Basil Lourié. The Notion of Number in the Triadology of Eastern Patristics. Vol. 1. No. 1. 2016

Publication Details

The Notion of Number in the Triadology of Eastern Patristics
Title in the language of publication: Понятие числа в триадологии восточной патристики
Basil Lourié
Doctor of Philosophy, Leading Research Fellow at the Institute of the National Research University Higher School of Economics, Campus in Perm.
Address: 38 Studencheskaya Ulitsa, Perm 614070, Russia.
P. 289–311.
Language: Russian
Document type: Research Article
 Acknowledgments:  The present study is a part of a larger project No. 16-18-10202, “History of the Logical and Philosophical Ideas in Byzantine Philosophy and Theology”, implemented with a financial support of the Russian Science Foundation.


A classification of the presently available logical interpretations of the Christian understanding of the triunity of God is proposed. There are four main types: (1) 3 = 3 (“trivializing” interpretation, where the unity is understood as one or other kind of collectivity, that is, not on the same reality level as each of the three: “Tritheism” of John Philoponus and all the modern “analytical” Triadologies put forward so far); (2) “3” = 1 (not the hypostases as beings existing per se but only their individualising features/relationes are real: Damian of Alexandria and the mainstream of the Latin scholasticism, including Thomism); (3) card(3) = 1 (the hypostases are real as three beings existing per se but infinite, whereas the unity of God is a kind of the common cardinality of these three different but ordered infinities: Duns Scotus’s line in the Latin scholasticism but also some earlier rationalising theologies, e. g., Babai the Great); 3 = 1 (true paradox and paraconsistent logic: the mainstream of the Byzantine theology since the 4th to the 15th cent.). The type (4) poses a problem of the very notion of number. It is obvious that this number is no longer natural (as in types (1) and (2)) nor consistent at all (as in type (3)). It is obvious that the notion of number implied in type (4) would be perfectly fitting with Poincaré’s intuitivist understanding of number but incompatible with the set-theoretical interpretations/definitions of number, because they imply the notion of pair. In the Byzantine Triadology, no pair is permissible: it implies such counting to three where two is skipped. Instead of the pair, this Triadology implies a triad, which is indissoluble to the elements, and where the logical addition operation, instead of the iteration of the ordinary (binary) exclusive disjunction, is a different connective called ternary exclusive OR, first described by Emil Post in 1941 and even now little known to the logicians. The number three implied in the Trinity is the minimal one in the series of such paraconsistent numbers. Some properties of these numbers are described, especially non-extensionality. 


analytical theology, paraconsistent logic, infinity, Triadology, non-extensionality, ternary exclusive OR, Evagrius Ponticus.


Benevitch G. I., Biryukov D. S., Choufrine A. M. (coll.) (2014) Prep. Maksim Ispovednik: Polemika s origenizmom i monoenergizmom [St. Maximus the Confessor: Polemics against Origenism and Monoenergism]. Second ed. St. Petersburg: Izd-vo Olega Abyshko (Biblioteka khristianskoi mysli; Vizantiiskaya filosofiya. T. 16 [The Library of Christian Thought; Byzantine Philosophy. Vol. 16]; Σμάραγδος φιλοκαλίας). (in Russian).

Bocheński J. M. (1989) “The Cracow Circle”. The Vienna Circle and the Lvov-Warsaw School (ed. by K. Szaniawski). Dordrecht: Kluwer Academic Publishers (Nijhoff International Philosophy Series. Vol. 38): 9–18.

Da Costa N., Béziau J.-Y. (2015) “Is God Paraconsistent?” [abstract]. Handbook of the 1st World Congress on Logic and Religion. João Pessoa, Abril 15, 2015 (ed. by R. S. Silvestre, J.-Y. Béziau). Brazil [s.l., s.d.]: 25.

Frankenberg W. (ed.) (1912) Euagrius Pontikus. Berlin: Weidmannsche Buchhandlung (Abhandlungen der könglichen Gesellschaft der Wissenschaften zu Göttingen. Philologisch-Historische Klasse, n.s. Bd. 13.2).

Gallay P. (ed.) (1978) Grégoire de Nazianze. Discours 27–31 (Discours théologiques). Paris: Éditions du Cerf (Sources chrétiennes. Vol. 250).

Geach P. T. (1972) Logic Matters. Oxford: B. Blackwell, 1972.

Guillaumont A. (1985) Les six centuries des Kephalaia Gnostica d’Évagre le Pontique. Édition critique de la version syriaque commune et édition d’une nouvelle version syriaque, intégrale, avec une double traduction française. Turnhout: Brepols (Patrologia orientalis. T. 28, f. I) (First publ. 1958).

Ivanov V. L. (2010) “Intensivnaya velichina sovershenstva: Beskonechnost’ kak sushchestvennoe ponyatie v teologii i filosofii Ioanna Dunsa Skota, OMB” [The Intensive Magnitude of Perfection: Infinity as an Essential Concept in Theology and Philosophy of John Duns Scotus, OFM]. Kosmos i dusha. Vyp. 2: Ucheniya o prirode i myshlenii v Antichnosti, Srednie veka i Novoe vremya [Cosmos and Soul. Issue 2: Doctrines of Nature and Thinking in Antiquity, Middle Age, and Early Modern Time] (ed. by P. P. Gaidenko, V. V. Petrov). Moscow: Progress-traditsiya: 379–431. (in Russian).

