0. Introduction: Back from Leibniz
Modal logic is a rare non-theological domain where the ways of the Eastern and Western Christian philosophies parted. Regardless of theology, the philosophical ontology of Dionysius the Areopagite and Maximus the Confessor was different from that of Augustinus, Boetius, and Thomas Aquinas, even if both Eastern and Western traditions shared the same classical heritage. East and West were thinking differently not only when thinking God but even when thinking creature, that is, not only in theology but even in philosophy.
The Eastern and Western modal approaches met each other somewhere near Leibniz and especially in Leibniz’s own works, albeit in a quite different theological context. It is useful to understand this difference before trying to translate Dionysius the Areopagite into the modern formal language that goes back directly to Leibniz, the main inspirer of Clarence I. Lewis in his seminal monograph on the modal logic.
The main issue is over mutual relation between purely logical possibilities and ontology. For the West, the typical approach was that which was aptly coined by Simo Knuuttila “extensional interpretation of modality,” namely, that the possibilities must be “dealt with from the point of view of their actuality in history without an idea of alternative domains.” This was not the only available approach, however, even in the West. Its alternative, also in the West, was a “décosmologisation radicale du concept de possible,” even before Duns Scot, which allowed operating with “pure” logical possibilities and, in this way, to overcome the extensional approach. Both approaches had roots in Aristotle or, at least, in the mediaeval understanding of Aristotle. Leibniz and, shortly before him, some Jesuits started establishing links between these logical possibilities and ontology, which resulted into the concepts of the Pre-established Harmony.
In the Byzantine East, the logical possibilities were not necessarily considered as free from any ontological/cosmological meaning, and so, some concepts in the vein of “pre-established harmony” were a matter of course. Dionysius the Areopagite’s teaching on the non-existence of the evil is, in this aspect, a kind of Theodicy, as Leibniz would call it were he acquainted with Dionysius somewhat deeper. The theological premises, however, are here quite different from those of Leibniz and his Jesuit predecessors.
The main difference is in defining of the very source of perturbation of the strictly determined order of things, the concept of free will. Leibniz and like-minded Jesuits escaped the total predestination via doctrines of “vagueness” of the concept of each individual man. The divine predestination establishes only “vague” concepts, which are to be sharpened with the free choice made by the created beings themselves between different possibilities. The omnipotence of God is here limited by the principle of “moral necessity,” that is, a necessity to God of turning the scale to the best at any outcome of creature’s free choice. The concept of “moral necessity” imposed on God (by God himself, of course) was elaborated by the Spanish Jesuits Diego Ruiz de Montoya (1562–1632) and Diego Granado (1571–1632), who were preoccupying of avoiding both dangers of predestinationalism and what they called “Semipelagianism.”
The danger of “Semipelagianism” consisted in limitation of the divine omnipotence with the human or angelic will. Instead, Spanish Jesuits invented a peculiar way of divine self-limitation without involving any created will. God himself creates the rational beings as “vague” concepts (the attitude shared by Leibniz and defended by him against criticisms of Arnaud) and, then, pre-establishes the best consequences for any possible outcomes of their free choices. All possible “world histories” (or, shortly, “possible worlds”) are equally “predestined,” and so, no casual chain is created by the non-divine free will.
This doctrine looked, nevertheless, as denigrating the omnipotence of God to many Catholic (including Jesuit) and Protestant scholars. However, even less it was theologically compatible with the standard Eastern doctrines on the free will. What the West called “Semipelagianism” was the normative doctrine of the whole Christian East. Such polemics as that which took place between John Cassian, an Eastern-minded Western theologian and a direct disciple of the great monastic Fathers of the Egyptian desert, and Prosper of Aquitaine, a disciple of Augustine of Hippo and the most prominent distributor of the Augustinian anti-Pelagian views, have never took place in the East. In the East, nobody saw any problem in considering the divine omnipotence as limited by the free will of the rational beings.
