The Ways of Byzantine Philosophy Leontius of Byzantium and His... · The ways of Byzantine philosophy / Mikonja Knežević, editor. — Alham-bra, California : Sebastian Press, Western

The Ways of Byzantine Philosophy

The Ways of Byzantine Philosophy

Edited by Mikonja Knežević

Sebastian Press

Alhambra California

The ways of Byzantine philosophy Mikonja Knežević editor mdash Alham-

bra California Sebastian Press Western American Diocese of the Ser-

bian Orthodox Church Faculty of Philosophy Kosovska Mitrovica 2015

476 pages 23 cm

(Contemporary Christian thought series no 32)

ISBN 978-1-936773-25-1

1 PhilosophymdashByzantine Empire 2 Philosophy Ancient 3 Philosophy

Medieval 4 Christian philosophy 5 ChristianitymdashPhilosophy 6 Ortho-

dox Eastern ChurchmdashByzantine EmpiremdashDoctrinesmdashHistory 7 Ortho-

dox Eastern ChurchmdashTheology 8 Philosophy and religionmdashByzantine

Empire 9 TheologiansmdashByzantine Empire 10 Christian saintsmdashByzan-

tine EmpiremdashPhilosophy 11 Byzantine empiremdashChurch history 12

Byzantine empiremdashCivilization I Knežević Mikonja 1978ndash II Series

ContentsGeorgi Kapriev

Philosophy in Byzantium and Byzantine Philosophy 1

Dušan KrcunovićHexaemeral Anthropology of St Gregory of NyssaldquoUnarmed Manrdquo (ἄοπλος ὁ ἄνθρωπος) 9

Torstein Theodor TollefsenSt Gregory the Theologian on Divine Energeiain Trinitarian Generation 25

Ilaria L E RamelliProclus and Christian Neoplatonism Two Case Studies 37

Dmitry BirjukovHierarchies of Beings in the Patristic ThoughtGregory of Nyssa and Dionysius the Areopagite 71

Johannes ZachhuberChristology after Chalcedon and the Transformationof the Philosophical Tradition Reflections on a neglected topic 89

Joseacute Mariacutea NievaAnthropology of Conversion in Dionysius the Areopagite 111

Filip IvanovićEros as a Divine Name in Dionysius the Areopagite 123

Basil LourieacuteLeontius of Byzantium and His ldquoTheory of Graphsrdquoagainst John Philoponus 143

i

Vladimir CvetkovićThe Transformation of Neoplatonic PhilosophicalNotions of Procession (proodos) and Conversion (epistrophe)in the Thought of St Maximus the Confessor 171

Gorazd KocijančičMystagogy ndash Today 185

Uroš T TodorovićTranscendental Byzantine Body Reading Dionysiusthe Pseudo-Areopagite Gregory of Nyssa and Plotinusin the Unfolded Marble Panels of Hagia Sophia 197

Slobodan ŽunjićJohn Damascenersquos ldquoDialecticrdquo as a Bondbetween Philosophical Tradition and Theology 227

Scott AblesJohn of Damascus on Genus and Species 271

Ivan ChristovNeoplatonic Elements in the Writings of Patriarch Photius 289

Smilen MarkovldquoRelationrdquo as Marker of Historicity in Byzantine Philosophy 311

Nicholas LoudovikosThe Neoplatonic Root of Angst and the Theology of the RealOn Being Existence and Contemplation Plotinus ndash Aquinas ndash Palamas 325

Dmitry MakarovThe First Origin Thinking and Memory in the Byzantine Philosophyof the Late Thirteenth and Early Fourteenth CenturiesSome Historico-Philosophical Observations 341

Ioannis PolemisManuel II Palaiologos between Gregory Palamas and Thomas Aquinas 353

ii

Constantinos AthanasopoulosDemonstration (ἀπόδειξις) and its Problems for St Gregory PalamasSome Neglected Aristotelian Aspects of St Gregory PalamasrsquoPhilosophy and Theology 361

Mikonja KneževićAuthority and Tradition The Case of Dionysius Pseudo-Areopagitein the Writing ldquoOn Divine Unity and Distinctionrdquo by Gregory Palamas 375

Milan ĐorđevićNicholas Cabasilas and His Sacramental Synthesis 391

Panagiotis Ch AthanasopoulosScholarios vs Pletho on Philosophy vs Myth 401

George ArabatzisByzantine Thinking and Iconicity Post-structural Optics 429

iii

Leontius of Byzantium and His ldquoTheoryof Graphsrdquo against John Philoponus

Basil Lourieacute

1 IntroductionWho1 was the prototype of the Acephalus in the Solutio argumentorum a

Severo objectorum (CPG 6815) [thereafter Solutio] by Leontius of Byzantium2

Some early scholars believed that it was Severus of Antioch in person3Even Aloys Grillmeier continued ndash probably after Brian E Daley4 ndash to say that1 The article was written with the support of the Russian Foundation for Basic Research pro-

ject Nr 13ndash33ndash01026 ldquoThe Function of Concept of ForcePossibility in Aristotlersquos NaturalPhilosophyrdquo I would like to express my gratitude to Dmitry Birjukov for his continuoushelp and fruitful discussion of related topics and to Dirk Krausmuumlller ndash for both discussionson Leontius of Byzantium and improving my translations into English from Greek

2 The works of Leontius will be quoted according to the unpublished PhD thesis by Brian EDaley Leontius of Byzantium A Critical Edition of His Works with Prolegomena Oxford Univer-sity 1978 [thereafter B Daley Leontius] (with page numbers only) but providing as well thereferences to the columns of PG 86

3 Friedrich Loofs evaluated Severusrsquo authorship of a hypothetical polemical work answeredby Leontius in the Solutio as only ldquowahrscheinlichrdquo F Loofs Leontius von Byzanz und diegleichnamigen Schriftsteller der griechischen Kirche 1 Buch Das Leben und die polemischen Wer-ke des Leontius von Byzanz TU III 1ndash2 Leipzig J C Hinrichsrsquosche Buchhandlung 1887 35However Johannes Peter Junglas without further argumentation was going as far as con-sidering the Leontiusrsquo work as the only remaining source of the text of the lost Severusrsquopolemical work whose existence to Junglas was no longer hypothetical but quite certainldquoDemnach hatte Leontius eine polemische Schrift Severs als Vorlage seiner Arbeit Die vonLeontius in der Epilysis vorgebrachten ἀπορίαι Severs sind bez ihrer Richtigkeit kontrollier-bar an uns noch erhaltenen Fragmenten Seversrdquo J P Junglas Leontius von Byzanz Studienzu seinen Schriften Quellen und Anschauungen Forschungen zur Christlichen Literatur- undDogmengeschichte Bd 7 H 3 Paderborn F Schoumlningh 1908 3ndash4 here 3)

