On the very concept of harmony in Leibniz

Review of Metaphysics

Volumn 54, Issue 1, 2000, Pages 99-125

  Carlin, Laurence ^a  

^a UNIVERSITY OF WISCONSIN OSHKOSH   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034258851     PISSN: 00346632     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Review

References (118)

1. See, for example G. W. Leibniz, Hauptschriflen zur Grundlegung der Philosophie, ed. Ernst Cassirer (Hamburg: Felix Meiner, 1966), 2:556. An English translation is in G. W. Leibniz, Leibniz: Selections, trans. and ed. Phillip Weiner (New York: Scribners, 1951), 185. In what follows, if an English translation is available, I cite it after the original language source. If no English translation is cited, then none is available, and the translation is my own.
2. See, for example G. W. Leibniz, Hauptschriflen zur Grundlegung der Philosophie, ed. Ernst Cassirer (Hamburg: Felix Meiner, 1966), 2:556. An English translation is in G. W. Leibniz, Leibniz: Selections, trans. and ed. Phillip Weiner (New York: Scribners, 1951), 185. In what follows, if an English translation is available, I cite it after the original language source. If no English translation is cited, then none is available, and the translation is my own.
3. See, for example, G. W. Leibniz, Die Philosophischen Schriften von Gottfried Wilhelm Leibniz, ed. C. I. Gerhardt (Berlin: Weidman, 1875-1890; reprint, Hildesheim: Olms, 1961), 6:599; G. W. Leibniz, Philosophical Writings, trans. and ed. Mary Morris and G. H. R. Parkinson (London: Dent, 1973), 196.
4. See, for example, G. W. Leibniz, Die Philosophischen Schriften von Gottfried Wilhelm Leibniz, ed. C. I. Gerhardt (Berlin: Weidman, 1875-1890; reprint, Hildesheim: Olms, 1961), 6:599; G. W. Leibniz, Philosophical Writings, trans. and ed. Mary Morris and G. H. R. Parkinson (London: Dent, 1973), 196.
5. See, for example, Leibniz, Die Philosophischen Schriften, 6:622; G. W. Leibniz, Philosophical Essays, trans. and ed. Roger Ariew and Daniel Garber (Indianapolis: Hackett, 1989), 224.
6. See, for example, Leibniz, Die Philosophischen Schriften, 6:622; G. W. Leibniz, Philosophical Essays, trans. and ed. Roger Ariew and Daniel Garber (Indianapolis: Hackett, 1989), 224.
7. More specifically, it seems to me that when it comes to discussions of the very concept of harmony, as opposed to various remarks concerning its applications, most of the relevant texts occur in the 1670s. Thereafter, the only extended discussion I am aware of is not until 1714 in a letter written to Christian Wolff. See G. W. Leibniz, Briefweschel zwischen Leibniz und Christian Wolff, ed. C. I. Gerhardt (Hildesheim: Olms, 1963), 166; Leibniz, Philosophical Essays, 230. In the latter part of this paper, however, I will suggest reasons for thinking that there is significant continuity in his thought on this topic.
8. More specifically, it seems to me that when it comes to discussions of the very concept of harmony, as opposed to various remarks concerning its applications, most of the relevant texts occur in the 1670s. Thereafter, the only extended discussion I am aware of is not until 1714 in a letter written to Christian Wolff. See G. W. Leibniz, Briefweschel zwischen Leibniz und Christian Wolff, ed. C. I. Gerhardt (Hildesheim: Olms, 1963), 166; Leibniz, Philosophical Essays, 230. In the latter part of this paper, however, I will suggest reasons for thinking that there is significant continuity in his thought on this topic.
9. The former quotation is from G. W. Leibniz, Sämtliche Schriften und Briefe, ed. German Academy of Sciences (Darmstadt and Berlin: Berlin Academy, 1923-), 2d ser., 1:98; the latter is from 6th ser., 1:484. It is worth mentioning that I have not found any other passages where Leibniz used these last two expressions to define harmony. However, this does not seem too important, since the idea expressed in this terminology appears to be the same idea expressed using other, more frequently used, terminology.
10. See Leibniz, Sämtliche Schriften und Briefe, 6th ser., 1:475, 477, 479, 484, and 2d ser., 1:283. According to 6th ser., 2:283, Harmonia . . . est unitate plurimorum, which translates more exactly as "harmony is the unity of pluralities." Again, the idea appears to be the same. See also, G. W. Leibniz, Textes Inédits, ed. Gaston Grua (Paris: Presses Universitaires de France, 1948), 12-13.
11. See Leibniz, Sämtliche Schriften und Briefe, 6th ser., 1:475, 477, 479, 484, and 2d ser., 1:283. According to 6th ser., 2:283, Harmonia . . . est unitate plurimorum, which translates more exactly as "harmony is the unity of pluralities." Again, the idea appears to be the same. See also, G. W. Leibniz, Textes Inédits, ed. Gaston Grua (Paris: Presses Universitaires de France, 1948), 12-13.
12. See Leibniz, Sämtliche Schriften und Briefe, 6th ser., 1:475, 477, 479, 484, and 2d ser., 1:283. According to 6th ser., 2:283, Harmonia . . . est unitate plurimorum, which translates more exactly as "harmony is the unity of pluralities." Again, the idea appears to be the same. See also, G. W. Leibniz, Textes Inédits, ed. Gaston Grua (Paris: Presses Universitaires de France, 1948), 12-13.
