Leibniz, Logic & the Trinity
The following excerpts are taken from Maria Rosa Antognazza’s Leibniz on the Trinity and the Incarnation: Reason and Revelation in the Seventeenth Century, translated by Gerald Parks, and published by Yale University Press in 2007. All emphasis will be mine.
Having overcome the first two objections regarding, respectively, the uselessness of reason and the danger of a complete dissolution of the supernatural character of revelation, Theologus still has to face the most intricate problem: that of the validity of human logical and metaphysical principles in the divine sphere. The line of reasoning followed by Theologus takes its basic conception of the analogia entis (analogy of being) from the Thomist school. The metaphysical and logical principles (and in particular the principle of noncontradiction) are common to both the human and the divine spheres, since they are the principles of being in general (ens in genere), which is common both to God and to his creatures.21 Although God does not need the syllogistic arguments typical of discursive reasoning, this takes nothing away from their general validity, which in the final analysis derives from the principle of noncontradiction.22 To maintain the nonvalidity of this principle in the divine sphere would mean the destruction of the distinction between true and false with respect to God: that is, “we could simultaneously admit and reject the Deity or the Trinity; we could simultaneously in the same respect be pious and Atheists, Catholics and Arians.”23 The case of the laws of nature is different. They are valid only in the natural world and can be changed by divine omnipotence.24 But, at this point, can one really speak of divine omnipotence if what is contradictory is impossible also for God?25 By way of reply, Theologus gets his interlocutor to admit that for God to do what is contradictory would amount to a diminution of his perfection or, in other words, it would mean admitting that God could be non-God. Therefore, far from being a limitation on divine perfection as regards omnipotence, the validity of the principle of noncontradiction also in the divine sphere is, so to speak, the ‘seal’ of divine perfection.26 Having gradually lost ground, Misosophus clutches onto his last argument: “Let me admit (since thus you urge) this principle of contradiction also in divine matters; but let me not admit that we can judge well in divine matters which one may be contradictory.”27 Theologus brushes away the objection, stating that “if we have eyes and memory we can also judge of contradiction” and that “in more difficult matters” (as in the divine sphere) “there is only need of more attention.”28 The implicit basis for this reply is once again the analogia entis: if one admits (as even Misosophus does in the end) that the basic logical and metaphysical principles of being in general (ens in genere) are valid both for the divine sphere and for the human sphere, there is no reason to deny that human reason, regulated by such principles (first of all by that of noncontradiction), is able to judge noncontradictoriness in the divine sphere as well.
Therefore the principle of noncontradiction has absolute validity; there are no truths against reason, nor is there a double philosophical and theological truth. Leibniz never tires of repeating this.29 In particular, in a text composed probably between February and October 1685, the principle of noncontradiction is defended as the ultimate criterion for distinguishing between truth and falsehood both in the natural world and in the supernatural sphere,30 and consequently as the foundation of the distinction between what is above reason and what is against reason.31 And Leibniz insists that this is true without exceptions, also in the case of the most problematic mystery of all, the mystery of the Trinity. That is, defending the mystery of the Trinity by admitting an exception to the basic logical principle (directly based on the principle of noncontradiction) that things that are identical to a third thing are identical to one another (quae eadem sunt eidem tertio sunt eadem inter se) ends up leading to consequences contrary to what one desires: namely, to the confirmation of the Socinian thesis that this mystery is irrational and therefore is to be rejected as false.32