4 Brian E Daley without mentioning Richardrsquos criticisms (see below n 6) continued to in-sist on the existence of a lost Severusrsquo work behind Leontiusrsquo polemics ldquoAlthough thereis no mention of Severus in the body of the text the title identifies him as the source ofobjections if this is true the most likely date for the workrsquos composition would be the timewhen both Severus and Leontius were in Constantinople between the winter of 535 andMarch 536rdquo B Daley Leontius xxxiii Thus Daley tried to treat the title Ἐπιλύσεις τῶν ὑπὸΣευήρου προβεβλημένων συλλογισμῶν in the most literalistic way even though he himselfwas realising that this is not the unique option Even Richard Cross calls the Acephalus ldquoaplaceholder for Severus as the full title of the work suggestsrdquo R Cross ldquoIndividual Naturesin the Christology of Leontius of Byzantiumrdquo Journal of Early Christian Studies 10 (2002) 245ndash

143

Basil Lourieacuteldquothe headless onerdquo of the Solutio ldquoreally speaks for Severusrdquo5 It is not the casehowever As Marcel Richard has shown the Acephalus is a collective imageof Severianist critics of Leontiusrsquo previous work Contra Nestorianos et Eutychi-anos (CPG 6813) [= CNE]6 Marcel Richard believed that Leontiusrsquo audience washere neo-Chalcedonian rather than properly Severianist ldquoLeacuteonce ne nousdit pas en effet qursquoil a eacuteteacute repris par les monophysites mais que beaucoupde gens ont trouveacute son systegraveme peu efficace contre le monophysisme et luiont reprocheacute drsquoavoir neacutegligeacute certaines objections de ces heacutereacutetiques rdquo thenRichard concluded that Leontiusrsquo interlocutor is ldquoun neacuteo-chalceacutedonienrdquo7

I for one once proposed to identify the Acephalus with John Philoponus(regardless of whether Philoponus did criticize CNE or not) ndash however withno proper explanation of historical circumstances and without appropriatereservations8 I was then sharing Michel van Esbroeckrsquos conviction that theDe Sectis (CPG 6823) with its polemics against Philoponus is a work by Leontiusof Byzantium and is to be dated to the period from 543 to 5519 However nowI am convinced by Uwe Langrsquos criticism of van Esbroeckrsquos analysis and rees-tablishment of the traditional for the twentieth-century scholarship dateof the De Sectis between 580 and 608 which precludes its attribution to Le-ontius of Byzantium10 Therefore after having excluded the De Sectis from

365 here 254 This remark in Crossrsquo mouth is especially odd because Cross himself providesa long note (255 n 29) dealing with difference between Acephalusrsquo and Severusrsquo positionsand then calls Acephalus ldquothe [fictitious] Severan opponent of Leontiusrdquo (259 squarebrackets by Cross)

5 A Grillmeier with Th Hainthaler Christ in Christian Tradition vol 22 The Church of Con-stantinople in the Sixth Century tr P Allen J Cawte London Mowbray Louisville KY West-minster John Knox Press 1995 [original publ 1989] 193

6 Thus Marcel Richard in his decisive criticisms of Loofsrsquo argumentation ldquoContre cette hy-pothegravese nous pouvons alleacuteguer le fait que Leacuteonce srsquoadresse toujours agrave ses adversaires aupluriel (col 1916C 1937A)rdquo moreover Richard put forward chronological reasons againstthe very possibility of a direct polemic against Severus by Leontius M Richard ldquoLeacuteoncede Byzance eacutetait-il origeacuteniste rdquo Revue des eacutetudes byzantines 5 (1947) 31ndash66 (repr idem Operaminora t 2 Turnhout Brepols 1976 Nr 57) here 58 esp n 2

7 M Richard ldquoLeacuteoncehelliprdquo 58ndash59 here 588 В М Лурье при участии В А Баранова История византийской философии Форматив-

ный период [B Lourieacute with a participation of V Baranov The History of the ByzantinePhilosophy The Formative Period] St Petersburg Axioma 2006 [thereafter IVF] 334ndash348a Serbian translation available В Лурjе уз сарадњу В А Баранова Историja византиj-ске философиjе Формативни период Превела с руског Jелена Капустина СремскиКарловци Нови Сад Издавачка књижарница Зорана Стоjaновића 2010

9 M van Esbroeck ldquoLe lsquoDe Sectisrsquo attribueacute agrave Leacuteonce de Byzance (CPG 6823) dans la versiongeacuteorgienne drsquoArsegravene Iqaltoelirdquo Bedi Kartlisa 42 (1984) 35ndash42 and idem ldquoLa date et lrsquoauteurdu lsquoDe Sectisrsquo attribueacute agrave Leacuteonce de Byzancerdquo in C Laga J A Munitiz L Van Rompay edsAfter Chalcedon Studies in Theology and Church History offered to Professor Albert Van Roey for HisSeventieth Birthday Orientalia Lovaniensia Analecta 18 Leuven Peeters 1985 415ndash424

10 U M Lang ldquoThe Date of the Treatise lsquoDe Sectisrsquo Revisitedrdquo Orientalia Lovaniensia Periodica 29(1998) 89ndash98 The most convincing part of Langrsquos argumentation is to my opinion chrono-logy of publication of Philoponusrsquo ldquotritheisticrdquo works criticized in the De Sectis I am unawareof van Esbroeckrsquos reaction to this paper

144

Leontius of Byzantium and His ldquoTheory of Graphsrdquo against John Philoponusconsideration we have no direct evidence for any discussion between Leon-tius of Byzantium and John Philoponus This is not to say however that sucha discussion did not take place Moreover we still have a witness preservedby Germanos of Constantinople (early eighth century) that it was Leontiuswho answered Philoponus in defence of the Council of Chalcedon Germanoshowever means the whole work of Leontius rather than any specific treat-ise11 Germanosrsquo source is unknown