13. Leibniz, Textes Inédits, 12.
14. In what follows, I temporarily leave aside Leibniz's utilization of the notion of "proportion" and focus instead on "order," a notion which he used more frequently in this context. We shall see, however, that the two notions were closely related for Leibniz for both were used to designate certain intelligible relations between entities.
15. Another implication of the passage, evident from Leibniz's claim that "the greater the variety and the unity in variety, this variety is harmonious to a higher degree," is that harmony admits of degrees: two sets of entities may each be harmonious, yet one may be more harmonious. I leave aside this complication for now and return to it after pursuing a more satisfactory formulation of harmony.
16. Leibniz, Die Philosophischen Schriften, 4:431; Leibniz, Philosophical Essays, 39.
17. Leibniz, Die Philosophischen Schriften, 4:431; Leibniz, Philosophical Essays, 39.
18. Leibniz, Die Philosophischen Schriften, 7:312; Leibniz, Philosophical Writings, 78-9.
19. Leibniz, Die Philosophischen Schriften, 7:312; Leibniz, Philosophical Writings, 78-9.
20. Some commentators may see in passages such as the two just quoted, the theological claim that God - due to his infinite wisdom - could not create a world which lacked order because infinitely wise beings always act with order (or according to rules, laws, principles). That is, according to this reading, disorderly worlds may be metaphysically possible, but they are not ones God could create (and so are not really possible worlds, I suppose). But if this is Leibniz's point it is difficult to see why he did not just come out and say it. Moreover, both passages make the claim that we cannot even "imagine" or "conceive" of an unorderly arrangement because there is always a mutually ordering relationship to be found. There is no mention - or even suggestion - that any point being made here is relative to divine wisdom. The point seems purely one of logic. On this, see Gregory Brown's "Compossibility, Harmony, and Perfection in Leibniz," The Philosophical Review 96 (1987): 173-203.
21. G. W. Leibniz, Die Leibniz-Handschriften der Königlichen, Öffentlichen Bibliothek zu Hannover, ed. Eduard Bodemann (Hildesheim: Olms, 1966), 124.
22. Leibniz, Die Leibniz-Handschriften, 70.
23. Leibniz, Opuscules et Fragments Inédits de Leibniz, ed. Louis Couterat (Paris: Felix Alcan, 1903), 476. The first of these definitions is dated by watermark from the early 1690s (compare Robert Adams, Leibniz: Determinist, Theist, Idealist [Oxford: Oxford University Press, 1994], 235). I have been unable to obtain a dating of the second. The third is from a table of definitions dated from 1702-4. Notice that the sense of the third is slightly different from the other two. The first two have it that an ordered relation is one in which the elements can be distinguished, whereas the third says that the elements are distinguished [discriminatur]. I doubt that much hinges on this, but it is unfortunate since the third again threatens triviality: for if an ordered relation is one in which, say, a finite mind can distinguish the elements (as in the first two definitions), that would presumably indicate a certain level of order-perhaps the one we are looking for. But this is not suggested by the third definition. At any rate, I have found no indication that Leibniz changed his mind on the issue, and, in fact, as we shall see, there is evidence that Leibniz believed the first two definitions to be the more accurate. For this reason I shall lean primarily on them in what follows. (Perhaps the third is a slip, in that it omits any form of the verb possum?)
24. Leibniz, Opuscules et Fragments Inédits de Leibniz, ed. Louis Couterat (Paris: Felix Alcan, 1903), 476. The first of these definitions is dated by watermark from the early 1690s (compare Robert Adams, Leibniz: Determinist, Theist, Idealist [Oxford: Oxford University Press, 1994], 235). I have been unable to obtain a dating of the second. The third is from a table of definitions dated from 1702-4. Notice that the sense of the third is slightly different from the other two. The first two have it that an ordered relation is one in which the elements can be distinguished, whereas the third says that the elements are distinguished [discriminatur]. I doubt that much hinges on this, but it is unfortunate since the third again threatens triviality: for if an ordered relation is one in which, say, a finite mind can distinguish the elements (as in the first two definitions), that would presumably indicate a certain level of order-perhaps the one we are looking for. But this is not suggested by the third definition. At any rate, I have found no indication that Leibniz changed his mind on the issue, and, in fact, as we shall see, there is evidence that Leibniz believed the first two definitions to be the more accurate. For this reason I shall lean primarily on them in what follows. (Perhaps the third is a slip, in that it omits any form of the verb possum?)
25. Leibniz, Die Philosophischen Schriften, 7:290; Leibniz, Philosophical Writings, 146.
26. Leibniz, Die Philosophischen Schriften, 7:290; Leibniz, Philosophical Writings, 146.
27. Ibid.
28. Leibniz, Textes Inédits, 13.
29. Leibniz, Leibniz und Christian Wolff, 170-1; Leibniz, Philosophical Essays, 233-4.
30. Leibniz, Leibniz und Christian Wolff, 170-1; Leibniz, Philosophical Essays, 233-4.
31. Leibniz, Textes Inédits, 12-13.
32. It also has the virtue of linking the notion of harmony with that of perfection. The question of how exactly these two concepts are related in Leibniz's thought is a vexing question which I steer clear of here. For discussion of various aspects of the issue, see Gregory Brown, "Compossibility, Harmony, Perfection"; chapter 2 of Donald Rutherford, Leibniz and the Rational Order of Nature (Cambridge: Cambridge University Press, 1995); David Blumenfeld, "Perfection and Happiness in the Best Possible World," in The Cambridge Companion to Leibniz, ed. Nicholas Jolley (Cambridge: Cambridge University Press, 1994), 382-410.