At this point, the key move is to show that this logical principle is not denied in the dogma of the Trinity. Leibniz, therefore, in a series of texts composed between 1678 and 1688, gave shape to his line of defense against the accusation of contradiction.33 The ‘formula’ of the Trinity can be expressed in the following terms: the Father (B) is God (A), the Son (C) is God (A), the Holy Spirit (D) is God (A); B, C, and D are different from one another; nonetheless, A is only one.34 Now, to affirm at the same time the oneness of A and the diversity of B, C, and D would seem to involve a clear contradiction.35 According to the principle that things that are identical to a third thing are identical to one another, given the oneness of A, one should necessarily conclude that B, C, and D are identical to one another; in the terms of the Trinity, there would be no distinction between Father, Son, and Holy Spirit. The only way to save this distinction, without falling into contradiction, would be to admit the plurality of A; that is, one would have to affirm Tritheism.36 At stake here is the very concept of number, originated by the definition of unity and plurality, which in its turn presupposes the definition of identical and different.37 Leibniz would seem to be in a blind alley. But he writes in Circa Geometrica Generalia that “the contradiction is removed by a distinction.”38 The solution is given to him by a distinction widely used in the Protestant theology of his time: the distinction between essentialiter (essentially) or ousiōdōs and personaliter (as a person) or hypostatikōs, that is, between two opposite ways of predicating the names of God.39 Thus, God taken absolutely or essentially (Deus absolute seu essentialiter sumtus) indicates God considered from the standpoint of the divine essence, numerically one, in which the three persons participate; God taken relatively or as a person (Deus relative seu personaliter sumtus) indicates one of the persons of the Trinity, equally participating in the single divine essence. Thus, in the propositions “The Father is God,” “The Son is God,” and “The Holy Spirit is God,” the term “God” means something different from the term “God” that appears in the proposition “God is One [Unus est Deus]”: in this last case God considered absolutely or essentially is meant, whereas in the previous propositions the meaning is God considered relatively or as a person. That is, Leibniz calls attention to the fact that the propositions “The Father is God” and “God is One” are to be considered reduplicative propositions.40 The proposition 1) “The Father is God” is to be specified in the following proposition: 1.i) “God, insofar as he is considered relatively or as a person [quatenus relative seu personaliter sumtus], is the Father,” or equivalently, 1.ii) “God, insofar as he is one or another person of the divinity [quatenus una aliqua persona divinitatis], is the Father”; the proposition 2) “God is One” is to be specified in the following proposition: 2.i) “God, insofar as he is considered absolutely or essentially [quatenus absolute seu essentialiter sumtus], is One,” or equivalently, 2.ii) “God, insofar as he contains all persons or insofar as he is threefold in persons [quatenus omnes personas continens seu trinus in personis], is One.”41 Now, although God taken relatively and God taken absolutely are really the same thing (just as “Peter” and “The Apostle who denied Christ” are the same thing), in propositions 1.i) and 2.i) God (taken relatively) and God (taken absolutely) cannot be substituted one for the other, since these propositions fall into the class of cases in which “we are not dealing with the thing but with the way of conceiving it [non de re sed modo concipiendi agitur].”42 Coming back to the example of Peter, although “Peter” and “the Apostle who denied Christ” are the same and can therefore normally be substituted for one another, this is not true when we are considering not the ‘thing’ (res) but the way of conceiving it (modus concipiendi). Thus, in the proposition “Peter insofar as he was the Apostle who denied Christ, just so far he sinned,” “the Apostle who denied Christ” cannot be replaced by “Peter”: that is, one cannot say that “Peter insofar as he was Peter sinned.”43 Or again, although “a trilateral figure and a triangle are the same thing,” when we say “a triangle considered as such has 180 degrees,” the term “triangle” (triangulus) cannot be replaced by that of “trilateral figure” (trilaterus), since a given property (having 180 degrees) is predicated of a subject on the basis of a particular way of considering the subject (precisely as a triangle and not as a trilateral figure).44 In the same way, in the propositions “God is the Father” and “God is One” the two predicates “Father” and “One” are attributed to the subject (God) on the basis of different ways of considering the subject: in the first case “as taken relatively or personally” (or “as one of the persons of the Godhead”); in the second case “as taken absolutely or essentially” (or “as containing all persons or threefold in persons”). The subject of the first proposition can therefore not be substituted for the subject of the second (and vice versa), since these are propositions in which “we are dealing not with the thing but with the way of conceiving it”; the two subjects, although they are really the same thing, are considered according to different aspects, and it is precisely this difference in the way of considering them (the modus considerandi) that justifies the predications, respectively, of “Father” and “One.”