The whole discussion on the free will, in both East and West, was theologically preconditioned by the discussion of the Fall and the meaning of the Baptism. The anti-Pelagianism of Augustine was based on his doctrine of the original sin as a hereditary culpability making the human will incapable to perform the right choice by itself; thus, the infant Baptism is a necessity for remission of the original sin and to free the free will. This doctrine was absolutely alien to the Christian East. Here, even the most opposite to each other Antiochene and Alexandrine theological schools were agreed that the infants need no remission of sins because they are sinless; they could be baptised, however, in order to communicate them the supernatural life. Only a remote parallel with Augustine’s teaching on the original sin as a feature of the human nature acquired after the Fall is to be detected in Julian of Halicarnassus’ (first half of the sixth cent.) “aphthartodocetic” teaching on the difference of the human nature in Christ and in us after the Fall. This ephemeral teaching was abandoned by the Julianists themselves to the late sixth century.
Therefore, it was directly the human and angelic free will that limited, in the Eastern Christian theologies, the divine omnipotence. Nevertheless, the divine providence acts in each point of the causal chain in continuous interaction with the free will of each rational creature. The latter continuously chooses whether to cooperate with the divine operation (“energy”) or not. This results certainly into a kind of harmony leaded by the divine providence, and this harmony certainly is foreknown by God, but it is not to say that this harmony is pre-established by God alone. It is rather continuously established than pre-established, and not by God alone but by God in cooperation with the rational creatures.
Diego de Montoya, when arguing that the divine knowledge and love act not only in creature in general but also in each particular created being, was referring, among others, to Dionysius’ doctrine of the omnipresent divine eros (DN 4): “Dionysius (see the whole chapter 4 of the On Divine Names) teaches, that the love for the creatures prompted God to communicate to each one of them, according to its capacity, participation to his goodness.” This is the part of Jesuits’ and Leibniz’s theological background that they shared with the Eastern patristic tradition: the omnipresence and operating love of God reaches each particular creature without exception. They were, however, differing in further understanding of this interaction between the God and the created being. In both cases, this understanding leaded to some kind of “intensional” interpretation of modality.
 I call this author as he called himself, without the prefix “pseudo-.” For the historical circumstances of composition of the Corpus, with a discussion of all available viewpoints, s. B. Lourié, “Peter the Iberian and Dionysius the Areopagite: Honigmann—van Esbroeck’s Thesis Revisited,” Scrinium. Revue de patrologie, d’hagiographie critique et d’histoire ecclésiastique 6 (2010): 143-212. According to this reconstruction, the Corpus was composed through the following steps: 1) vision of heavenly hierarchies by John the Eunuch at the (most probably, first) celebration of the Dormition of the Virgin in Gethsemane in 444, 2) composition of the core of the Corpus after John’s death by his close friend and cellmate Peter the Iberian in the late 460s or somewhat later, and 3) pseudonymisation of the Corpus after the death of Peter in 491 by the monks of the monastery in Maiouma founded by the émigrés from Crete, who were close to Peter during his life. This procedure was destined to use the Corpus as a weapon against the Book of Holy Hierotheos, the manifesto of the Origenistic Palestinian monks of this time. This is the same monastery where Severus, future patriarch of Antioch (512—518), was tonsured monk (near 491). Severus will be the first who quotes Dionysius in a theological discussion (between 518 and 528, most probably, in the middle of the 520s). The Corpus in the present form is to be dated to ca 500 or several years earlier. The Christology of the Corpus was acceptable for the official Church of its time, whose teaching was formulated in the Henotikon of the Emperor Zeno (482) and accepted by the Eastern patriarchates, including both adversaries and partisans of the Council of Chalcedon, whereas not by Rome. Thus, the influence of the Corpus became widespread regardless of the issue of Monophysitism.
 C. I. Lewis, A Survey of Symbolic Logic. Berkeley: University of California Press, 1918, 5-18, 373-387; cf. N. Rescher, “Leibniz’s Interpretation of His Logical Calculi,” The Journal of Symbolic Logic 19 (1954): 1-13; repr. in: idem, Collected Papers. Vol. X: Studies in the History of Logic. Heusenstamm: Ontos Verlag, 2006, 141-151.
 S. Knuuttila, “Medieval Modal Theories and Modal Logic,” in: D. M. Gabbay, J. Woods (eds.), Handbook of the History of Logic. Vol. 2: Mediaeval and Renaissance Logic, Amsterdam: Elsevier, 2008, 505-578, here 507, 511.
 J. Schmutz, “Qui a inventé les mondes possibles ?” in: J.-C. Bardout, V. Jullien (eds.), Les mondes possibles. Cahiers de philosophie de l’Université de Caen, 42; Caen: Presses universitaires de Caen, 2006, 9-45, here 25 and n. 40. I am very grateful to Jacob Schmutz for providing me a copy of this valuable paper.