33. It also has the virtue of linking the notion of harmony with that of perfection. The question of how exactly these two concepts are related in Leibniz's thought is a vexing question which I steer clear of here. For discussion of various aspects of the issue, see Gregory Brown, "Compossibility, Harmony, Perfection"; chapter 2 of Donald Rutherford, Leibniz and the Rational Order of Nature (Cambridge: Cambridge University Press, 1995); David Blumenfeld, "Perfection and Happiness in the Best Possible World," in The Cambridge Companion to Leibniz, ed. Nicholas Jolley (Cambridge: Cambridge University Press, 1994), 382-410.
34. It also has the virtue of linking the notion of harmony with that of perfection. The question of how exactly these two concepts are related in Leibniz's thought is a vexing question which I steer clear of here. For discussion of various aspects of the issue, see Gregory Brown, "Compossibility, Harmony, Perfection"; chapter 2 of Donald Rutherford, Leibniz and the Rational Order of Nature (Cambridge: Cambridge University Press, 1995); David Blumenfeld, "Perfection and Happiness in the Best Possible World," in The Cambridge Companion to Leibniz, ed. Nicholas Jolley (Cambridge: Cambridge University Press, 1994), 382-410.
35. See Leibniz, Textes Inédits, 547, where Leibniz admits to being a nominalis, "at least provisionally." I cannot see that anything in the passage explains this qualifier. He adds "that it suffices to posit substances as real things and to assert truths about these." See also, "Preface to An Edition of Nizolius," in Leibniz, Die Philosophischen Schriften, 4:138; translation in G. W. Leibniz, Philosophical Papers and Letters, trans. and ed. Leroy Loemker (Dordrecht: Reidel, 1969), 121.
36. See Leibniz, Textes Inédits, 547, where Leibniz admits to being a nominalis, "at least provisionally." I cannot see that anything in the passage explains this qualifier. He adds "that it suffices to posit substances as real things and to assert truths about these." See also, "Preface to An Edition of Nizolius," in Leibniz, Die Philosophischen Schriften, 4:138; translation in G. W. Leibniz, Philosophical Papers and Letters, trans. and ed. Leroy Loemker (Dordrecht: Reidel, 1969), 121.
37. See Leibniz, Textes Inédits, 547, where Leibniz admits to being a nominalis, "at least provisionally." I cannot see that anything in the passage explains this qualifier. He adds "that it suffices to posit substances as real things and to assert truths about these." See also, "Preface to An Edition of Nizolius," in Leibniz, Die Philosophischen Schriften, 4:138; translation in G. W. Leibniz, Philosophical Papers and Letters, trans. and ed. Leroy Loemker (Dordrecht: Reidel, 1969), 121.
38. G. W. Leibniz, New Essays on Human Understanding, trans. and ed. Peter Remnant and Jonathan Bennett (Cambridge: Cambridge University Press, 1981), 227. The pagination of this work follows that of the original language text in Leibniz, Sämtliche Schriften und Briefe, 6th ser., vol. 6. Thus, I will only cite the former henceforth.
39. G. W. Leibniz, New Essays on Human Understanding, trans. and ed. Peter Remnant and Jonathan Bennett (Cambridge: Cambridge University Press, 1981), 227. The pagination of this work follows that of the original language text in Leibniz, Sämtliche Schriften und Briefe, 6th ser., vol. 6. Thus, I will only cite the former henceforth.
40. Leibniz, New Essays, 265.
41. Sometimes Leibniz makes this point via his famous dictum that "there are no purely extrinsic denominations, which have absolutely no foundation in the thing itself denominated"; Leibniz, Opuscules et Fragments, 520; Leibniz, Philosophical Essays, 32.
42. Sometimes Leibniz makes this point via his famous dictum that "there are no purely extrinsic denominations, which have absolutely no foundation in the thing itself denominated"; Leibniz, Opuscules et Fragments, 520; Leibniz, Philosophical Essays, 32.
43. Leibniz, New Essays, 146.
44. Note also the following passage from the New Essays: "I believe that qualities are just modifications of substances, and that the understanding adds relations. . . . However, although relations are the work of the understanding they are not baseless and unreal. The primordial understanding is the source of things; and the very reality of all things other than simple substances consists only in their being a foundation for the perceptions or phenomena of simple substances"; Leibniz, New Essays, 146.
45. See, for example, the passages gathered by Benson Mates, The Philosophy of Leibniz: Metaphysics and Language (Oxford: Oxford University Press, 1986), 224-5. Concogitabilitas is perhaps best translated as "a thinking together."
46. Quoted from Mates, The Philosophy of Leibniz, 224. The original Latin can be found in Massimo Mugnai's Leibniz's Theory of Relations (Stuttgart: Franz Steiner Verlag, 1992), 155, See also Leibniz, Textes Inédits, 547; Leibniz, Opuscules et Fragments, 9; and Leibniz, Philosophical Papers and Letters, 525.
47. Quoted from Mates, The Philosophy of Leibniz, 224. The original Latin can be found in Massimo Mugnai's Leibniz's Theory of Relations (Stuttgart: Franz Steiner Verlag, 1992), 155, See also Leibniz, Textes Inédits, 547; Leibniz, Opuscules et Fragments, 9; and Leibniz, Philosophical Papers and Letters, 525.
48. Quoted from Mates, The Philosophy of Leibniz, 224. The original Latin can be found in Massimo Mugnai's Leibniz's Theory of Relations (Stuttgart: Franz Steiner Verlag, 1992), 155, See also Leibniz, Textes Inédits, 547; Leibniz, Opuscules et Fragments, 9; and Leibniz, Philosophical Papers and Letters, 525.