Leibniz sums it up in De Trinitate:
That principle that things that are the same to a third thing are the same to each other, if identity is taken with the greatest rigor, has a place in divine matters no less than in natural affairs. When we say “the father is God” and “the son is God,” and “God is One [Unus est Deus],” both father and son, surely the father and the son are the same, unless “God” in the first two propositions is understood as a person of the Godhead and in the last one as the divine nature or the absolute singular substance that we call God. Hence we say that the three persons of the Godhead are yet not three Gods, and in this sense we make some distinction between the person of the Godhead and God, for if between two words there is a difference in the plural usage, so that one cannot replace the other, there will also be between the same some difference in the singular, since the plural form is a repetition of the singular.45
The idea of identity in diversity between “God taken absolutely” and “God taken relatively” is expressed by Leibniz in a formulation he had already used in the Defensio Trinitatis in the wake of the logical doctrine of Johannes Raue:46 “Although the father is not the son, yet the father is he who is [est is qui est] the son, namely, the one God in number.”47 Leibniz adds in De Lingua Philosophica (On Philosophical Language): “For in the Trinity these two things are different: ‘to be God the father,’ and ‘to be he who is [illum qui est] God the father.’ For God the son is not God the father, and yet he is the very one who is [est ille ipse qui est] God the father, namely the one most high God.”48 The same idea is expressed in De Trinitate (On the Trinity): “When it is said that ‘the same one who is [idem ille qui est] the father is also the son,’ the meaning is that in the same absolute substance of God there are two relative substances differing in number from one another. . . . Is it possible to say: ‘the father is that only one God [unicus ille Deus]’? I think not, but the father as partaking of the divine nature which is one in number.”49 That is, when one says that the Father, Son, and Holy Spirit are the same God, one means that they partake of the same divine essence, which is one in number. (Chapter 5. The Conformity of Faith with Reason, pp. 69-73)
31. The occasion arises from the discussion of the theory of virtualitates (De Non Violando Principio Contradictionis in Divinis contra Honoratum Fabri; A VI, 4, 2340; VE, 1831): “They want such virtualities to be the divine nature and the person of the word [personam verbi (that is, the second person of the Trinity)], which although in reality [realiter] they are the same identical thing, yet likewise are in relation to contradictory predicates as if they were really distinguished. Some people want these to be found in created things.” Against this second statement, the Jesuit father Honoratus Fabri speaks out: virtual distinctions cannot be allowed in the natural sphere as they are contrary to the principle of noncontradiction, without which no knowledge would be possible. The supernatural sphere is different: here, one must accept on faith many things that are greater than our capacity for understanding (see A VI, 4, 2340–2341; VE, 1831–1832; Fabri’s position is picked up and criticized in the Nouveaux Essais, book IV, chap. XVIII, § 9; A VI, 6, 498). Fabri’s reasoning implies the equivalence between “against reason” and “above reason,” which is a direct consequence of the negation of the absolute validity of the principle of noncontradiction. Now, Leibniz points out, if one abolishes the distinction between ‘above’ and ‘against’ reason, the way is made clear for every absurdity that would claim to be revealed. In other words, there is no longer any possibility of discerning true from false in the religious sphere: to cite the two most striking examples, it becomes impossible to demonstrate the existence of God, or to defend the dogma of the Trinity (see A VI, 4, 2341; VE, 1832). All positions—the atheist or the theist, the Trinitarian or the Antitrinitarian—would be equally valid or, seen from the opposite standpoint, equally without foundation. “It is therefore wiser and saner to say,” concludes Leibniz, “that neither in divine nor in created things can contradictory propositions be admitted.” (A VI, 4, 2341; VE, 1832).
