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Pure Positivity in Leibniz

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Thinking and Calculating

Part of the book series: Logic, Epistemology, and the Unity of Science ((LEUS,volume 54))

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Abstract

The notion of ‘pure positivity’ plays a pivotal role in Leibniz’s version of the ontological argument. In his view, it establishes the possibility of the Ens perfectissimum, thereby providing the premise missing from other versions of the argument. As he puts it very briefly around 1685: ‘the most perfect Being is possible, because it is nothing other than pure positivity’. It may be tempting to dismiss ‘pure positivity’ as a hastily contrived notion introduced in a desperate attempt to support the ontological argument. In this paper, I will discuss Leibniz’s conception of pure positivity, exploring its connection with his notions of perfection, pure act, being, reality, absolute, and infinite. I will come to the conclusion that ‘pure positivity’, far from being a feeble, ad hoc attempt to rescue the ontological argument, constitutes a fundamental feature of Leibniz’s metaphysics that aligns with well-documented key commitments of his philosophical thought.

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Notes

  1. 1.

    For a full discussion see Antognazza (2018), from which I am drawing.

  2. 2.

    See esp. A VI 3, 572 (trans. by Adams 1994: 145): ‘one [property] would express the exclusion of the other, and so one of them would be the negative of the other, which is contrary to the hypothesis, for we assumed that they are all affirmative.’ For an insightful discussion see Adams (1994: 142–148, see esp. 145).

  3. 3.

    See A VI 3, 572, 575, 577, and 578–9. Interestingly, the same type of argument is employed by Eckhard in his exchange with Leibniz (see letter of 19 April 1677; A II 12, 495–6).

  4. 4.

    Cf. Adams (1994: 173).

  5. 5.

    See also Ens Perfectissimum Existit (c. November 1676); A VI 3, 575: ‘Perfectiones, sive formae simplices, sive qualitates absolutae positivae’.

  6. 6.

    Cf. A VI 3, 578, quoted above.

  7. 7.

    See also a key text on the infinite, probably written around 1698, recently transcribed and translated from Leibniz’s manuscript by Richard T. W. Arthur and Osvaldo Ottaviani (De Scientia Infiniti, LH 35, 7, 10, Bl. 5r-8v): ‘Porro ex his rerum praedicatis quae mens nostra intelligit, alia sunt absoluta, alia limitationem involvunt. Absoluta constant realitate pure positiva, atque adeo perfectionem indicant, solaque recensentur inter attributa substantiae supremae’ (‘Furthermore, of those predicates of things which our mind understands, some are absolute, some involve limitation. Absolute ones consist in a purely positive reality and therefore indicate perfection, and are the only ones counted among the attributes of the supreme substance’). I am very grateful to Richard Arthur and Osvaldo Ottaviani for drawing my attention to this text, and for generously sharing their transcription and translation, from which I am quoting. As they note, this important piece has previously appeared only in an obscure nineteenth-century publication (Gerhardt 1875: 595–608).

  8. 8.

    Cf. A II 12, 488 (April 1677): ‘perfection is every attribute, or every reality’; A II 12, 543 (Summer 1677): ‘as I would prefer to define it, perfection is degree or quantity of reality or [seu] essence’; Elementa verae pietatis, c. 1677–8 (A VI 4, 1358): ‘Perfection is degree or quantity of reality. Hence perfectissimum is what has the highest degree of reality’. In his exchange with Leibniz on the ontological argument, Arnold Eckhard insists that perfectissimum can be substituted with realissimum, the latter being a rougher way to express what the former expresses in a more sophisticated manner (cf. A II 12, 527, 541: ‘Perfecti vocabulum non est inutile, quia id Latine dicit, quod reale barbare effert’).

  9. 9.

    Cf. also LH 35, 7, 10, Bl. 5r-8v (quoted above, n. 7).

  10. 10.

    A VI 4, 625: ‘Ens vel Aliquid est cui competit terminus positivus, ut A, B, C, si scilicet in explicatione non sit resolvendus in mere privativum. Adhibeo autem hic Terminos Concretos. Nihil est cui non competit nisi terminus mere negativus, nempe si N non est A, nec est B, nec C, nec D, et ita porro, ita ut nullus reperiatur terminus positivus qui ejus sit praedicatum, tunc N dicitur esse Nihil. Itaque Axioma illud vulgare, Non entis nulla sunt attributa, continet ipsius Nihili seu non Entis definitionem’.

  11. 11.