Thus the question about possible direct polemics between Philoponusand Leontius could be reopened I have nothing to object against Richardrsquosconclusion that Leontius aimed at a (neo-)Chalcedonian audience but mypoint is that this audience was especially alarmed by John Philoponusrsquo unify-ing idea which has been proposed on the eve of the Constantinopolitan Coun-cil of 553 In this sense the prototype of the Acephalus is John Philoponus asthe author of the Arbiter

2 The Solutio Problems of DatingFrom the text of the Solutio we know that it is a continuation of a previ-

ous work by Leontiusrsquo CNE (p 773ndash15 1916C) However the general chrono-logy of Leontiusrsquo works ndash and his life as well ndash is not very precise It heavilydepends on our presuppositions concerning his identity with other person-alities bearing the same name I will try to avoid here using any suppositionsgoing beyond the texts Thus we can follow the ldquocommon opinionrdquo that CNEis datable to either the 530s12 or early 540s (not later than 543) that is beforethe Justinianrsquos decree against the ldquoThree Chaptersrdquo (543 or early 544)13 This11 Germanos of Constantinople in the De haeresibus et synodis (CPG 8020) ch 33 says that Philo-

ponus μᾶλλον δὲ Ματαιόπονος ldquostruggled against the Councilrdquo (κατὰ τῆς συνόδου ἠγωνί-ζετο) and ldquoalmost agreed with Origen in his teaching about resurrectionrdquo (μικροῦ καὶ τῷὨριγένει συμπνέων εἰς τοὺς περὶ ἀναστάσεως λόγους) Leontius however ldquo[hellip] composed avery appropriable book defending this Council and has written down in it many witnessesof the notion of duality [sc of the natures in Christ] and this is why this book is calledthe Leontiardquo (Λεόντιος δὲ ὁ τῆς ἑρήμου μόναχος βιβλίον συνέθηκεν εὐαπόδεκτον ὑπὲρ τῆςτοιαύτης συνόδου ἐνιστάμενος πολλὰς δὲ μαρτυρίας ἐν αὐτῷ καταγράψας περὶ τῆς διϊκῆςφωνῆς ὅθεν καὶ Λεόντια τὸ βιβλίον ἐκ τούτου ἐκλήθη) (PG 98 69Cndash72A) I proposed a recon-struction of Philoponusrsquo teaching on the resurrection in B Lourieacute ldquoJohn Philoponus on theBodily Resurrectionrdquo Scrinium 9 (2013) 91ndash100 an enlarged Russian translation В М Лу-рье ldquoИдентичность человеческой личности по Иоанну Филопону физическое тело впространстве и человеческое тело по воскресении [The Identity of the Human Personal-ity according to John Philoponus the Physical Body in the Space and the Human Body afterthe Resurrection]rdquo Εἶναι Проблемы Философии и Теологии 1 1 (2012) 307ndash339 the relevantpages of IVF (243ndash248) contain my earlier erroneous views

12 Thus Daley and almost the whole previous scholarship although with important exceptions(see the next note) ldquo[hellip] its [CNErsquos] content seems to belong best in the heated theologicalatmosphere of the 530srdquo B Daley Leontius xxxiindashxxxiii here xxxiii

13 Marcel Richard opts for the exact date just before the decree against the ldquoThree Chaptersrdquo543 M Richard ldquoLeacuteoncehelliprdquo 50ndash53 et passim whereas David Evans accepts the interval from540 to 543 D B Evans Leontius of Byzantium An Origenist Christology Dumbarton Oaks Stud-ies 13 Washington DC Dumbarton Oaks Center for Byzantine studies 1970 2ndash3

145

Basil Lourieacutedating ldquoprior to 544rdquo seems to me results from the text of CNE without anyparticular assumption concerning the identity of Leontius However dealingwith the Solutio we have nothing except this terminus post quem A priori it isunclear whether Leontius wrote his Solutio soon after publication of CNE orthat he revisited his polemics after having several years spent

Thus for the Solutio our main terminus ante quem is the date of the deathof Leontius ndash which is unfortunately unknown Anyway it is within thelimits of probability that he was still alive and active at least for about onedecade beyond the early 540s that is up to the time of the Second Council ofConstantinople (553) This decade is to be defined as the most probable timeof composition of the Solutio

3 The Polemical ContextThe author of the Solutio needs to explain throughout the whole of his

treatise why the ldquoone composite hypostasisrdquo of the Chalcedonians does notmean the same as the ldquoone composite naturerdquo of the anti-ChalcedoniansThis eternal polemical motive between the partisans and the adversaries ofthe Council of Chalcedon is interpreted in this work of Leontius ndash not in CNE ndashquite unusually Leontius tries to explain the difference between the notionsof hypostasis and particular nature because he does admit from the very be-ginning that the humanity of Christ is not a general nature but a particularone This is neither the common opinion of the Chalcedonian authors nor Le-ontiusrsquo own attitude in CNE This feature of the Solutio passed scarcely noticedby the patristic scholars with a unique and important exception of RichardCross14 At least nobody realised here the fact of a radical deviation from theChalcedonian tradition already established in the epoch of Leontius and be-ing perpetuated by Maximus the Confessor and the Christological doctrinesof the defenders of the holy icons in the ninth century

From the early sixth century and then again from the early ninth cen-tury onwards we see Chalcedonian Orthodoxy insisting that the Logos be-came incarnated in the common nature of humankind This was certainlytaken to be the consensus patrum already in the eighth century because in