 Cf. Schmutz, op. cit., and, for a modern reconstruction of modalities in Aristotle in the same lines, pace Jaakko Hintikka’s most accepted reconstruction, J. Van Rijen, Aspects of Aristotle’s Logic of Modalities, Dordrecht: Kluwer Academic Publishers, 1989. Van Rijen’s view is partially corroborated by Matthews’ analysis of Aristotle’s intensionality: G. B. Matthews, “Container Metaphysics according to Aristotle’s Greek Commentators,” in: R. Bosley, M. Tweedale (eds.), Aristotle and His Medieval Interpreters. Canadian Journal of Philosophy Supplementary vol. 17; Calgary: University of Calgary Press, 1992, 17-23. This short paper is still valuable as an introduction to the topics relevant to modality in the Byzantine Aristotle. Unfortunately, the whole matter of modalities in Byzantine interpreters of Aristotle, especially in John Philoponus (the most important among them for both East and West), is still almost unexplored.
 Cf., S. K. Knebel, “Leibniz, Middle Knowledge, and the Intricacies of World Design,” Studia Leibnitiana 28 (1996): 199-210, esp. 208-210. The author is among those who argue for a direct influence of Jesuits on Leibniz. What is certain, it is the fact that, at least, some of their relevant publications were available to Leibniz.
 Leibniz’s mentions of Dionysius (according to the database Kumuliertes Personenverzeichnis (zur Akademie-Ausgabe): http://www.gwlb.de/Leibniz/Leibnizarchiv/Veroeffentlichungen/Personendatenbank/index.php ) leave a feeling that he was, for Leibniz, an ancient theologian who wrote about angelical hierarchies, one among other authoritative but remote figure of the past.
 Cf. especially S. K. Knebel, Wille, Würfel, und Wahrscheinlichkeit. Das System der moralischen Notwendigkeit in der Jesuitenscholastik, 1550–1700. Paradeigmata 21; Hamburg: Meiner, 2000, and his earlier papers: idem, “Necessitas moralis ad optimum. [I]. Zum historischen Hintergrund der Wahl der besten aller möglichen Welten,” Studia Leibnitiana 23 (1991): 3-24; idem, “Necessitas moralis ad optimum. (II). Die früheste scholastische Absage an den Optimismus. Eine unveröffentlichte Handschrift Jorge Hemelmans S.J. von 1617,” Theologie und Philosophie 67 (1992): 514-555; idem, “Necessitas moralis ad optimum. (III). Naturgesetz und Induktionsproblem in der Jesuitenscholastik während des zweiten Drittels des 17. Jahrhunderts,” Studia Leibnitiana 24 (1992): 182-215; idem, “Necessitas moralis ad optimum. (IV). Repertorium zur Optimismusdiskussion im 17. Jahrhundert,” Studia Leibnitiana 25 (1993): 201-208. Cf., more recently, with pointing out several important unclosed problems, M. Murray, “Pre-Leibnizian Moral Necessity,” The Leibniz Review 14 (2004): 1-28.
 Actual in the Counterreformation context, cf. De servo arbitrio by Luther (1517).
 Another Jesuit, a correspondent of Leibniz and the translator of his Theodicy into Latin, Bartholomew Des Bosses (1668–1738), who was the first to expose Jesuit connexions of Leibniz’s ideas on moral necessity (without, however, claiming any direct dependence), explained in this way Leibniz’s modal thinking: no wonder, he wrote, that “non paucos” (quite a few) Protestants turn out to be not abhorring the (Jesuit doctrine of the) scientia media, while abhorring the Semipelagianism, “[e]t hos fortasse praecipuem indigitare voluerit Leibnitius” (“and Leibniz probably would especially wish to demonstrate this,” that is, his negation of Semipelagianism and tacit acceptation of the Molinist “middle knowledge” doctrine); B. Des Bosses, “Monitum Interpretis,” in: G. G. Leibnitius, Tentamina Theodicaeae de bonitate Dei, libertate hominis et origini mali, T. I, Francofurti: C. J. Bencard, 1719, [separate foliation], here f. 6v. For Leibniz and the “middle knowledge,” s. esp. Knebel, “Leibniz, Middle Knowledge...”
