Abstract
I argue that the two standard accounts of compossibility—the so-called logical and lawful accounts—are in fact not incompatible, competing solutions to the same problem, but rather complementary solutions to two different problems. Only a version of the so-called logical account grounded in Leibniz’s logic of relations will yield a satisfactory account of incompossibility as a notion capable of generating a conceptual divergence among worlds. The lawful account cannot provide such an account, although it does provide important parts of the solution to another problem, namely that of the relative goodness of worlds. I also respond to the main objection made against the logical approach, namely that it violates Leibniz’s conception of the independence of monads, arguing that the objection rests on a misconception of what monadic independence consists in. I explore further Leibniz’s notion of incompossibility, distinguishing this “strong” kind of inter-worldly incompatibility from a “weak” kind of intra-worldly incompatibility, which does not generate differences between worlds, but only differences in time. In the final section of the paper, I argue how we humans, on the level of phenomena, are able to distinguish weakly from strongly incompatible (i.e. incompossible) individuals by means of a “soft” criterion of congruity.
I am grateful to Ohad Nachtomy for his many comments and corrections. Unless otherwise indicated, translations are my own.
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Notes
- 1.
The distinction was first explicitly made in Wilson (<CitationRef CitationID="CR31" >1993</Citation Ref>).
- 2.
I borrow this short and concise definition from Messina and Rutherford (<CitationRef CitationID="CR21" >2009</Citation Ref>, 962).
- 3.
In a very early text, Leibniz explicitly refers to Scotus’s notion of compossibility when discussing the Eucharist (see Refutatio hypotheseis Thomae Angli, 1668 (?), A.VI.i.506–7, note 7).
- 4.
According to Mates, still under the sway of Russell’s reading of Leibniz, relational predicates must be eliminated from the account of compossibility under the pretext that Leibniz is logically committed to reducing relational predicates to non-relational ones—an assertion which, as we know now, is just wrong. See Mates (<CitationRef CitationID="CR18" >1972</Citation Ref>).
- 5.
On the combinatorial model of compossibility, see Leibniz, Dialogue entre Poliandre et Théophile (1679), A VI.iv 2231–2 and De veritatibus primis (1680), A.VI.iv 1443. See also Wilson (<CitationRef CitationID="CR32" >2000</Citation Ref>, 4–8).
- 6.
I will not discuss here how much the consideration of the relation between richness in essence and simplicity of laws contributes to the determination of bestness. A number of other factors––physical, moral, aesthetic, etc.—enter into that complex determination. It is a topic that requires a treatment of its own (for one possible account, see Blumenfeld <CitationRef CitationID="CR1" >1995</Citation Ref>, 382–410). The point here is simply that, strictu sensu, that discussion has little or nothing to do with the problem of compossibility as such.
- 7.
See for example the Conversatio cum Domino Episcopo Stenonio de libertate, November 1677, A.VI.iv.1380/CP, 123: “Whatever is, either is per se, i.e., exists through itself, or per aliud, i.e. exists through another. If it is per se, then the reason for its existence is derived from its own nature, i.e., its essence contains existence.” On this definition, of course, no created substance—exactly because it is created—is per se independent.
- 8.
See for example Essais de théodicée, §61, GP.VI.136/H.156: “[. . .] the physical influence of one of these substances on the other is inexplicable [. . .]”; ibid. §290, GP.VI.289/H.303–4: “As for spontaneity, it belongs to us insofar as we have within us the source of our actions, as Aristotle rightly conceived [. . .]. I maintain that our spontaneity suffers no exception and that external things have no physical influence upon us [. . .]”; ibid. §300, GP.VI.295–6/H.309: “[. . .] in the course of nature each substance is the sole cause of all its actions, and [. . .] it is free of all physical influence from every other substance, save the customary co-operation of God.”
- 9.
Leibniz to De Volder, 6 July 1701, LDV.208–9. See also Essais de théodicée, §7, GP.VII.107/H.128: “For it must be known that all things are connected in each one of the possible worlds: the universe, whatever it may be, is all of one piece, like an ocean: the least movement extends its effect there to any distance whatsoever, even though this effect becomes less perceptible in proportion to the distance.”