14 See R Cross ldquoIndividual Natureshelliprdquo Before him this fact had been first noticed ndash but leftwithout any substantial analysis ndash by M Richard ldquoLeacuteonce de Jeacuterusalem et Leacuteonce de Byz-ancerdquo Meacutelanges de science reacuteligieuse 1 (1944) 35ndash88 here 60ndash61 repr in idem Opera minorat 3 Turnhout Brepols 1977 Nr 59] and then was briefly analysed by A Grillmeier Christin Christian Tradition vol 22 189ndash193 but see Crossrsquo criticism of the latter (R Cross ldquoIn-dividual Natureshelliprdquo 246ndash247) which I consider quite justified (not to say that the wholecontext of this later Leontiusrsquo Christology needs to be studied in the context of Philoponusand Eutychius of Constantinople see below) Brian Daley has tried to show that even inCNE Leontius held the same opinion about the nature of Christ as in the Solutio (B Daley ldquolsquoARicher Unionrsquo Leontius of Byzantium and the Relationship of Human and Divine in ChristrdquoStudia Patristica 24 (1993) 239ndash265 here 248ndash252) but his argumentation is convincingly cri-ticised by R Cross ldquoIndividual Natureshelliprdquo 248ndash250 cf also my analysis in the next section

146

Leontius of Byzantium and His ldquoTheory of Graphsrdquo against John Philoponusthe early ninth century we see this postulate as the common ground of bothiconoclastic and anti-iconoclastic theologies Moreover we see the same ideaalready in Maximus the Confessor in the seventh century However in gen-eral the situation in the sixth and seventh centuries was different and notwithout the participation of Leontius of Byzantium15

Near 519 we see Severus of Antioch writing against a Chalcedonian Ser-gius the Grammarian (Contra impium Grammaticum)16 Sergius in his polem-ical work in defence of the Council of Chalcedon (written in the 510s nowavailable through Severusrsquo quotation only) mentioned that the Logos was in-carnated into the common nature of humankind This point becomes a sub-ject of a long refutation on the part of Severus ndash although still somewhereon the margin of the polemic Severusrsquo point was a reductio ad absurdum ifthe humanity of the Christ is the common nature of the whole humankindthen the Logos is incarnated not into a particular human Jesus but intoeverybody17

Unfortunately we donrsquot know whether this refutation by Severus was inturn addressed by somebody from the Chalcedonian camp In the middleof the same (sixth) century we see however that the contrary opinion isshared by such Chalcedonians as our Leontius and patriarch Eutychius ofConstantinople (552ndash565 577ndash582 one of the key theological figures of thisepoch)18

There was an established tradition going back to the understanding ofldquoparticular naturerdquo in the Isagoge of Porphyry of equating this term with theChristian notion of hypostasis19 Richard Cross in his very valuable articleon Leontius argues that there was as well another tradition represented at15 For an outline of the relevant doctrines see IVF16 P Allen C T R Hayward Severus of Antioch London New York Routledge 2004 44ndash4617 I Lebon Severi Antiocheni Liber contra impium Grammaticum Oratio prima et secunda CSCO

vols 111ndash112 Scr Syri tt 58ndash59 (Ser IV t IV) Paris E typographeo republicae 1938 166ndash172130ndash134 (txttr) The title of the corresponding chapter II 18 ldquoInvestigatio confu-tationis clare significans hanc assertionem lsquoChristus est in duabus substantiis secundumcommune substantiae significationem ܒܫܘܘܕܥܐ) ܓܘܢܝܐ rsquo(ܕܐܘܣܝܐ ad stultissimam duce-re blasphemiam scilicet ad id quod sancta Trinitas toti humanitatis generi incarnata cen-seaturrdquo (166130) The next two chapters (II 19ndash20) are dedicated to the same topic (ibid172ndash179134ndash139) Insisting that in Christ there is neither human nature nor hypostasisSeverus avoids any precising of his own understanding of the notion of particular nature

18 For Eutychus of Constantinople in his historical context especially his dependency on theo-logical views of Philopon see B Lourieacute ldquoUn autre monotheacutelisme le cas de ConstantindrsquoApameacutee au VIe Concile Œcumeacuteniquerdquo Studia Patristica 29 (1997) 290ndash303 idem ldquoLe secondiconoclasme en recherche de la vraie doctrinerdquo Studia Patristica 34 (2000) 145ndash169 and IVFpassim but esp 261ndash267

19 Cf IVF passim but esp 524ndash525 where I mention the recent discussion between J-Cl Lar-chet and D Bathrellos which seems to me now finished with the review of Bathrellosrsquo mono-graph The Byzantine Christ Person Nature and Will in the Christology of Saint Maxim the ConfessorOxford 2004 by Larchet Revue drsquohistoire eccleacutesiastique 101102 (2006) 182ndash185 359 see herethe further bibliography Bathrellosrsquo idea that according to Maximus the Confessor thehuman nature of Christ is allegedly a particular one is disproved by Larchet as well as bythe evidence referred to in IVF

147

Basil Lourieacuteleast by John of Damascus and Leontius in the Solutio assuming the exist-ence of ldquoindividual naturesrdquo Cross coined the latter term himself referringto John of Damascusrsquo and Leontiusrsquo definitions of the natures ἐν ἀτόμῳ20

Cross proposes a distinction between the ldquoparticular naturesrdquo (φύσεις με-ρικαί) ndash which indeed do not exist according to the Chalcedonians includ-ing both John of Damascus and Leontius ndash and ldquoindividual naturesrdquo whichare not the same thing as the hypostases and which do really exist ndash at leastaccording to John and Leontius in the Solutio The ldquoparticular naturesrdquo areproduced as an abstraction from the hypostases when their individual char-acteristics are taken off whereas the ldquoindividual naturesrdquo preserve their in-dividual characteristics without being identical to the hypostases

I have to note that Crossrsquo explanation is hardly acceptable even for Johnof Damascus it is normally held that Johnrsquos ldquoindividual naturesrdquo are an-other term for the hypostases and so far there is hardly one other scholarwho would follow Crossrsquo understanding Moreover Crossrsquo interpretation ofthis term in John of Damascus remained unknown to the later generationsof Chalcedonian theologians including Nicephorus of Constantinople andTheodore the Studite who were dealing with the problem of the humanityof Christ And a further question remains namely why it is not a hypostasisif it contains hypostatic characteristics of a human person Jesus21 This isa powerful argument to assume that Crossrsquo interpretation was unknown toJohn of Damascus himself as well

Anyway in the interpretation of Leontiusrsquo Solutio Cross (and those beforehim) overlooked the very key moment In my opinion Leontius in the Solutioconceded to his Severianist adversary in the acknowledgement of the ldquopar-ticular naturesrdquo but gave this notion a very specific interpretation

