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.


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© Basil Lourié, 2016

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