32. See De Non Violando Principio Contradictionis in Divinis; A VI, 4, 2341–2342; VE, 1832: “And altogether the Mystery of the Holy Trinity is to be explained thus so as to avoid a real contradiction, or indeed we will desert to the Antitrinitarians. Nay, regarding the principle of human reasoning things that are equal to a third thing are equal to one another; (since it is founded on the principle of non-contradiction), it is to be said altogether that it is not violated indeed even in divine matters, otherwise in every haughty argumentation anything could be asserted about God with impunity; nor will syllogisms be made in Theological matters, nor will modes and figures [of the syllogism] belong there. Therefore we must beware lest by asserting such things we confirm a heresy, and altogether we must explain the mystery of the Trinity in such a way that such stumbling blocks are avoided.” See also De Trinitate (A VI, 4, N. 416; VE, N. 75)…
34. See Notationes Generales (A VI, 4, 552; VE, 185): “The Father is God, the son is God, the Holy Spirit is God; and the father is neither the son nor the Holy Spirit, and the Son is neither the father nor the Holy Spirit, and the Holy Spirit is neither the father nor the son, (that is, of these three none is identical to another of them) and yet they will not be three, but still one.”
35. See ibid.: “If B is A, and C is A, yet B and C are the same, then it is said that there is only One A; if in truth B and C are not identical, there is a plurality of As. Hence it is clear that the definition of One and many presupposes the definition of ‘same’ and ‘different’ as more simple [concepts]. If B is A and C is A, and B, C are not the same, there are said to be two As. If, besides, it is added that D is A, and none of these B, C, D is identical to another of them, it will be said that there are three As, and so forth. The symbol attributed to Saint Athanasius seems to be in conflict with this definition . . . clearly, if God is taken in the same sense, when it is said the father is God, etc., as when it is said: God is One, then, at any rate, either this implies a manifest contradiction or the concept men have of one and many is changed, which is not to explain the mystery, but to talk nonsense.”
36. See Examen Religionis Christianae (A VI, 4, 2364–2365; VE, 2418): “Moreover, the Sacred Monuments of the Christians teach that the most high God (who by reason itself is established to be only one in number) is nonetheless triune in persons. . . . But this is to be received in such a way that every suspicion of Tritheism is avoided. Therefore when it is said, the Father is God, the Son is God, the Holy Spirit is God, and these three are different from one another (so that the Father is not the Son or the Holy Spirit, nor is the Son the Holy Spirit or the Father, nor is the Holy Spirit the Father or the Son), this is to be understood in such a way that nonetheless there are not three gods, but only one, albeit triune in persons. Indeed, the Antitrinitarians say that this is contradictory, and the plural number means nothing else than that three different things, each of whom is God, are said to be three gods, nor can several different things in number be one in number.”
37. Notationes Generales, A VI, 4, 552; VE, 185 (see note 35); De Deo Trino, A VI, 4, 2291–2292; VE, 661 (see note 47) and Circa Geometrica Generalia, 147: “If B is A, and C is A, and B is not C, nor is C B, it will be said that there are two As. But if B is A, and C is A and D is A; and B is not C nor D, and C is also not B nor D, and D is neither B nor C, it will be said that there are three As. And so on. And generally when there is not only one A, they are said to be many. And this is the origin of Numbers; and this very expression is observed in Athanasius’ symbol, although there its use seems to contradict this definition.”
41. See Notationes Generales (A VI, 4, 552–553; VE, 185): “It should therefore be known that when we say: There is only one God, we mean God taken absolutely, or, as is commonly said, essentially, of whom there are three persons, in one essence in number; when indeed we say The Father is God, the Son is God, etc., we do not mean God taken absolutely, containing all persons or triune in persons, nor even can it be said that the father or the son is triune in persons, but we mean God taken relatively or, as they say, personally, or one or another person of the Godhead.” In a passage of the Examen Religionis Christianae, later replaced, Leibniz writes (A VI, 4, 2364; VE, 2418): “It is necessary, for the sake of avoiding contradiction, that this word God be taken with a somewhat variable meaning, and understood a little differently when we say The Father is God or the son is God from when we say There is only one God, for the father cannot be said thus to be one in number, as simultaneously to be triune in persons, or that three persons, so to speak, constitute him; for it would be absurd and unheard of in the Church to say that in the father there is the father, son and Holy Spirit, or that the father is constituted by the father, son and Holy Spirit. Therefore, in the former expression, by the word God we mean a person of the Godhead, and in the latter that absolute substance which is only one in number, but which contains [complectitur] three persons of the Godhead.” The final version, much more concise, goes (A VI, 4, 2365; VE, 2418–2419): “But these [the Antitrinitarians] ought to think that the Church does not want the Father, for example, or the Son to be triune in persons, but to be one person of the Godhead. Therefore, though the persons are multiplied, God, who is triune in persons, is not multiplied, nor therefore are there three gods on account of there being three persons.”
