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LEIBNIZ, GOTTFRIED WILHELM (b. Leipzig,
Germany, 1 July 1646; d. Hannover, Germany,
14 November 1716), mathematics, philosophy, metaphysics.
the development of modern logic can be traced back
to Leibniz. In this connection, it is fortunate that
(in the absence of any publications of Leibniz) there
is a tradition of correspondence beginning with letters
between Leibniz, Oldenburg, and Tschirnhaus. The
emphasis here, as exemplified in the logic theories of
Ploucquet, Lambert, and Castillon, is on the intensional
interpretation of logical calculi.
While there is an affinity between the theory of
monads and Russell's logical atomism, a direct
influence of the more metaphysical parts of the
theory of monads on the history of scientific thought
is difficult to prove. Particular results, such as the
biological concept of preformation (accepted by
Haller, Bonnet, and Spallanzani) or the discovery of
sensory thresholds, though related to the theory of
monads in a systematic way, became detached from
it and followed their own lines of development. Yet
the term “monad” played an important role with
Wolff, Baumgarten, Crusius, and, at the beginning,
with Kant (as exemplified in his Monadologica
physica of 1756), then later with Goethe and Solger as
well. Vitalism in its various forms, including the
“biological romanticism” of the nineteenth century
(the Schelling school), embraced in general the
biological interpretation of the theory of monads,
but this did not amount to a revival of the metaphysical
theory. It is more likely that vitalism simply
represented a reaction against mechanism, a tradition
to which Leibniz also belonged.
NOTES
1. Duns Scotus, Questiones super universalibus Porphyrii
(Venice, 1512), Quest. 3.
2. L. Couturat, ed., Opuscules et fragments inédits de
Leibniz
(Paris, 1903; Hildesheim, 1966), p. 594.
3. G. W. Leibniz, Sämtliche Schriften und Briefe, VI, 2,
pp. 258-276.
4. T. Hobbes, Elementorum philosophiae (London, 1655),
sectio prima: de corpore, pars tertia, cap. 15, §2 and §3.
5. Sämtliche Schriften und Briefe, VI, 2, p. 264.
6. Ibid., p. 266.
7. Ibid., p. 231.
8. Ibid., pp. 221-257.
9. Ibid., p. 257.
10. Sämtliche Schriften und Briefe, II, 1, p. 172.
11. Ibid., pp. 488-490.
12. G. W. Leibniz, Die philosophischen Schriften, C. I. Gerhardt,
ed., IV, p. 444; cf. p. 369.
13. Sämtliche Schriften und Briefe, II, 1, p. 508.
14. P. Costabel, Leibniz et la dynamique (Paris, 1960), p.
106.
15. G. W. Leibniz, Mathematische Schriften, C. I. Gerhardt,
ed., VI, pp. 230-231. The manuscript called Essay de dynamique
by Gerhardt is not earlier than 1698.
16. P. Costabel, op. cit., p. 105.
17. Ibid., p. 12.
18. Sämtliche Schriften und Briefe, VI, 6, p. 487.
19. L. Couturat, op. cit., p. 430.
20. Die philosophischen Schriften, VII, p. 32.
21. Principia mathematica, *3. 47.
22. Die philosophischen Schriften, VII, pp. 228-247. Cf. L.
Couturat, op. cit., pp. 246-270.
23. Sämtliche Schriften und Briefe, VI, 1, p. 183.
24. Die philosophischen Schriften, VII, p. 301.
25. Ibid., IV, pp. 447-448.
26. Ibid., VII, pp. 270-279.
27. G. W. Leibniz, Textes inédits, G. Grua, ed. (Paris,
1948), I,
p. 287.
28. Die philosophischen Schriften, VII, p. 309. Cf. L. Couturat,
op. cit., p. 525.
29. L. Couturat, op. cit., p. 515.
30. Sämtliche Schriften und Briefe, VI, 6, p. 230.
31. Die philosophischen Schriften, VII, p. 219.
32. Ibid., IV, p. 469.
33. Ibid., III, p. 645.
34. Ibid., IV, p. 447.
35. Mathematische Schriften, VII, p. 326.
36. Die philosophischen Schriften, II, p. 97.
37. Nicholas of Cusa, De docta ignorantia, Bk. II, ch. 7.
38. Die philosophischen Schriften, II, p. 304.
39. Ibid., IV, p. 483.
40. Principes de la nature et de la grâce, A. Robinet,
ed., p. 27.
41. Discours de métaphysique, G. le Roy, ed., p. 50.
42. Die philosophischen Schriften, I, p. 416.
43. Ibid., II, p. 58.
44. Mathematische Schriften, VI, p. 236.
45. Die philosophischen Schriften, II, p. 372.
46. Ibid., IV, p. 482.
47. Ibid., IV, p. 491. Cf. II, p. 450.
48. Ibid., VII, p. 415.
49. Ibid., VII, p. 401.
50. Mathematische Schriften, VII, p. 18.
51. Die philosophischen Schriften, VII, p. 364.
52. Ibid., II, p. 270. Cf. Mathematische Schriften, VI, p.
247.
53. Mathematische Schriften, II, p. 184.
54. Die philosophischen Schriften, VII, p. 404. Cf. IV, p. 444
and L. Couturat, op. cit., p. 594.
JÜRGEN MITTELSTRASS
ERIC J. AITON
LEIBNIZ: Mathematics
Leibniz had learned simple computation and a little
geometry in his elementary studies and in secondary
schools, but his interest in mathematics was aroused
by the numerous remarks on the importance of the
subject that he encountered in his reading of philosophical
works. In Leipzig, John Kuhn's lectures on
Euclid left him unsatisfied, whereas he received some
stimulation from Erhard Weigel in Jena. During his
student years, he had also cursorily read introductory
works on Cossist algebra and the Deliciae physicomathematicae
of Daniel Schwenter and Philipp
Harsdörffer (1636-1653) with their varied and mainly
practical content. At this stage Leibniz considered
himself acquainted with all the essential areas of
mathematics that he needed for his studies in logic,
which attracted him much more strongly. The very
modest specialized knowledge that he then possessed
is reflected in the Dissertatio de arte combinatoria