49. Quoted from Mates, The Philosophy of Leibniz, 224. The original Latin can be found in Massimo Mugnai's Leibniz's Theory of Relations (Stuttgart: Franz Steiner Verlag, 1992), 155, See also Leibniz, Textes Inédits, 547; Leibniz, Opuscules et Fragments, 9; and Leibniz, Philosophical Papers and Letters, 525.
50. Quoted from Mates, The Philosophy of Leibniz, 224. The original Latin can be found in Massimo Mugnai's Leibniz's Theory of Relations (Stuttgart: Franz Steiner Verlag, 1992), 155, See also Leibniz, Textes Inédits, 547; Leibniz, Opuscules et Fragments, 9; and Leibniz, Philosophical Papers and Letters, 525.
51. Some commentators doubt whether or not Leibniz can consistently wed the view that (a) things are not related by anything real beyond the relata and their properties with the view that (b) the reality of relations is dependent on the mind. See, for example, chapter 12 of Mates, The Philosophy of Leibniz: Metaphysics and Language; Jan Cover, "Relations and Reduction in Leibniz," Pacific Philosophical Quarterly 70 (1989): 185-211; Jan Cover, "Review of Massimo Mugnai's Leibniz's Theory of Relations," The Leibniz Society Review 5 (1995): 1-10. Given that relations result as soon as the relevant relata are posited, Cover expresses the doubt clearly: "Where then arises the place for any contribution by the intellect - for any obvious sense in which relations are 'dependent upon the mind'?" As Cover sees it, if his and Mates's account "is correct, the deep ontological facts serving as truthmakers for relational claims include nothing whatsoever about the role of the mind"; Cover, "Review of Massimo Mugnai's Leibniz's Theory of Relations," 4 and 5. For an attempt to answer this challenge, see Massimo Mugnai's "Reply to Cover," The Leibniz Society Review 5 (1995): 11-14.
52. Some commentators doubt whether or not Leibniz can consistently wed the view that (a) things are not related by anything real beyond the relata and their properties with the view that (b) the reality of relations is dependent on the mind. See, for example, chapter 12 of Mates, The Philosophy of Leibniz: Metaphysics and Language; Jan Cover, "Relations and Reduction in Leibniz," Pacific Philosophical Quarterly 70 (1989): 185-211; Jan Cover, "Review of Massimo Mugnai's Leibniz's Theory of Relations," The Leibniz Society Review 5 (1995): 1-10. Given that relations result as soon as the relevant relata are posited, Cover expresses the doubt clearly: "Where then arises the place for any contribution by the intellect - for any obvious sense in which relations are 'dependent upon the mind'?" As Cover sees it, if his and Mates's account "is correct, the deep ontological facts serving as truthmakers for relational claims include nothing whatsoever about the role of the mind"; Cover, "Review of Massimo Mugnai's Leibniz's Theory of Relations," 4 and 5. For an attempt to answer this challenge, see Massimo Mugnai's "Reply to Cover," The Leibniz Society Review 5 (1995): 11-14.
53. Some commentators doubt whether or not Leibniz can consistently wed the view that (a) things are not related by anything real beyond the relata and their properties with the view that (b) the reality of relations is dependent on the mind. See, for example, chapter 12 of Mates, The Philosophy of Leibniz: Metaphysics and Language; Jan Cover, "Relations and Reduction in Leibniz," Pacific Philosophical Quarterly 70 (1989): 185-211; Jan Cover, "Review of Massimo Mugnai's Leibniz's Theory of Relations," The Leibniz Society Review 5 (1995): 1-10. Given that relations result as soon as the relevant relata are posited, Cover expresses the doubt clearly: "Where then arises the place for any contribution by the intellect - for any obvious sense in which relations are 'dependent upon the mind'?" As Cover sees it, if his and Mates's account "is correct, the deep ontological facts serving as truthmakers for relational claims include nothing whatsoever about the role of the mind"; Cover, "Review of Massimo Mugnai's Leibniz's Theory of Relations," 4 and 5. For an attempt to answer this challenge, see Massimo Mugnai's "Reply to Cover," The Leibniz Society Review 5 (1995): 11-14.
54. Some commentators doubt whether or not Leibniz can consistently wed the view that (a) things are not related by anything real beyond the relata and their properties with the view that (b) the reality of relations is dependent on the mind. See, for example, chapter 12 of Mates, The Philosophy of Leibniz: Metaphysics and Language; Jan Cover, "Relations and Reduction in Leibniz," Pacific Philosophical Quarterly 70 (1989): 185-211; Jan Cover, "Review of Massimo Mugnai's Leibniz's Theory of Relations," The Leibniz Society Review 5 (1995): 1-10. Given that relations result as soon as the relevant relata are posited, Cover expresses the doubt clearly: "Where then arises the place for any contribution by the intellect - for any obvious sense in which relations are 'dependent upon the mind'?" As Cover sees it, if his and Mates's account "is correct, the deep ontological facts serving as truthmakers for relational claims include nothing whatsoever about the role of the mind"; Cover, "Review of Massimo Mugnai's Leibniz's Theory of Relations," 4 and 5. For an attempt to answer this challenge, see Massimo Mugnai's "Reply to Cover," The Leibniz Society Review 5 (1995): 11-14.