4 A New Understanding of ldquo(Particular) NaturerdquoFrom the very beginning of the dialogue Leontiusrsquo alter ego the Ortho-

dox acknowledges that the human nature in Christ is a particular natureThe dialogue starts with the following ldquoobjection of the Acephalusrdquo ldquoThehuman nature which the Logos received was it that which is considered inthe species or in an individualrdquo (ch 1 p 7716ndash17 1916Dndash1917A ἈντίθεσιςἈκεφάλου Φύσιν ὁ Λόγος ἀναλαβὼν ἀνθρωπίνην τὴν ἐν τῷ εἴδει θεωρου-μένην ἢ τὴν ἐν ἀτόμῳ ἀνέλαβεν)

The Orthodox at first asks whether there is a difference between thesetwo kinds of natures (7718ndash19 1917A) The Acephalus answers that indeedthere is a difference one is considered in a plurality whereas another in the20 R Cross ldquoIndividual Natureshelliprdquo 251ndash265 cf his earlier paper idem ldquoPerichoresis Dei-

fication and Christological Predication in John of Damascusrdquo Mediaeval Studies 62 (2000)69ndash124

21 For a detailed review of these ninth-century doctrines on hypostasis as well as their sixth-century forerunner Eulogius of Alexandria see B Lourieacute ldquoLe second iconoclasmehelliprdquo

148

Leontius of Byzantium and His ldquoTheory of Graphsrdquo against John Philoponusunique numberrdquo (7720 1917A [hellip] ἡ μὲν ἐν πλήθει θεωρεῖται ἡ δὲ ἐν ἐνὶτῷ ἀριθμῷ) The Orthodox tries to explain that in both cases the nature isthe same regardless of whether it is considered in a unique individual or in aplurality (7711ndash785 1917AB) ndash in the same manner as the same white colour(ἡ λευκότης) could be considered in either a unique instance or in a pluralityof objects (εἴτε ἓν εἴτε πλείονα) (7721ndash27 1917A)

The Acephalus however needs to obtain an unequivocal answer ldquoThus[Christ] received a particular nature (Τὴν τινὰ οὖν ἀνέλαβε φύσιν)rdquo ndash ldquoYesbut one that is the same as the species (Ναὶ ἀλλὰ τὴν αὐτὴν οὖσαν τῷ εἴδει)rdquoanswers the Orthodox This answer allows to the Acephalus to pose his mainquestion ldquoBut what is the difference between this and the hypostasis (Τίδὲ παρὰ ταύτην ἡ ὑπόστασις)rdquo (786ndash8 1917B) The whole treatise then turnsout to be the answer of the Orthodox

Let us recall what we would have been prepared to hear from the Leontiusknown to us from CNE ldquothere could be no nature that is essence without ahypostasisrdquo a hypostasis is a nature but not vice versa a nature is not a hypo-stasis ldquothe nature has meaning of being whereas the hypostasis has also thatof separate being the former has the meaning of species whereas the latterreveals the particular [hellip] The definition of the hypostasis is either what isthe same according to nature but different according to number or what iscomposed of different natures but has the communion of being together andin each otherrdquo22

Briefly we could expect from Leontius the answer that the hypostasisproduces a difference in number that is the difference of physical objectswhereas the nature does not produce such a difference The real answer ofLeontius is somewhat strange ldquo[The hypostasis differs from the particularnature in that] the participation in it produces a different [object] and not adifference (Ὅτι τὸ μετέχειν αὐτῆς ἄλλον ποιεῖ οὐκ ἀλλοῖον)rdquo (789 1917B)Acephalusrsquo first reaction is to check whether the Orthodox changed the tra-ditional definition of the hypostasis ndash but he did not Instead the Orthodoxbasically confirmed Acephalusrsquo understanding of the hypostasis applied tothe humanity of Christ (in Acephalusrsquo wording that ldquothe humanity of Christis separated from the common [humanity] with the differentiating charac-teristicsrdquo23)

If the traditional understanding of hypostasis as a particular being re-mains unchallenged then according to the Acephalus his opponent has to

22 Ἀνυπόστατος μὲν οὖν φύσις τουτέστιν οὐσία οὐκ ἂν εἴη ποτέ οὐ μὴν ἡ φύσις ὑπόστασις ὅτιμηδὲ ἀντιστρέφει Ἡ μὲν γὰρ ὑπόστασις καὶ φύσις ἡ δὲ φύσις οὐκέτι καὶ ὑπόστασις ἡ μὲνγὰρ φύσις τὸν τοῦ εἶναι λόγον ἐπιδέχεται ἡ δὲ ὑπόστασις καὶ τὸν τοῦ καθrsquo ἑαυτὸ εἶναι καὶἡ μὲν εἴδους λόγον ἐπέχει ἡ δὲ τοῦ τινός ἐστι δηλωτική [hellip] ὑποστάσεως δὲ ὅρος ἢ τὰ κατὰτὴν φύσιν μὲν ταὐτὰ ἀριθμῷ δὲ διαφέροντα ἢ τὰ ἐκ διαφόρων φύσεων συνεστῶτα τὴν δὲτοῦ εἶναι κοινωνίαν ἅμα τε καὶ ἐν ἀλλήλοις κεκτημένα [hellip] (CNE I 1 93ndash14 1280AB)

23 Οὐκ ἦν οὖν τοῖς ἀφοριστικοῖς ἰδιώμασιν ἡ τοῦ Χριστοῦ ἀνθρωπότης τοῦ κοινοῦ τὸ ἴδιοναὐτοῦ χωρίζουσα (7813ndash14 1917C) cf 7815ndash26 1917CD

149

Basil Lourieacuteacknowledge that the particular nature shares with the hypostasis its mostobvious feature namely the producing of numerical difference Thus heasks (this question opens ch 2 of the Solutio) ldquoBut do you really say that al-though the hypostasis reveals the divided and self-standing the number andespecially the number two means something different from that Becauseany number (consists) in the quantity and only the one is non-quantitativeHowever even if to the one (belongs) the non-quantitativity and because ofthis it is individual to the two and any other number (belong) the quantityand the divisibilityrdquo24

Leontius as we know him from CNE would have nothing to object Indeedin CNE I4 he said

