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Leibniz, Acosmism, and Incompossibility

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Leibniz on Compossibility and Possible Worlds

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Leibniz claims that God acts in the best possible way, and that this includes creating exactly one world. But worlds are aggregates, and aggregates have a low degree of reality or metaphysical perfection, perhaps none at all. This is Leibniz’s tendency toward acosmism, or the view that there this no such thing as creation-as-a-whole. Many interpreters reconcile Leibniz’s acosmist tendency with the high value of worlds by proposing that God sums the value of each substance created, so that the best world is just the world with the most substances. I call this way of determining the value of a world the Additive Theory of Value (ATV), and argue that it leads to the current and insoluble form of the problem of incompossibility. To avoid the problem, I read “possible worlds” in “God chooses the best of all possible worlds” as referring to God’s ideas of worlds. These ideas, though built up from essences, are themselves unities and so well suited to be the value bearers that Leibniz’s theodicy requires. They have their own value, thanks to their unity, and that unity is not preserved when more essences are added.

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  1. 1.

    On the connection between secondary matter and aggregates, see FB.26-7/AG.274.

  2. 2.

    On the connection between matter and phenomena, see LDV.302-3.

  3. 3.

    See, for example, Rutherford 1994; Adams 1994, 244–247; Lodge 2001, and Palkoska 2010.

  4. 4.

    I support the connection between reality and perfection in Sect. <InternalRef ID="Sec5">3.2</CitationRef>. For the connection between unity and reality, see especially A.II.ii.174-193/LA.113-29.

  5. 5.

    Jeffrey McDonough provides an excellent example of such a search. His tertium quid is the structure of space and time as a sort of receptacle for extended substances. No substance rules out any other by its nature, but only certain combinations will fit into the available space. See McDonough 2010.

  6. 6.

    This point and the whole discussion of the ATV owes much to a similar argument in Kagan 1988.

  7. 7.

    Why should God have such models? There is a story to tell about the origin (but not the creation) of divine ideas in God’s self-reflection. On this, see especially Nachtomy 2007.

  8. 8.

    For a dispute about whether essences are best seen as the intentional content of divine ideas, or as identical to those ideas, see Nachtomy 2007, 14–16 and Newlands 2013, 165n26.

  9. 9.

    See Leibniz’s early dialogue on continua, Pacidius Philalethi (RA.180-1) and the letter to De Volder of 30 June 1704 (LDV.302-3).

  10. 10.

    Leibniz presents the two paradigms together in Remarques sur les objections de M. Foucher (GP.IV.491-2/AG.147).

  11. 11.

    There is another way to resolve this tension. Leibniz states immediately after the extended Theodicy passage that the operations of the divine mind are ordered by priority. The extraction operation is available only after God contemplates the individual possibles and constructs systems from them. This ordering of operations does not directly imply, however, that the objects operated upon are themselves ordered by priority relations in Leibniz’s paradigmatic sense.

  12. 12.

    For more on the Hegelian sense of the term, see Hegel, G. W. F. 1984, 432 and Melamed 2010, 80.

  13. 13.

    See Brandon Look and Donald Rutherford’s introduction to their translation of the correspondence with Des Bosses (LR.xxxviii-lxxl).

  14. 14.

    Leibniz tended toward an eliminativist or nihilist position on such entities. See Levey 2002.

  15. 15.

    The argument from fungibility is adapted from Chappell 2013.

  16. 16.

    For a guide to some of Leibniz’s thoughts on love relevant to this argument, see Parkinson 1994, 211.

  17. 17.

    Leibniz thought that there were infinitely many possible substances, and there are infinite subsets of infinite sets. On the assumption that each substance in any given infinite set has a value greater than some specified lower limit, it would be impossible to compare two created worlds each with infinitely many substances using the ATV. Probably, there is way to put the summing view that avoids this problem. For a discussion of the difficulty in comparing worlds each with infinitely many substances, see Brown 2006, 108–109.

  18. 18.

    Leibniz does forcibly and repeatedly assert and argue that there are merely possible substances. For example, “there are an infinity of possible things which, nevertheless, do not exist” (A.VI.iv.1445/AG.19).

  19. 19.

    I discuss the relation between harmony and perfection in Sect. 4.1.

  20. 20.

    This strategy was inspired by Robert Adams’s note that understanding hypothetical necessity involves drawing “the right line between attributes of God that are, and that are not, to be taken into account in the basic concepts of possible worlds” (Adams 1994, 20). Samuel Newlands richly develops a similar idea in Newlands 2010.

  21. 21.

    Both internal and external faults would be grounded in relations, either among the essences that compose an uncreated world or between two uncreated worlds. These relations would be ideal or mind-dependent, as per Leibniz’s theory of relations, but then again the relata would be as well.

  22. 22.

    See, for example, GP.VII.87/L.426.

  23. 23.

    See, for example, DM §9, Leibniz’s letter to De Volder of 20 June 1703 (LDV.266-7), and the Monadology §§56–8.

  24. 24.

    See, for example, Principium meum est, quicquid existere potest, et aliis compatibile est, id existere (A.VI.iii.581-2/L.168-9).

  25. 25.

    Compare, for example, Monadology §57 (GP.VI.616/AG.220).

  26. 26.

    For more on the wisdom and the economy of volitions, see the Conversation sur la liberte et le destin (Grua.481-2/SLT.99) and the Theodicy (GP.VI.240/H.206).

  27. 27.

    Elizabeth Anscombe elaborates a similar conception, in which paradigmatic willing involves acting: “The primitive sign of wanting is trying to get [. . .]” (Anscombe 2000, 68).

  28. 28.

    On these issues, see especially the DM §§14 and 35–6 (A.VI.iv.1549–50 and 1584–7/AG.46–7 and 66–8).

  29. 29.

    For an alternative interpretation of these passages, see Carlin 2000, 102–106.


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Feeney, T. (2016). Leibniz, Acosmism, and Incompossibility. In: Brown, G., Chiek, Y. (eds) Leibniz on Compossibility and Possible Worlds. The New Synthese Historical Library, vol 75. Springer, Cham.

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