55. Some commentators doubt whether or not Leibniz can consistently wed the view that (a) things are not related by anything real beyond the relata and their properties with the view that (b) the reality of relations is dependent on the mind. See, for example, chapter 12 of Mates, The Philosophy of Leibniz: Metaphysics and Language; Jan Cover, "Relations and Reduction in Leibniz," Pacific Philosophical Quarterly 70 (1989): 185-211; Jan Cover, "Review of Massimo Mugnai's Leibniz's Theory of Relations," The Leibniz Society Review 5 (1995): 1-10. Given that relations result as soon as the relevant relata are posited, Cover expresses the doubt clearly: "Where then arises the place for any contribution by the intellect - for any obvious sense in which relations are 'dependent upon the mind'?" As Cover sees it, if his and Mates's account "is correct, the deep ontological facts serving as truthmakers for relational claims include nothing whatsoever about the role of the mind"; Cover, "Review of Massimo Mugnai's Leibniz's Theory of Relations," 4 and 5. For an attempt to answer this challenge, see Massimo Mugnai's "Reply to Cover," The Leibniz Society Review 5 (1995): 11-14.
56. Leibniz, Textes Inédits, 13.
57. In this sense, then, harmony is perhaps most appropriately viewed as a second-order relation, for it to supervene on other relations. More on this later.
58. Leibniz, Textes Inédits, 13.
59. See also Leibniz, Die Philosophischen Schriften, 2:438; Leibniz, Philosophical Essays, 199, where Leibniz writes: "God views not only the individual monads and the modifications of each monad, but also their relations, and in this consists the reality of relations and truths." Presumably, this includes harmonious relations too. For discussions of the role of the divine mind in grounding the reality of substances, their relations, phenomena, see Adams, Leibniz: Determinist, Theist, Idealist, 258 and following; Gregory Brown, "God's Phenomena and the Pre-established Harmony," Studia Leibnitiana 19 (1987): 200-14.
60. See also Leibniz, Die Philosophischen Schriften, 2:438; Leibniz, Philosophical Essays, 199, where Leibniz writes: "God views not only the individual monads and the modifications of each monad, but also their relations, and in this consists the reality of relations and truths." Presumably, this includes harmonious relations too. For discussions of the role of the divine mind in grounding the reality of substances, their relations, phenomena, see Adams, Leibniz: Determinist, Theist, Idealist, 258 and following; Gregory Brown, "God's Phenomena and the Pre-established Harmony," Studia Leibnitiana 19 (1987): 200-14.
61. See also Leibniz, Die Philosophischen Schriften, 2:438; Leibniz, Philosophical Essays, 199, where Leibniz writes: "God views not only the individual monads and the modifications of each monad, but also their relations, and in this consists the reality of relations and truths." Presumably, this includes harmonious relations too. For discussions of the role of the divine mind in grounding the reality of substances, their relations, phenomena, see Adams, Leibniz: Determinist, Theist, Idealist, 258 and following; Gregory Brown, "God's Phenomena and the Pre-established Harmony," Studia Leibnitiana 19 (1987): 200-14.
62. See also Leibniz, Die Philosophischen Schriften, 2:438; Leibniz, Philosophical Essays, 199, where Leibniz writes: "God views not only the individual monads and the modifications of each monad, but also their relations, and in this consists the reality of relations and truths." Presumably, this includes harmonious relations too. For discussions of the role of the divine mind in grounding the reality of substances, their relations, phenomena, see Adams, Leibniz: Determinist, Theist, Idealist, 258 and following; Gregory Brown, "God's Phenomena and the Pre-established Harmony," Studia Leibnitiana 19 (1987): 200-14.
63. Notice that (d) differs from the previous (d) used in (R) to characterize a Leibnizian relation in that I have dropped the phrase "in some fashion." I take it that when it comes to characterizing harmony, (e) provides the manner in which the members of S must be considered together, namely, in such fashion that they achieve the relevant standard of order. Of course, we still need an explanation of the latter.
64. Leibniz, Die Leibniz-Handschriften, 70 and 124.
65. While it is not clear now why "order" should be understood as imposing a certain unity on the set, I shall eventually speculate on this matter.
66. Leibniz, Die Philosophischen Schriften, 7:290; Leibniz, Philosophical Writings, 146.
67. Leibniz, Die Philosophischen Schriften, 7:290; Leibniz, Philosophical Writings, 146.
68. Ibid.
69. Leibniz, Die Philosophischen Schriften, 4:422-3; Leibniz, Philosophical Papers and Letters, 291-2. See also Leibniz, New Essays, 254-5.
70. Leibniz, Die Philosophischen Schriften, 4:422-3; Leibniz, Philosophical Papers and Letters, 291-2. See also Leibniz, New Essays, 254-5.
71. Leibniz, Die Philosophischen Schriften, 4:422-3; Leibniz, Philosophical Papers and Letters, 291-2. See also Leibniz, New Essays, 254-5.
72. Leibniz, Die Philosophischen Schriften, 3:247; Leibniz, Philosophical Essays, 287. See also Leibniz, New Essays, 255-6. In what follows, I shall use the terms "idea" and "concept" interchangeably. However, it must be stressed that strictly speaking these are not equivalent for Leibniz. Ideas, according to him, are more like dispositions, so that one can be said to have ideas even when one is not presently conscious of them. Concepts on the other hand are essentially content bearing entities. Thus, when one actualizes an idea, it becomes a "concept" or "notion." See Leibniz, Die Philosophischen Schriften, 4:452; Leibniz, Philosophical Essays, 59. Provided we bear this in mind, no harm should result from using these terms interchangeably for both pertain to the realm of conceptualization as opposed to sensory presentings.