One can discover that things of different species join in relationshipswith things of the same species in varying ways for in respects inwhich things of like species are joined with things of different spe-cies they differ towards each other and in the respects in which theydiffer from things of different species they are joined to each otherFor they are distinguished from each other but joined to things ofother species by number and they are joined to each other but distin-guished from things of other species by definition (τῷ μὲν γὰρ ἀριθμῷπρὸς ἑαυτὰ διακρινόμενα τοῖς ἑτεροειδέσι συνάπτεται τῷ δὲ ὅρῳ πρὸςἑαυτὰ συναπτόμενα τῶν ἑτεροειδῶν διακέκριται) (1425ndash154 1285Dndash1288A)25

Thus Leontius (ldquothe Orthodoxrdquo) would have to choose between only twokinds of distinction ldquoby numberrdquo and ldquoby definitionrdquo The former is applic-able to the hypostases the latter to the natures If the human individualityof Jesus was different ldquoby numberrdquo from other human hypostases then hishumanity is a separate hypostasis and this regardless of the Chalcedoniansrsquoefforts to cover their crypto-Nestorianism If it is different only ldquoby defini-tionrdquo then one has to acknowledge that the humanity of Christ is a separateparticular nature ndash which further would be easy to present as a constitutivecomponent of the composite μία φύσις τοῦ Θεοῦ Λόγου σεσαρκομένη in aSeverianist sense Both Leontius and his opponent would not allow any φύσιςἀνυπόστατος (ldquoa nature without hypostasisrdquo) the particular nature of Jesusrsquohumanity would be confined together with the nature of divinity within thehypostasis of the Logos

The real amplitude of problem could be realised from the further Chris-tological discussions in Byzantium starting from the Christological contents

24 Ἀλλrsquo ἐκεῖνο οὐκ ἂν εἴποις ὡς ἡ μὲν ὑπόστασις τὸ διῃρημένον καὶ καθrsquo ἑαυτὸ ὑπάρχον δηλοῖὁ δὲ ἀριθμὸς καὶ μάλιστα τῆς δυάδος ἄλλο τι παρὰ τοῦτο σημαίνει Πᾶς γὰρ ἀριθμὸς ἐνποσότητι μονὰς δὲ μόνη ἄποσον εἰ δὲ τῆς μονάδος τὸ ἄποσον καὶ διὰ τοῦτο ἄτομον δυάδοςἄρα καὶ παντὸς ἀριθμοῦ τὸ ποσὸν καὶ διῃρημένον (7827ndash31 1917Dndash1920A)

25 B Daleyrsquos tr ldquolsquoA Richer Unionrsquohelliprdquo 251 Italics by Daley

150

Leontius of Byzantium and His ldquoTheory of Graphsrdquo against John Philoponusof the second quarrel on the holy icons in the ninth century onwards26 Thesimultaneous application of the two conditions ndash the presence of the hypo-static characteristics of Jesus in the humanity of Christ together with theabsence of any human hypostasis in this humanity ndash turned out to be logic-ally paraconsistent as Eulogius of Alexandria (late sixth century) warned inadvance at the beginning of the discussion when it was only one hundredyears old This is one of the key problems of the Orthodox dogmatics wherethe Fathers had recourse to the paraconsistent logic (as it had been calledsince the 1970s a logic which does not avoid the contradictions but relies onthem)27 Leontius of Byzantium remained outside of this non-classical main-stream of patristic logical thought in Christology His personal contributionalthough unaccepted by further tradition and never going beyond classicallogic is nevertheless most interesting from the viewpoint of the history ofboth mathematics and cognitive science

Leontius (ldquothe Orthodoxrdquo) surprises his opponent with an idea that hasnever been heard before or after him28 namely there is a third kind of dis-tinction or more precisely the second kind of distinction ldquoby numberrdquo

5 The Second Kind of Numerical Distinction ldquoby Relationrdquo (ἐν σχέσει)Now we arrived to the moment when we have to read carefully the part

of Leontiusrsquo text (Solutio 2) which is mostly overlooked by the scholars And Imust apologize for such a long quotation from a monologue of the Orthodox(791ndash23 1920BC)Οὐκοῦν ἐπειδὴ ἀριθμοῦ καὶ τῶν περὶ Surely then if you have recalled the num-αὐτὸν ἰδιωμάτων ἐμνήσθης ἀναγκα- ber and its features it is necessary to sayῖον ἐκεῖνο εἰπεῖν ὡς ἀριθμὸς διττὸς that ldquonumberrdquo could be said in two meaningsλέγεται ὁ μέν τις ἁπλῶς καὶ καθrsquo ἑαυ- One meaning is somewhat simple and per seτὸν ὁ δὲ ἐν σχέσει καὶ πράγμασι θε- whereas another is considered in relationship

26 See eg B Lourieacute ldquoLe second iconoclasmehelliprdquo idem ldquoUne dispute sans justes Leacuteon de Chal-ceacutedoine Eustrate de Niceacutee et la troisiegraveme querelle sur les images sacreacuteesrdquo Studia Patristica 42(2006) 321ndash339 idem ldquoMichel Psellos contre Maxime le Confesseur lrsquoorigine de lrsquo lsquoheacutereacutesiedes physeacutetheacutesitesrsquordquo Scrinium 4 (2008) 201ndash227

27 There is so far no comprehensive introduction to the paraconsistent logics in the FathersAs a first sketch one can see B Lourieacute ldquoThe Philosophy of Dionysius the Areopagite AnApproach to Intensional Semanticsrdquo in T Nutsubidze C B Horn B Lourieacute with the Col-laboration of A Ostrovsky Georgian Christian Thought and Its Cultural Context Memorial Volumefor the 125th Anniversary of Shalva Nutsubidze (1888ndash1969) Texts and Studies in Eastern Chris-tianity 2 Leiden Boston Brill 2014 81ndash127 The paraconsistent logical constructions wereformed from the classical ldquoblocksrdquo in the same manner as in the Quantum physics the non-classical phenomena are described in classical terms used according to Niels Bohrrsquos ldquocor-respondence principlerdquo Thus even a correct study of these ldquoblocksrdquo taken alone that isregardless of the theological intuition they serve to express would not allow one to graspthe paraconsistent way of thinking