- 10.
Leibniz to Fontenelle, 7 April 1703, FC.227-8, translated in SLT.137 (modified: Strickland translates, somewhat tendentiously, the expression cela ne se peut by the more technical modal expression “it is impossible.”).
- 11.
Leibniz, Confessio philosophi, 1673 [comment added in January 1678], A.VI.iii.121/CP.41.
- 12.
Compare with D’Agostino’s critical discussion of Mates: “[Mates] seems to reject the quite plausible suggestion that incompossibility of substances be identified with logical incompatibility of concepts or, as he puts it, with logical inconsistency” (D’Agostino <CitationRef CitationID="CR5" >1976</Citation Ref>, 129).
- 13.
A.VI.ii.498: “Est ergo compatibilitas rerum, compossibilitas propositionum.”
- 14.
A.VI.iv.389: “Si ex propositione A est, sequitur B non est, tunc vicissim ex propositione B est, sequitur A non est, et A, B, dicentur incompatibilia, quae non possunt esse ambo.”
- 15.
A.VI.iv.390, translated in Di Bella (<CitationRef CitationID="CR9" >2005</Citation Ref>, 241).
- 16.
A number of texts suggest that Leibniz attempted to formulate that distinction in terms of differences in natural priority, simplicity, and perfection. See Quid sit natura prius, 1679, A.VI.iv.181: “When two posited things contradict, one contradicts the other, the one that is prior in nature is prior in time [. . .]. In nature, that which is prior in terms of time is simpler, what is posterior is more perfect”; Definitiones notionum metaphysicarum atque logicarum, 1685 (?), A.VI.iv.629: “what is prior in time is that which is incompatible with something posited, and which is simpler”; Genera terminorum. Substantiae, 1683–1685 (?), A.VI.iv.569: “If then there are two [terms] of which one is prior in nature and the other posterior, and which are incompatible, one of them will be prior in time and the other posterior.” For a lucid study of those texts, see Rauzy (<CitationRef CitationID="CR27" >1995</Citation Ref>, 31–46).
- 17.
Leibniz to Des Bosses, mid-October 1708, L. 112–3. See also Leibniz to Des Bosses, 16 October 1706, LR.78–9: “[. . .] the universal connection and order of the world, which relations with respect to time and place produce [universali connexione et ordine mundi, quem faciunt relationes ad tempus et locum].” See finally Reponse aux reflexions contenues dans la seconde Edition du Dictionnaire Critique de M. Bayle, GP.IV.568: “Space and Time taken together make up the possibilities of an entire universe, in such a way that these orders (that is to say, Space and Time) encloses [quadrent] not only that which is actually exists but also that which could fall into place [. . .].”
- 18.
Leibniz, Vorarbeiten, 1671–1672, A.VI.ii.492: “Congruum est quod facile compossibile est.”
- 19.
Leibniz, “Remarques sur le Livre sur l’origine du mal, publié depuis peu en Angleterre,” § 21, in Essais de théodicée, GP.VI.423/H.428. Note that Leibniz uses the Latin adjective congrua in two different ways. It is sometimes used in the mathematical “transitive” sense to describe a geometrical relation between two figures. Thus, according to Initia mathematica, De quantitate, “those [things] are congruent which, if they differ, only can be distinguished by means of something external [congrua sunt, quae si diversa sunt, non nise respecta ad externa discerni potest]” (GM.VII.29). However, in this context, Leibniz uses the term in a logical “intransitive” sense to express the internal coherence or consistency of a single set of possibles or possible world. Here, I reserve the terms congruence/congruent for the first meaning, and congruity/congruous for the second.
- 20.
See Nachtomy (<CitationRef CitationID="CR24" >2006</Citation Ref>, 85–93, and infra, Sect. 2).
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Lærke, M. (2016). Compossibility, Compatibility, Congruity. In: Brown, G., Chiek, Y. (eds) Leibniz on Compossibility and Possible Worlds. The New Synthese Historical Library, vol 75. Springer, Cham. https://doi.org/10.1007/978-3-319-42695-2_6
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