73. Leibniz, Die Philosophischen Schriften, 3:247; Leibniz, Philosophical Essays, 287. See also Leibniz, New Essays, 255-6. In what follows, I shall use the terms "idea" and "concept" interchangeably. However, it must be stressed that strictly speaking these are not equivalent for Leibniz. Ideas, according to him, are more like dispositions, so that one can be said to have ideas even when one is not presently conscious of them. Concepts on the other hand are essentially content bearing entities. Thus, when one actualizes an idea, it becomes a "concept" or "notion." See Leibniz, Die Philosophischen Schriften, 4:452; Leibniz, Philosophical Essays, 59. Provided we bear this in mind, no harm should result from using these terms interchangeably for both pertain to the realm of conceptualization as opposed to sensory presentings.
74. Leibniz, Die Philosophischen Schriften, 3:247; Leibniz, Philosophical Essays, 287. See also Leibniz, New Essays, 255-6. In what follows, I shall use the terms "idea" and "concept" interchangeably. However, it must be stressed that strictly speaking these are not equivalent for Leibniz. Ideas, according to him, are more like dispositions, so that one can be said to have ideas even when one is not presently conscious of them. Concepts on the other hand are essentially content bearing entities. Thus, when one actualizes an idea, it becomes a "concept" or "notion." See Leibniz, Die Philosophischen Schriften, 4:452; Leibniz, Philosophical Essays, 59. Provided we bear this in mind, no harm should result from using these terms interchangeably for both pertain to the realm of conceptualization as opposed to sensory presentings.
75. Leibniz, Die Philosophischen Schriften, 3:247; Leibniz, Philosophical Essays, 287. See also Leibniz, New Essays, 255-6. In what follows, I shall use the terms "idea" and "concept" interchangeably. However, it must be stressed that strictly speaking these are not equivalent for Leibniz. Ideas, according to him, are more like dispositions, so that one can be said to have ideas even when one is not presently conscious of them. Concepts on the other hand are essentially content bearing entities. Thus, when one actualizes an idea, it becomes a "concept" or "notion." See Leibniz, Die Philosophischen Schriften, 4:452; Leibniz, Philosophical Essays, 59. Provided we bear this in mind, no harm should result from using these terms interchangeably for both pertain to the realm of conceptualization as opposed to sensory presentings.
76. Leibniz, Die Philosophischen Schriften, 3:247; Leibniz, Philosophical Essays, 287. See also Leibniz, New Essays, 255-6. In what follows, I shall use the terms "idea" and "concept" interchangeably. However, it must be stressed that strictly speaking these are not equivalent for Leibniz. Ideas, according to him, are more like dispositions, so that one can be said to have ideas even when one is not presently conscious of them. Concepts on the other hand are essentially content bearing entities. Thus, when one actualizes an idea, it becomes a "concept" or "notion." See Leibniz, Die Philosophischen Schriften, 4:452; Leibniz, Philosophical Essays, 59. Provided we bear this in mind, no harm should result from using these terms interchangeably for both pertain to the realm of conceptualization as opposed to sensory presentings.
77. Leibniz writes: "Whether one says ideas, or whether one says notions, whether one says distinct ideas, or whether one says definitions (at least, when the idea is not absolutely primitive), it is all the same thing"; Leibniz, Die Philosophischen Schriften, 3:248. The bit in parentheses signals a qualification. Leibniz also held that some ideas are primitive, where that is understood as an idea which is not composite or one which does not contain other ideas. Primitive ideas, then, do not yield to definitions because they do not yield to decomposition or resolution.
78. Leibniz, New Essays, 256.
79. Margaret Wilson criticizes Leibniz here for running together two senses of "confused," one of which pertains to sense perception (which is confused because it contains an infinity of petites perceptions which cannot be filtered out), the other pertaining to ideas and notions. According to this objection, Leibniz holds that "the necessary confusedness of our perceptions of colors, odors, etc., is . . . taken to show that we only (can only?) have confused ideas of these qualities"; Margaret Wilson, "Confused Ideas," Rice University Studies 63 (1977): 129. But this reading of Leibniz strikes me as mistaken, at least with respect to some ideas. Leibniz makes it clear in the New Essays that with respect to things which appear confused to the senses, we can, at the same time, have distinct ideas of those things. Thus, for example, in the New Essays, he accuses Locke of the same view which Wilson attributes to him: "This example shows that the idea is being confounded with the image. If I am confronted with a regular polygon, my eyesight and my imagination cannot give me a grasp of the thousand which it involves: I have only a confused idea both of the figure and of its number until I distinguish the number by counting. But once I have found the number, I know the given polygon's nature and properties very well, insofar as they are those of a chiliagon, The upshot is that I have this [distinct] idea of a chiliagon, even though I cannot have the image of one: one's senses and imagination would have to be sharper and more practiced if they were to enable one to distinguish such a figure from a polygon which had one side less"; Leibniz, New Essays, 261. Thus, Leibniz seems to have held that one could possess a distinct idea of something (in this case, a thousand-sided figure) but nonetheless lack the sensory repertoire for distinct sensory perception of it So it does not seem that he could argue from the confusion of a sensory perception of something to the confusion of the ideas of those same things.