43. Ibid.: “If A is B and B is A, then A and B are said to be identical. That is, A and B are the same thing, if one can always be substituted for the other (except for those cases in which we are not speaking of the thing in itself but of the way of conceiving it, in which they differ. Thus Peter and The Apostle who denied Christ are the same, and one term can take the place of the other; except when I consider this very way of conceiving, which some call reflexive, as for example, when I say Peter insofar as he was the Apostle who denied Christ, just so far he sinned, I cannot substitute Peter in each case, viz., I cannot say Peter insofar as he was Peter sinned).” This text, like the two cited in the following note, are used by Mugnai, Leibniz’ Theory of Relations, 108–109, to illustrate one of the two uses made by Leibniz of reduplicative operators (in particular quatenus), i.e., in the determination of “those particular contexts which violate the principle of substitutivity salva veritate . . . Leibniz recognizes that there are limits to the application of the principle of substitutivity, and identifies them in those contexts where a given property is predicated of a subject according to a particular mode of consideration (modus considerandi).”
44. Specimina Calculi Rationalis, April–October 1686* (A VI, 4, 810; VE, 1935): “A ∞ B means A and B are the same, that is, they can be substituted for one another everywhere. (Unless it is prohibited, which occurs in them when some term is asserted to be considered in a certain respect, as, for example, although a three-sided figure [trilaterum] and a triangle [triangulum] are the same thing, yet if you say a triangle as such has 180 degrees, the term three-sided figure cannot be substituted for it. There is, in this sentence, something material.)” See also Principium Scientiae Humanae, winter 1685–1686* (A VI, 4, 672; VE, 1003–1004): “Moreover, reduplicative propositions are to be excepted; in them we try to speak about some term in such a strict fashion that we cannot wish to substitute it. For they are reflexive and behave with respect to thoughts as material propositions do with respect to words.” Cf. Mugnai, Leibniz’ Theory of Relations, 108–109…
47. See De Deo Trino, A VI, 4, 2291–2292; VE, 661: “There are three persons of the Divinity, of whom there is one essence in number. We do not demonstrate this Mystery of faith by reason, but we only illustrate it and defend it against objections. Now, the most powerful of the objections is this: if three [entities] are different from one another, and any one of them is God, it follows that there are three Gods. For if the father is God, and the son is God, and the Holy Spirit is God, and the father is not the son, nor the Holy Spirit; and the Son is not the father or the Holy Spirit, and lastly the Holy Spirit is not the father or the son; either it will have to be said that there are three gods or that we do not know what one and many mean, and therefore in just such a manner it may even be denied that father, son and grandson are three men; or, the reason will have to be adduced as to why we call these three men, and deny that those are three gods. We shall reply, although the father is not the son, yet the father is he who is [est is qui est] the son, namely, the one God in number. This cannot be said of two men, father and son, and this is the real reason for the difference.”
48. A VI, 4, 889; VE, 360. The reference to Johannes Raue’s doctrine of the copula is explicit in the passage immediately prior to the one cited (see A VI, 4, 889; VE, 359).
49. A VI, 4, 2346; VE, 274. The explanation given in the Notationes Generales (A VI, 4, 553; VE, 186) is less clear, although it can be brought back to the one expounded above: “In the same way the Holy Trinity is not in conflict with this principle that things which are identical to a third thing are identical to each other, for when the father and son are said to be the same God, there God does not mean either the triune God, nor a person of the Godhead, but the same or One God is said to partake of the numerically same divine essence [ejusdem numero divinae essentiae].” (Ibid., pp. 212-216)
Further Reading
James White’s Definition of the Trinity