 For a theological exposition of his “Semipelagianism,” s., first of all, V. Codina, El aspecto cristologico en la espiritualidad de Juan Casiano. Orientalia Christiana Analecta 175; Roma: PIO, 1966, 67-73 et passim.
 It is still disputable whether John Cassian’s polemics was aimed at Augustine himself, but, anyway, to say the least, Cassian “...was not an Augustinian in any meaningful sense of the term,” as said the scholar who tried to smooth all disagreements between Cassian and Augustine (A. M. C. Casiday, Tradition and Theology in St John Cassian. Oxford Early Christian Studies; Oxford: Oxford UP, 2006, 102; cf. ibid., 112-117, where the author tries to withdraw Augustine from Cassian’s attack while sacrifices Prosper of Aquitaine). On the influence of Prosper’s anti-Cassian polemics, s. forthcoming thesis of Jérémy Delmulle “Prosper d’Aquitaine contre Jean Cassien. Le Liber contra collatorem: introduction, édition critique, traduite et annotée et étude de la réception,” to appear in the series Sources chrétiennes.
 D. Weaver, “From Paul to Augustine: Romans 5:12 in Early Christian Exegesis,” St. Vladimir’s Theological Quarterly 27 (1983): 187-206; idem, Parts 2-3 “The Exegesis of Romans 5:12 among the Greek Fathers and Its Implications for the Doctrine of Original Sin: The 5th-12th Centuries,” Ibid. 29 (1985): 133-159, 231-257. As a general but more theological than scholarly exposition, s. J. Romanides, The Ancestral Sin. A comparative study of the sin of our ancestors Adam and Eve according to the paradigms and doctrines of the first- and second-century Church and the Augustinian formulation of original sin. Tr. G. S. Gabriel. Ridgewood, NJ: Zephyr Publishers, 1998; cf., for a larger theological perspective, a useful review of G. E. Demacopoulos and A. Papanikolaou, “Augustine and the Orthodox: the ‘West’ in the East,” in: G. E. Demacopoulos, A. Papanikolaou (eds.), Orthodox Readings of Augustine, Crestwood, NY: St. Vladimir’s Seminary Press, 2008, 11-40. The most important available study in the field is now, to my opinion, that of J.-Cl. Larchet, Maxime le Confesseur, médiateur entre l’Orient et l’Occident. Théologie et sciences religieuses. Cogitatio Fidei; Paris: Cerf, 1998, 77-124 (ch. II: La question de l’hérédité adamique).
 R. Draguet, Julien d’Halicarnasse et sa controverse avec Sévère d’Antioche sur l’incorruptibilité du corps du Christ. Universitatis Catholica Lovaniensis. Dissertationes ad gradum magistri in Facultate Theologica… ser. 2, 12; Louvain: Univ. Catholique de Louvain, 1924, 118-127. For the most up-to-date introduction, s. B. Lourié, “Julianism,” in: S. Uhlig (ed.), Encyclopaedia Aethiopica. Vol. 3. Wiesbaden: Harrassowitz Verl., 2007, 308-310.
 The texts of the Corpus Areopagiticum will be quoted according to the critical editions: B. R. Suchla, Corpus Dionysiacum I. Patristische Texte und Studien 33. Berlin: W. de Gruyter, 1990 (for De divinis nominibus = DN) and G. Heil, A. M. Ritter, Corpus Dionysiacum II. Patristische Texte und Studien 36. Berlin: W. de Gruyter, 1991 (all the rest), but the references will be given within the text as following: abbreviated title (DN, MT), chapter, paragraph, column and part of column (from A to D) in PG 3. English translation according to Rolt, Clarens Edwin. Dionysius the Areopagite: On the Divine Names and the Mystical Theology. London: SPCK, 1920; electronic edition at http://www.ccel.org/ccel/rolt/dionysius.html.
 Dionysius de divin[is] nom[inibus] toto fere cap. 4. docet, amorem erga creaturas impulisse deum, ut unicuique pro suo captu suae bonitatis participationem communicaret; D. R. de Montoya, Commentaria ac Disputationes in primam partem sancti Thoma. De voluntate dei, et propriis actibus eius, Lugduni: Iacobi, Andreae, & Matthaei Prost, 1630, 42.