of Chicago Press, 1993), 179-80.
11. See also Cantor, "Berkeley's The Analyst Revisited," 673 and n. 15.
12. Jesseph, Berkeley's Philosophy of Mathematics, 116.
13. Berkeley, "On the Algebraic game," in The Works of George Berkeley, G.N. Wright (ed.) (London, 1843), 2:74.
14. Jesseph does acknowledge and even insist upon this point: see Berkeley's Philosophy of Mathematics, 117-118, on the early Berkeley's hostility to the pursuit of pure mathematics divorced from its application to practice.
15. David Hilbert, "On the Infinite," in Paul Benacerraf and Hilary Putnam (eds.), Philosophy of Mathematics: Selected Readings (Oxford: Blackwell, 1964), 134-51, here 141.
16. See Jonathan Bennett, Locke, Berkeley, Hume: Central Themes (Oxford: Oxford University Press, 1971), 54-5.
17. E.T. Bell, The Development of Mathematics (New York & London: McGraw-Hill Book Company, Inc., second edition, 1945), 174;
18. Morris Kline, Mathematical Thought from Ancient to Modern Times (New York: Oxford University Press, 1972), 252-4.
19. William Frend, The Principles of Algebra (London, 1796), ix-xi.
20. Frend, The Principles of Algebra: Part the Second (London, 1799), vii.
21. Frend, "Remarks on the Number of Negative and Impossible Roots in Algebräick Equations," in Francis Maseres (ed.), Tracts on the Resolution of Affected Algebräick Equations (London, 1800), 471-9, here 476.
22. Maseres, Tracts on the Resolution of Affected Algebräick Equations, preface, Iv.
23. See also his Tracts on the Resolution of Cubick & Biquadratick Equations (London, [1803]), v-vi.
24. Maseres, appendix to Frend's The Principles of Algebra, 254.
25. "Report to the Twenty-Second Annual General Meeting," Memoirs of the Royal Astronomical Society, 12 (1842) 455-73, here 461.
26. Augustus de Morgan, "On the Early History of Infinitesimals in England," The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, fourth series, 4 ( 1852) 321-30, here 329 n.