    It is worth quoting the whole passage: ‘Privativum non-A. Non-non-A idem est quod A. Positivum est A, si scilicet non sit non-Y quodcunque, posito Y similiter non esse non-Z et ita porro. Omnis terminus intelligitur positivus, nisi admoneatur eum esse privativum. Positivum idem est quod Ens. Non Ens est quod est mere privativum, seu omnium privativum, sive non-Y, hoc est non-A, non-B, non-C, etc. Idque est quod vulgo dicunt nihili nullas esse proprietates’ (Generales Inquisitiones; A VI 4, 740).

  12. 12.

    Cf. for instance A VI 6, 48 / NE 48; A VI 6, 378 / NE 378; Méditation sur la notion commune de la justice (in Mollat / PW 45–64); Dutens IV 280 / PW 71–2. In Antognazza (2016a) I argue that the overall inspiration of Leibniz’s thought is broadly Platonic (cf. pp. 114–115). See also Antognazza (2016b). Prominent Leibniz scholars who have stressed the Platonic (and/or Christian-Platonic; Neoplatonic) inspiration of Leibniz’s philosophy include Rutherford (1995), Mercer (2001), Riley (1996), (2003), and Jolley (2005).

  13. 13.

    On the meaning of ‘absolute’, cf. Adams (1994: 115), referring to texts in which Leibniz explicitly opposes ‘absolute’ to ‘limited’ or uses ‘absolute’ in the sense of ‘unconditioned’ or ‘unqualified’.

  14. 14.

    Definitiones notionum ex Wilkinsio, c. 1685–1686 (A VI 4, 36): ‘ABSOLUTUM est, cujus conceptus est illimitatus seu extra quod nihil in eodem genere sumi potest, seu cujus conceptus est capax quantitatis, et nullos tamen involvit limites. Hinc concipi potest Extensio absoluta, sed non circulus absolutus. Videtur hoc sensu idem esse absolutum quod maximum. Deus est Ens absolutum neque enim ulla datur realitas sive perfectio, quae in Deo non sit. Optime dicemus Absolutum esse in suo genere pure positivum.’ In this text, Leibniz is expanding a series of definitions given by John Wilkins (1668). On p. 35 Wilkins writes: ‘ABSOLUTENESS, Independent, Freehold. DEPENDENCY, Under’.

  15. 15.

    LH 35, 7, 10, Bl. 5r-8v (transcription and translation by Arthur and Ottaviani): ‘ubi simplex ac pura realitas intelligitur, eo ipso constituitur Maximum in rebus possibile seu absolute infinitum, in quo duratio, diffusio, potentia, cognitio, et omnino quicquid inest, limite caret, et vicissim quicquid limite carere potest inest [;] caetera autem ex ipso oriuntur, idque DEUM appellamus. Itaque inest DEO omnis natura capax perfectionis, et unaquaeque harum naturarum perfecte seu absolute. Ut adeo sit Ens absolute absolutum. Nam si quod esset Ens tantum omnipraesens aut tantum omniscium, aut alia quadam certa natura perfectionis capace praeditum, in suo quidem genere absolutum foret, non tamen absoluta realitatis’.

  16. 16.

    For a detailed discussion of the issues raised in this section see Antognazza (2015), from which I am drawing.

  17. 17.

    Cf. Spinoza to Jarig Jelles, Epistola 50 in Spinoza (1925: Vol. 4), and Hegel’s 1816 review of Jacobi’s Werke in Hegel (2009: 9).

  18. 18.

    Cf. Adams (1994: 122–3).

  19. 19.

    Cf. Eckhard to Leibniz, 19 April 1677 (A II 12, 494–5): ‘philosophers do not distinguish perfect from Being [ens] if not as a mere distinction of reason. Indeed Being and positive are opposed to non-Being [non ens]. … where there is some positive entity, there is also perfection. … pain is not something positive but non-Being [non ens] and negation, and indeed also imperfection. … to be an entity, to be real, to be positive, and to exist do not differ among themselves … Being [Ens] and perfect do not differ from one another, as it is shown above. Accordingly, ens perfectissimum is identical to ens purum, or that which in no manner is non-Being [non ens]’.

  20. 20.

    A II 12, 515. Eckhard’s letter of reply of May 1677 stretches over almost forty pages (A II 12, 505–541).

  21. 21.

    For instance, in an earlier exchange, Eckhard notes that if there is something metaphysically real or positive in pain, pain will be materially in God, that is, its reality and positivity will be in God (A II 12, 488). It is implied that, on the contrary, pain as such (that is, formally) is not in God.

  22. 22.

    Cf. Leibniz to Eckhard, summer 1677 (A II 12, 543): ‘The concept which you assign to the Ens perfectissimum not only does not imply contradiction, but produces, or contains eminently, every other perfection’ (my emphasis).