Konstantinovsky J. (2009) Evagrius Ponticus: The Making of a Gnostic. Farnham: Ashgate (Ashgate New critical thinking in religion, theology, and biblical studies).

Lapointe S. (2011) Bolzano’s Theoretical Philosophy: An Introduction. Hampshire, New York: Palgrave Macmillan (History of Analytical Philosophy).

Lourié B. (1992) «Vzaimosvyaz’ problemy Filioque s ucheniem o obozhenii u pravoslavnykh bogoslovov posle sv. Fotiya» [The Relationship between the Problem of Filioque and the Deification Doctrine in Orthodox Theologians after St. Photius]. Patrologiya. Filosofiya. Germenevtika [Patrology, Philosophy, Hermeneutic]. St. Petersburg: Predpriyatie obshchestvennoi organizatsii «Leningradskii soyuz uchenykh» — «Vysshaya religiozno-filosofskaya shkola» (Trudy Vysshei religiozno-filosofskoi shkoly. Vyp. 1 [Proceedings of the Higher School of Religion and Philosophy. Issue 1]): 1–19. (in Russian).

Lourié B. (2005) “Damian of Alexandria”. Encyclopaedia Aethiopica (ed. by S. Uhlig). Vol. II: D – Ha. Wiesbaden: Harrassowitz Verlag: 77–78.

Lourié B. (2006) Istoriya vizantiiskoi filosofii. Formativnyi period [The History of Byzantine Philosophy: The Formative Period]. St. Petersburg: Axiōma. (in Russian).

Lourié B. (2014) “The Philosophy of Dionysius the Areopagite: An Approach to Intensional Semantics”. Georgian Christian Thought and Its Cultural Context. Memorial Volume for the 125th Anniversary of Shalva Nutsubidze (1888–1969) (ed. by T. Nutsubidze, C. B. Horn, B. Lourié, A. Ostrovsky). Leiden; Boston: Brill (Texts and Studies in Eastern Christianity. Vol. 2): 81–127.

Lourié B. (2016a) “The Paraconsistent Numbers and the Set Theory Implied in the Cappadocian Trinitarian Doctrine”. Logiko-filosofskie shtudii. Т. 13. № 2 [Logical and philosophical studies. Vol. 13. No. 2]: 56–57.

Lourié B. (2016b) “Nicephorus Blemmydes on the Holy Trinity and the Paraconsistent Notion of Numbers: A Logical Analysis of a Byzantine Approach to the Filioque”. Studia Humana. Vol. 5. No. 1: 40–54.

Lourié B. (2016c) “Temporality and a Metric for Created Natures in Gregory of Nyssa. Toward two recent monographs on his concept of time”. Scrinium. Journal of Patrology, Critical Hagiography, and Ecclesiastical History. Vol. 12: 340–351.

Lourié B. (forthcoming) “The Trinity from Six Groups: a Logical Explication of Byzantine Triadology by Joseph Bryennios”.

Lur’e V. [Lourié B.] (1989) “L’attitude de S.Marc d’Ephèse aux débats sur la procession du Saint-Esprit à Florence. Ses fondements dans la théologie post-palamite”. Annuarium Historiae Conciliorum. Vol. 21: 317–333.

McCord Adams M. (2008) “The Metaphysics of the Trinity in Some Fourteenth Century Franciscans”. Franciscan Studies. Vol. 66: 101–168.

Mossay J. (ed.) (1980) Grégoire de Nazianze. Discours 20–23. Paris: Éditions du Cerf (Sources Chrétiennes. Vol. 270).

Pelletier F. J., Hartline A. (2008) “Ternary Exclusive Or”. Logic Journal of the IGPL. Vol. 16. No. 1: 75–83.

Poincaré H. (1902) “Du rôle de l’intuition et de la logique en mathématiques”. Compte-rendu du deuxième Congrès international des mathématiciens tenu à Paris du 6 au 12 août 1900. Paris: Gautier-Villars: 115–130.

Post E. L. (1941) The Two-Valued Iterative Systems of Mathematical Logic. Princeton: Princeton University Press.

Simons P. (1997) “Bolzano on Collections”. Grazer philosophische Studien. Vol. 53: 87–108.

Steel C. (2003) “Beyond the Principle of Contradiction? Proclus’ ‘Parmenides’ and the Origin of Negative Theology”. Die Logik des Transzendentalen. Festschrift für Jan A. Aertsen zum 65. Geburtstag (hg. v. M. Pickavé). Berlin; New York: Walter de Gruyter (Miscellanea Mediaevalia. Bd. 30): 581–599.

Tuggy D. (2016) “Trinity” (First published July 23, 2009; substantive revision March 18, 2016). The Stanford Encyclopedia of Philosophy (ed. by E. N. Zalta). Retrieved from

Vasiliev N. A. (1989) “Voobrazhaemaya (nearistoteleva) logika” [Imaginary (Non-Aristotelian) Logic]. Vasiliev N. A. Voobrazhaemaya logika. Izbrannye Trudy [Imaginary Logic. Selected Papers] (ed. by V. A. Smirnov). Moscow: Nauka, 1989: 53–94. (in Russian).

© Basil Lourié, 2016

(Русский) Василий Лурье. Идентичность человеческой личности по Иоанну Филопону: физическое тело в пространстве и человеческое тело по воскресении.

Sorry, this entry is only available in Russian.