28 It could be likely that the same idea was implied by Eutychius of Constantinople but ourdata are too scarce to judge cf B Lourieacute ldquoUn autre monotheacutelismehelliprdquo

151

Basil Lourieacuteωρούμενος ὥσπερ λευκὸν ἥ τε λευ- and in things ndash in the same manner as ldquowhiterdquoκότης καὶ τὸ λευκασμένον Αὐτὴ τοί- is said about either the white paint or a thingνυν ἡ φύσις τοῦ ἀριθμοῦ καθrsquo ἑαυ- painted white Thus the nature of number it-τὴν οὔτε συνάπτει οὔτε διαιρεῖ οὐδὲ self is per se neither joining nor dividing be-γὰρ ἔχει ὑποκείμενα πράγματα ἀλλrsquo cause it does not contain real things as sub-ὥσπερ τὸ ἄνω καὶ τὸ κάτω πρὸς τὴν jects However in the same manner as ldquouprdquoσχέσιν λέγεται τοῦ ἀναβαίνοντος ἢ and ldquodownrdquo are defined in relationship to theκαταβαίνοντος αὐτὸ δὲ ἀπολύτως λε- ascending or the descending but when theyγόμενον οὐδrsquo ὁπότερόν ἐστιν ὅτι καὶ are said unconditionally they are nothing ofἀμφότερα δέχεται καὶ ἄνω μὲν ὡς the two because they can be understood inπρὸς κάτω κάτω δὲ ὡς πρὸς τὸ ἄνω both senses and ldquouprdquo is defined in relation toλέγεται ἀφορίζεται δὲ τῇ τοῦ ἀνιό- ldquodownrdquo whereas ldquodownrdquo in relation to ldquouprdquoντος καὶ κατερχομένου σχέσει οὕτως and they are to be discerned in relationship toκαὶ ὁ ἀριθμὸς αὐτὸς καθrsquo ἑαυτὸν οὔτε the ascending and descending ndash in the sameδιαιρεῖ οὔτε συναπτεῖ ἀλλrsquo ἀμφότερα manner the number too is itself and per seδέχεται τῇ ποιᾷ σχέσει οἷον ἡ δυὰς neither dividing nor joining but contain bothἡ τετρὰς καὶ ἑξῆς Εἰ μὲν γὰρ τὰς μο- in a certain relationship such as the two theνὰδας αὐτὰς θεωρεῖς ἐξ ὧν συνέστη- four etc Because if you consider the unitsκεν εἰς ταύτας διαιρεῖται εἰ δὲ τὴν they are composed from they are divided intoὁμάδα τούτων σκοπεῖς ἐκ τούτων συ- them whereas if you see them as a whole theyνάπτεται Δύο γὰρ καὶ δύο εἰ τύχοι are collected from them Thus two and twoεἰς τέσσαρα συντίθεται τὰ δὲ τέσσαρα taken together result into four whereas fourεἰς δύο καὶ δύο διαιρεῖται ὥστε πα- could be divided into two and two It is thusντὸς ἀληθέστερον τὴν φύσιν τοῦ ἀριθ- the most true to take the nature of number asμοῦ μηδὲν ἀφωρισμένον ἔχειν μήτε defined in no way neither as divided nor asτὸ διῃρημένον μήτε τὸ ἡνωμένον ἐν united but existing in one or another way de-δὲ τῇ τῶν πραγμάτων ἐπιπλοκῇ καὶ pending on its combination and compositionσυνθέσει τοῦτο ὑφίστασθαι with the real things

aἈπαίδευτον οὖν τὸ τῇ φύσει τοῦ Thus it would be uneducated to take as a lawἀριθμοῦ ἀναγκαίως τὴν διαίρεσιν that the nature of number is necessarily fol-τῶν πραγμάτων ἕπεσθαι νομοθετεῖν lowed by a division in the real things insteadἀλλὰ μὴ τῇ τῶν πραγμάτων ἡνο- of making the number a sign of real thingsμένων τε ἢ διῃρημένων φύσει τὸν either united or divided by nature revealingἀριθμὸν σημεῖον ποιεῖσθαι δηλωτι- the quantity of subjects which are able to beκὸν τοῦ πόσου τῶν ὑποκειμένων ἄλ- divided or joined together because of a differ-λου λόγου καὶ οὐ τοῦ ἀριθμοῦ ταῦτα ent reason than the number [hellip]διαιροῦντός τε καὶ συνάπτοντος [hellip]

Here we can take a break to evaluate what has been said so far The num-bers and their corresponding subjects (τὰ ὑποκείμενα) can correspond to twodifferent kinds of reality not only to the number of mutually divided realthings but also to the number of different positions within a unique real thingsuch as ldquouprdquo and ldquodownrdquo (ldquotoprdquo and ldquobottomrdquo) In the latter case the dif-

152

Leontius of Byzantium and His ldquoTheory of Graphsrdquo against John Philoponusferent positions can be defined only through each other according to theirmutual relationships

In the following part of the same monologue Leontius (the Orthodox)continues to explain his idea with different examples eg a ten-cubit pieceof wood whose unity did not undergo any division into ten different pieces(7926ndash28 1920C) A horse a human and a bull represent three differentnatures but they are not divided according to quantity (κατὰ τὸ ποσόν) butare different according to species (τὸ παρηλλαγμένον κατὰ τὸ εἶδος) Hegoes on to say however that ldquo[hellip] concerning three different men such asPeter Paul and John we would imply that they are divided and moreoverthat such is their amount (τρεῖς δὲ ἀνθρώπους εἰ τύχοι Πέτρον καὶ Παῦλονκαὶ Ἰωάννην τὸ διῃρημένον αὐτῶν μᾶλλον καὶ ὅτι τοσοῦτοι οὗτοι οἵδε παρι-στῶμεν)rdquo (7931ndash804 1920D)

Oddly enough Leontiusrsquo distinction between the two kinds of numbersand numerical difference passed unnoticed by the scholars who analysed theSolutio ndash despite the obvious fact that this is the central point of Leontiusrsquoexplanation of his understanding of the particular nature

