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Presumptions and Conjectures in Leibniz’s Legal Theory

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Part of the Logic, Argumentation & Reasoning book series (LARI,volume 7)


This paper focuses on the role of presumptions and conjectures in Leibniz’s legal theory. Both presumptions and conjectures are closely connected to the question of the burden of proof for presumptions lead to a shift of the burden. Thus, these notions play an essential role in the practice of litigation: the odds to win a given case are stacked against the party that has to bear the burden of proof. The paper analyses three different texts which bear upon the topic and stem from different phases of Leibniz’s production: the Elementa Juris Naturalis (1671), the De legum interpretatione, rationibus, applicatione, systemate (1678/1679), and the Nouveaux Essais sur l’entendement humain (1704, published posthumously in 1765). The aim of the paper is to elucidate how Leibniz developed a subtle theory of legal presumptions and conjectures. Moreover, the paper attempts a first formal reconstruction of this theory.


  • Legal presumptions
  • Legal conjectures
  • Law and logic
  • Leibniz

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  1. 1.

    Fortunately, new studies of the jurisprudence of Leibniz and translations of important texts have appeared recently, e.g. [3, 4, 6, 810, 1719, 3133].

  2. 2.

    For a German translation of parts of the EJN, see [8], pp. 89 sqq].

  3. 3.

    The roots of this plan probably go back to Leibniz’s teacher Erhard Weigel (1625–1699), who was a professor at the University of Jena and wanted to apply the Euclidean method to all branches of knowledge. For more information, see [22, pp. 38 sqq].

  4. 4.

    For more information, see [29, p. 329], [25, pp. 16 sqq], [11, pp. 79 sqq], [15, pp. 320 sqq] and [16], especially Sect. 4.5.

  5. 5.

    Recently, Blank [5] wrote about presumptions in the EJN from a philosophical point of view, stressing the difference between ontological and logical requirements. About presumptions in general, see [7, p. 426] and [1, p. 202]. For a first introduction to the juridical role of presumptions referring to DLI, see [9, pp. xxxiv–xxxvi].

  6. 6.

    Leibniz later deleted the heading. For a German translation, see [8, pp. 264 sqq].

  7. 7.

    Busche [8, pp. 265 sqq] translates “praesumitur” as “im Voraus annehmen”. Praesumere is a well defined legal terminus technicus and means “vermuten” in German.

  8. 8.

    Leibniz later deleted this headline.

  9. 9.

    Burckhardt [7, pp. 425 sqq] explains this theorem by making use of the idea of privation. See also [5, p. 214].

  10. 10.

    For more information about Leibniz’s concept of compossibility, see [28, p. 962] and especially Wilson’s [34, p. 1]. Her new ideas considers [24, pp. 105–6]. For a logical analysis of Leibniz’s compossibility (especially GP 3, 573), see Lenzen ([15, pp. 327–8] and [14, pp. 185 sqq]). Lenzen draws our attention especially to the connection of the concepts of “compossibility” and “possible world” and thinks that compossibility is not transitive. The transitivity of Leibniz’s compossibility is defended by [21, 27, p. 77] and [23, p. 55].

  11. 11.

    [8] translates “item” as “Das bedeutet:”. This is also misleading.

  12. 12.

    Thus, “Pr” is a kind of propositional operator that produces propositions out of propositions. Leibniz did not develop an explicit semantics for them, nor is this developed in the present paper. Leibniz deals with this notion on the one hand syntactically and on the other hand he deploys some intuititive semantics. Similar applies for “Fac”. In relation to “J” and “I”, one could treat “Fac” as an operator as well, even though it looks more natural to formulate it as a kind of predicate defined on actions. One way to formulate such kind of predicates is to make use of a more expressive language containing an infinite number of type of objects, such as in Martin-Löf’s Type Theory (see [20]). In such a setting we could formulate the following formation-rule for “J”: J(x): proposition (x: Action) in words: J(x) becomes a proposition provided x is substituted by a token of the type action – or alternatively by an element of the set of actions. For the general purposes of the present paper, the full development of such an underlying type-theoretical approach is not necessary. However, the reader might assume some formal typing system underlying the use of J while qualifying actions.

  13. 13.

    “Imò” as item again does not mean “thus”.

  14. 14.

    Translation according to [1, p. 204].

  15. 15.

    Blank [5, p. 215] thinks that the “presumption of justice” is a special case of the “presumption of possibility”. He refers to [1, pp. 206 sqq]. Leibniz does not make use of the concept “presumption of possibility” in the EJN. He only makes use of the concepts “easier” and “more possible” to justify the presumption that an action is just.

  16. 16.

    Recall the afore remark on the operators Pr and Fac.

  17. 17.

    As already mentioned: “Omne ergo praesumendum est facilius, non contra”.

  18. 18.

    [5, p. 216] gives an example.

  19. 19.

    For the Latin text, see [13, A VI 2, pp. 567 ll. 23 sqq].

  20. 20.

    Imò as item again does not mean: thus.

  21. 21.

    The full stop seems to be an error. “Justum” refers to “omitti”.

  22. 22.

    O(α) means “α is obligatory“, P(α) means “α is permitted” (Lenzen uses E “erlaubt” instead of P “permitted”) and V(α) means “α is prohibited”.

  23. 23.

    The negative formula ¬a expresses the omission of an action.

  24. 24.

    We add a negation to both parts of the biconditional: ¬¬O(α) ↔ ¬E(¬α). According to classical logic ¬¬O(α) is equivalent to O(α).

  25. 25.

    I have to mention that I got aware of this excellent text of Leibniz thanks to Marcelo Dascal. We studied his translation of DLI (see [9, pp. 79 sqq]) together in Konstanz, especially the passages about presumptions and conjectures. My analysis of this text is influenced by his ideas and his translation. For the complete Latin text of DLI, see [13, A VI 4 C, pp. 2782–2791].

  26. 26.

    Dascal’s translation omits necessario [9, p. 86]

  27. 27.

    Dascal adds surely.

  28. 28.

    Dascal: “the negative one” [9, p. 87].

  29. 29.

    Addition of Dascal.

  30. 30.

    Dascal: “someone else”.

  31. 31.

    Dascal: “are … reasonings”.

  32. 32.

    Of course, it is not at all easy to define impedimentum.

  33. 33.

    We find the same in a Latin letter of Leibniz to Werlhof, Prof. of Law in Helmstedt, written on 17 July 1696 [13, A I 12, pp. 740 sqq] translated in [9, p. 350]: “Every presumption of what is false (which is ordinarily called a legal and de jure [presumption] and usually believed not to admit contrary proof) is a fiction. I do not admit fictions in natural law”.

  34. 34.

    According to Leibniz, this rule can be found already in the Corpus Iuris Civilis (D. 50,17,1,9): “Semper in obscuris quod minimum est, sequimur”.

  35. 35.

    We only consider fewer requisites, not smaller ones.


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I want to thank Marcelo Dascal, who draw my attention to this aspect of the legal theory of Leibniz and Shahid Rahman, who made important comments on the draft of this paper.

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Correspondence to Matthias Armgardt .

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Armgardt, M. (2015). Presumptions and Conjectures in Leibniz’s Legal Theory. In: Armgardt, M., Canivez, P., Chassagnard-Pinet, S. (eds) Past and Present Interactions in Legal Reasoning and Logic. Logic, Argumentation & Reasoning, vol 7. Springer, Cham.

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