80. Margaret Wilson criticizes Leibniz here for running together two senses of "confused," one of which pertains to sense perception (which is confused because it contains an infinity of petites perceptions which cannot be filtered out), the other pertaining to ideas and notions. According to this objection, Leibniz holds that "the necessary confusedness of our perceptions of colors, odors, etc., is . . . taken to show that we only (can only?) have confused ideas of these qualities"; Margaret Wilson, "Confused Ideas," Rice University Studies 63 (1977): 129. But this reading of Leibniz strikes me as mistaken, at least with respect to some ideas. Leibniz makes it clear in the New Essays that with respect to things which appear confused to the senses, we can, at the same time, have distinct ideas of those things. Thus, for example, in the New Essays, he accuses Locke of the same view which Wilson attributes to him: "This example shows that the idea is being confounded with the image. If I am confronted with a regular polygon, my eyesight and my imagination cannot give me a grasp of the thousand which it involves: I have only a confused idea both of the figure and of its number until I distinguish the number by counting. But once I have found the number, I know the given polygon's nature and properties very well, insofar as they are those of a chiliagon, The upshot is that I have this [distinct] idea of a chiliagon, even though I cannot have the image of one: one's senses and imagination would have to be sharper and more practiced if they were to enable one to distinguish such a figure from a polygon which had one side less"; Leibniz, New Essays, 261. Thus, Leibniz seems to have held that one could possess a distinct idea of something (in this case, a thousand-sided figure) but nonetheless lack the sensory repertoire for distinct sensory perception of it So it does not seem that he could argue from the confusion of a sensory perception of something to the confusion of the ideas of those same things.
81. Leibniz, New Essays, 257-8.
82. Leibniz, New Essays, 261.
83. Leibniz, Opuscules et Fragments, 9; Leibniz, Philosophical Writings, 133.
84. Leibniz, Opuscules et Fragments, 9; Leibniz, Philosophical Writings, 133.
85. Note that this definition is good only if we are talking about that very heap in Leibniz's example and not any heap in general.
86. Leibniz, Hauptschriften, 2:131; Leibniz, Selections, 572.
87. Leibniz, Hauptschriften, 2:131; Leibniz, Selections, 572.
88. Leibniz, Die Philosophischen Schriften, 4:422; Leibniz, Philosophical Papers and Letters, 291.
89. Leibniz, Die Philosophischen Schriften, 4:422; Leibniz, Philosophical Papers and Letters, 291.
90. Leibniz, New Essays, 338. This same observation has been made, and developed into a "sociolinguistic hypothesis," in our own time, of course, by Hilary Putnam in his "The Meaning of 'Meaning'," in Mind, Language, and Reality: Philosophical Papers, vol. 2 (Cambridge: Cambridge University Press, 1975). Putnam writes: "The features that are generally thought to be present in connection with a general name - necessary and sufficient conditions for membership in the extension ('criteria'), etc. - are all present in the linguistic community considered as a collective body; but that collective body divides the 'labor' of knowing and employing these various parts of the 'meaning' of 'gold'" (p. 228). In Leibnizian terms, while many have a "clear" idea of gold, only some in the community (namely, assayers) have a "distinct" idea of gold.
91. Leibniz, New Essays, 338. This same observation has been made, and developed into a "sociolinguistic hypothesis," in our own time, of course, by Hilary Putnam in his "The Meaning of 'Meaning'," in Mind, Language, and Reality: Philosophical Papers, vol. 2 (Cambridge: Cambridge University Press, 1975). Putnam writes: "The features that are generally thought to be present in connection with a general name - necessary and sufficient conditions for membership in the extension ('criteria'), etc. - are all present in the linguistic community considered as a collective body; but that collective body divides the 'labor' of knowing and employing these various parts of the 'meaning' of 'gold'" (p. 228). In Leibnizian terms, while many have a "clear" idea of gold, only some in the community (namely, assayers) have a "distinct" idea of gold.
92. Leibniz, New Essays, 267.
93. Leibniz, New Essays, 267.
94. Leibniz, Textes Inédits, 13. It thus appears that harmony is what we might call a second-order relation, resulting as it does from other relations.
95. I earlier promised to say something about Leibniz's use of the term "proportion" in his claim from the Elementa that "where variety is without order, without proportion, there is no harmony"; Leibniz, Textes Inédits, 12. In a table of definitions from 1702-4, Leibniz defined a proportion as "the relation of two magnitudes, one of which can be determined with the help of the other given one"; Leibniz, Opuscules et Fragments, 476. Thus, like order, proportion is itself a relation among entities which enables one to distinguish the entities related one from another. Note also that things may be related to one another proportionally with respect to a number of objective qualities of those things, for example, size, shape, color, and so forth. Thus, there is every reason to believe that Leibniz's use of the term "proportion" in describing the relations between a collection of harmonious entities is not merely metaphorical, as might be supposed. Rather, like his notion of order, it is a term he apparently uses to designate intelligible relations among things.
96. I earlier promised to say something about Leibniz's use of the term "proportion" in his claim from the Elementa that "where variety is without order, without proportion, there is no harmony"; Leibniz, Textes Inédits, 12. In a table of definitions from 1702-4, Leibniz defined a proportion as "the relation of two magnitudes, one of which can be determined with the help of the other given one"; Leibniz, Opuscules et Fragments, 476. Thus, like order, proportion is itself a relation among entities which enables one to distinguish the entities related one from another. Note also that things may be related to one another proportionally with respect to a number of objective qualities of those things, for example, size, shape, color, and so forth. Thus, there is every reason to believe that Leibniz's use of the term "proportion" in describing the relations between a collection of harmonious entities is not merely metaphorical, as might be supposed. Rather, like his notion of order, it is a term he apparently uses to designate intelligible relations among things.
97. I make this point because it is controversial, of course, whether or not the set of, say, frogs, is something more than the sum of all frogs, namely, the frogs and the set. From what I can see, however, Leibniz's views on concept resolution commit him to the position that a given composite concept just is the sum of its component concepts and nothing more.