  23. 23.

    The Plotinian One is, of course, totally ineffable and beyond even the category of being.

  24. 24.

    LH 35, 7, 10, Bl. 5r-8v (transcription and translation by Arthur and Ottaviani).

  25. 25.

    LH 35, 7, 10, Bl. 5r-8v (transcription and translation by Arthur and Ottaviani).

  26. 26.

    LH 35, 7, 10, Bl. 5r-8v (transcription and translation by Arthur and Ottaviani): ‘certain circumscribing limits are added, excluding things beyond’; ‘the absolute is found in every notion or nature, as long as nothing limiting is added to it’; variant: ‘in addition to the nature of the absolute, limits are added, from which imperfection arises…’; variant: ‘it is necessary that limits are added to the nature of the absolute in order for anything more restricted to arise’.

  27. 27.

    LH 35, 7, 10, Bl. 5r-8v (transcription and translation by Arthur and Ottaviani): ‘absolutum est fons realitatis et prius limitato’; ‘Substantiae absolutae realitatis, seu summae perfectionis’.

  28. 28.

    Cf. also Leibniz to Pierre Bayle, c. 1702 (GP III 72).

  29. 29.

    See Adams (1994: 123–134).

  30. 30.

    Interestingly, in a text of c. 1683–1685, the notions of ‘absolute’ and ‘limited’ are employed to define the difference between God and creature under the category of ‘substance’: ‘Substantiae[.] Deus Ens absolutum. Creatura Ens limitatum’ (Genera Terminorum. Substantiae; A VI 4 567).

  31. 31.

    I am very grateful to Richard Arthur, Vincenzo de Risi, and the anonymous referees consulted by the editors for their feedback.

Abbreviations

A:

Leibniz, G. W. Sämtliche Schriften und Briefe. Ed. by the Academy of Sciences of Berlin. Series I-VIII. Darmstadt - Leipzig - Berlin, 1923 ff. Cited by series, volume, and page. The superscript ‘2’ after the volume number indicates the second edition of the volume.

Arthur:

Leibniz, G. W. The Labyrinth of the Continuum: Writings on the Continuum Problem, 1672–1686. Translated, edited, and with an introduction by R. T. W. Arthur. New Haven: Yale University Press, 2001.

Dutens:

Leibniz, G. W. Opera omnia, nunc primum collecta, in classes distributa, praefationibus et indicibus exornata. Ed. by L. Dutens. 6 vols. Geneva: De Tournes, 1768. Cited by volume and page.

GP:

Leibniz, G. W. Die Philosophischen Schriften. Ed. by C. I. Gerhardt. 7 vols. Berlin: Weidmannsche Buchhandlung, 1875–1890. Reprint, Hildesheim: Olms, 1960–1961. Cited by volume and page.

Grua:

Leibniz, G. W. Textes inédits d'après les manuscrits de la Bibliothèque Provinciale de Hanovre. Ed. by Gaston Grua. 2 vols. Paris: PUF, 1948.

LDB:

The Leibniz-Des Bosses correspondence. Translated, edited, and with an introduction by Brandon C. Look and Donald Rutherford. New Haven - London: Yale University Press, 2007.

Mollat:

Rechsphilosophisches aus Leibnizens Ungedruckten Schriften. Ed. by Georg Mollat. Leipzig: Verlag Robolski, 1885.

NE:

Leibniz, G. W. New Essays on Human Understanding. Ed. and trans. by Peter Remnant and Jonathan Bennett. Cambridge: Cambridge University Press, 1981.

PW:

The Political Writings of Leibniz. Trans. and ed. with an introduction by Patrick Riley. Cambridge: Cambridge University Press, 1972.

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Authors and Affiliations

  1. King’s College London, London, UK

    Maria Rosa Antognazza

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  1. Maria Rosa Antognazza
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Correspondence to Maria Rosa Antognazza .

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Editors and Affiliations

  1. Dipartimento di Lettere e Filosofia, Università di Firenze, Florence, Italy

    Francesco Ademollo

  2. Department of Humanities, Social Sciences, and Cultural Industries, Università di Parma, Parma, Italy

    Fabrizio Amerini

  3. Laboratoire SPHère, CNRS/Université Paris Cité, Paris, France

    Vincenzo De Risi

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Antognazza, M.R. (2022). Pure Positivity in Leibniz. In: Ademollo, F., Amerini, F., De Risi, V. (eds) Thinking and Calculating. Logic, Epistemology, and the Unity of Science, vol 54. Springer, Cham. https://doi.org/10.1007/978-3-030-97303-2_13

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