98. Indeed, this is Leibniz's own example. See Leibniz, New Essays, 403.
99. Russell Wahl pointed out to me that Leibniz's grounding the reality of relations, and thus the reality of harmony and distinct cogitability, in the divine mind seems to present a problem. God, qua perfectly omniscient being, can see all the connections in all the possible worlds, for there is no nondistinctly cogitable world for him. Thus, it would seem, then, that every possible world is harmonious. One might seek to defend Leibniz here by claiming that nonetheless, some worlds are more harmonious than others. But it is not clear to me that this defense will work, for again, there cannot be some worlds more distinctly cogitable than others with respect to God, for they are all equally intuitively intelligible to an omniscient being. I suppose one might reply that nonetheless some worlds are more harmonious with respect to finite minds. But then again Leibniz's remarks suggest that the actual world is the most harmonious simpliciter - without reference to any mind. In any event, it is an issue worth investigating, though I haven't the space to discuss it here. My thanks to Wahl for bringing this issue to my attention.
100. One issue that one would like to see clarified has to do with the difference between order and harmony. What exactly is the difference? I know of no texts where Leibniz addressed this question head-on. We know that harmony presupposes order such that a harmonious collection must exhibit order. And order, as we know, is a relation which holds among entities such that they may be distinctly conceived. But order, it would then seem, presupposes harmony too, for Leibniz suggests that wherever a collection of entities exhibits distinct cogitabilty, it exhibits a certain degree of harmony. But it cannot be (for Leibniz's sake, at least) that the two concepts are identical, for Leibniz often defined harmony, as we know, in terms of order. Perhaps, then, although the two concepts are not to be identified, they are nonetheless coextensive, such that wherever harmony is exhibited, order is exhibited and vice versa. One suggestion is this: order is a first-order relation between entities endowing them with a certain degree of distinct cogitability, while harmony is a second-order relation which supervenes upon relations of order. This would make sense of Leibniz's claim that it is more exactly from a collection of relations (of order?) that harmony results (see Leibniz, Textes Inédits, 13). This is admittedly speculative, as I have found the texts to be largely indeterminate on the exact difference between these two notions.
101. Leibniz, Leibniz und Christian Wolff, 170; Leibniz, Philosophical Essays, 233. Thus, it seems that one set of entities, as noted earlier, can be more harmonious than another. The greater the range of intelligible properties deducible from a set of entities (which, I suppose, is a function of the plurality of entities - that is, the more concepts there are to resolve - and the relations they bear to one another), the more hamonious is the collection.
102. Leibniz, Leibniz und Christian Wolff, 170; Leibniz, Philosophical Essays, 233. Thus, it seems that one set of entities, as noted earlier, can be more harmonious than another. The greater the range of intelligible properties deducible from a set of entities (which, I suppose, is a function of the plurality of entities - that is, the more concepts there are to resolve - and the relations they bear to one another), the more hamonious is the collection.
103. Leibniz, Leibniz und Christian Wolff, 170; Leibniz, Philosophical Essays, 233.
104. Leibniz, Leibniz und Christian Wolff, 170; Leibniz, Philosophical Essays, 233.
105. Leibniz, Textes Inédits, 12.
106. Here I have in mind, for example, the dispositional property of the heap to be arranged in a square, and the dispositional property of gold to resist solubility in aqua fortis. These examples of Leibniz's suggest that properties concerning how certain entities would react in certain situations are to be counted among the intelligible properties of that entity.
107. Wilson, "Confused Ideas," articulates some interesting difficulties associated with Leibniz's account of distinct cogitability, an account which obviously infects his notion of harmony.
108. Leibniz, Leibniz und Christian Wolff, 170, Leibniz, Philosophical Essays, 233; Leibniz, Die Philosophischen Schriften, 7:290; Leibniz, Philosophical Writings, 146; and Leibniz, Textes Inédits, 13.
109. Leibniz, Leibniz und Christian Wolff, 170, Leibniz, Philosophical Essays, 233; Leibniz, Die Philosophischen Schriften, 7:290; Leibniz, Philosophical Writings, 146; and Leibniz, Textes Inédits, 13.
110. Leibniz, Leibniz und Christian Wolff, 170, Leibniz, Philosophical Essays, 233; Leibniz, Die Philosophischen Schriften, 7:290; Leibniz, Philosophical Writings, 146; and Leibniz, Textes Inédits, 13.
111. Leibniz, Leibniz und Christian Wolff, 170, Leibniz, Philosophical Essays, 233; Leibniz, Die Philosophischen Schriften, 7:290; Leibniz, Philosophical Writings, 146; and Leibniz, Textes Inédits, 13.
112. Leibniz, Leibniz und Christian Wolff, 170, Leibniz, Philosophical Essays, 233; Leibniz, Die Philosophischen Schriften, 7:290; Leibniz, Philosophical Writings, 146; and Leibniz, Textes Inédits, 13.
113. See Leibniz, Die Philosophischen Schriften, 6: 622; Leibniz, Philosophical Essays, 224.
114. See Leibniz, Die Philosophischen Schriften, 6: 622; Leibniz, Philosophical Essays, 224.
115. Leibniz, Textes Inédits, 13.
116. Leibniz, New Essays, 146.
117. Leibniz, New Essays, 142.
118. An earlier version of this paper was read at the 1999 Intermountain Seminar in Early Modern Philosophy, University of Colorado, Denver, April 25, 1999. I would like to thank the participants for many helpful comments and suggestions. Thanks are also due to Mark Kulstad and Gregory Brown for their comments on earlier drafts.