6 Triadological ImplicationsThen Leontius reaches the most delicate domain of ldquotheologyrdquo that is

Trinitarian doctrine (θεολογία in contrast with οἰκονομίαldquoœconomyrdquo asthe doctrine of incarnation) The Acephalus will answer with an attendantargument of the anti-Chalcedonians that the meaning of such terms as ldquohy-postasisrdquo ldquonaturerdquo and ldquoessencerdquo must not be the same in the ldquoœconomyrdquoas in the ldquotheologyrdquo (8022ndash26 1921B) This part of the discussion focusedon the patristic testimonia is not especially original and so will be out of ourscope29 We need to read however in the light of the above explanation theTrinitarian idea of Leontius (804ndash10 1920Dndash1921A)

Ὥσπερ ἐπὶ τῆς ἁγίας Τριάδος Thus concerning the Holy Trinity we confessτρεῖς μὲν ὑπο στά σεις ὁμολογο- three hypostases but we profess as unique theirῦμεν μίαν δὲ τούτων φύσιν καὶ nature and essence without however acknow-οὐ σί αν καταγγέλομεν οὐδrsquo ὁπο- ledging any of them as having no being becauseτέραν μὲν τούτων ἀνούσιον γι- we do not define the number as a delimitationνώσκοντες οὐ μὲν καὶ ἀριθμὸν of quantity of essences knowing well that to-ἀφοριστικὸν ποσότητος οὐσιῶν gether with the latter the (idea of the) differentἐπιφημίζοντες εὖ εἰδότες τὸ essence is to be introduced ndash as indeed the Ariansἑτερούσιον ταύτῃ συνάγεσθαι ὃ effectuated when they dealing with the hypo-δὴ καὶ οἱ Ἀρειανοὶ συναισθόμε- stases that have their essence introduced the (no-νοι ταῖς ὑποστά σε σιν ἐνουσί- tion of) essence into the definition of hypostasis

29 It occupies the whole ch 3 of the Solutio (8022ndash8316 1921Bndash1925B) This topic continuedto be discussed in ch 6 (859ndash8614 1928Dndash1929D)

153

Basil Lourieacuteοις οὔσαις τὰς οὐσίας ἐπεφή- and in this way introduced [sc into the Trin-μιζον ταύτῃ τὸ ἑτεροούσιον ity] a com plication with the (idea of the) differentσυμπλέκοντες essenceAt the end of the quotation my translation becomes more verbose and explic-ative but I hope to grasp Leontiusrsquo idea adequately Leontius says that thethree hypostases are indeed existing and real but they are different fromeach other in the same ldquonumericalrdquo but ldquorelationalrdquo sense just as ldquouprdquo dif-fers from ldquodownrdquo This difference between the divine hypostases is opposedto the example of three really divided men Peter Paul and John which hasjust been referred to Thus Leontius would be certainly opposed to the fu-ture ldquoTritheismrdquo of John Philoponus

It is implied ndash in Leontius unlike Philoponus ndash that there is some real ob-ject the common nature that is divided into particular natures differenti-ated by their ldquopositionrdquo This kind of difference implies that the differentobjects (particular natures within the unique common nature) differ exclus-ively in relation to each other Applied to the Trinity this approach leads toa certain kind of Modalism rather than ldquoTritheismrdquo30

It is in such a ldquoModalistrdquo sense that I think one has to understand Leon-tiusrsquo earlier triadological formulation

For the nature of the Father the Son and the Holy Spirit is not fulfilling[or completing ndash οὐ γὰρ συμπληρωτική] so that it would be more in the onethan in the three In fact by nature the Trinity is the same as any one ofthose which are seen in the Trinity ([hellip] ὡς οὖν μᾶλλον ἐν τῷ ἑνὶ ἢ ἐν τοῖςτρισί καὶ τοῦτο τῇ φύσει ἡ Τριὰς ὅπερ ἂν ἕν τι τῶν ἐν Τριάδι θεωορουμένωντυγχάνοι) [hellip]31

30 Therefore Loofs was not right in his claim that ldquo[u]nser Verfasser selbst wuumlrde bei trithe-istischen Consequenzen ankommen wenn er der Anwendung seiner philosophischen Ge-danken auf die Trinitaumltslehre noch genauer nachgiengerdquo (F Loofs Leontius von Byzanzhellip 63)which has been pointed out by R Cross ldquoIndividual Natureshelliprdquo 260 n 44 However Crossrsquoown understanding of Leontius (ldquo[hellip] Leontius never abandons his belief that natures areuniversals his point about Christrsquos human nature is that it has the universal human natureas a partrdquo ibid) is not quite correct because to be numerically differentiated ldquoby relationrdquowithin a unity is not the same thing as to be a part of this unity In the field of ldquoTheologyrdquoCross summarises the passage of the Solutio quoted above in a not quite correct way ldquoTheArian worry is circumvented by claiming that although the three divine persons are notnatures or essences none is anousios ndash each divine person has the one divine naturerdquo andcontinues in a footnote ldquoThis is of course precisely the move made by Philoponus a fewyears laterrdquo (ibid 259 n 42) the mention of Philoponus refers to his ldquoTritheismrdquo UnlikePhiloponus however Leontius does not allow any individualisation of the hypostases ofthe Trinity other than their relations to each other This idea has something in commonwith the Scholasticism but is alien to the Byzantine patristic tradition cf a discussion ofa ldquorelationalrdquo understanding of the notion of hypostasis at the Council of Florence in 1439B Lourieacute ldquoLrsquoattitude de S Marc drsquoEphegravese aux deacutebats sur la procession du Saint-Esprit agraveFlorence Ses fondements dans la theacuteologie post-palamiterdquo Annuarium Historiae Conciliorum21 (1989) 317ndash333

31 CNE I 4 1514ndash17 1288B tr by Istvaacuten Perczel ldquoOnce Again on Dionysius the Areopagite andLeontius of Byzantiumrdquo in T Boiadjiev G Kapriev A Speer eds Die Dionysius-Rezeption im

154

Leontius of Byzantium and His ldquoTheory of Graphsrdquo against John PhiloponusHere the identity of any one hypostasis with the whole Trinity remains

unexplained32 but the new idea of the numerical difference ldquoby relationrdquoprovides a strong rational foundation to it If I dare to call such a decisionmodalistic I have in mind a ldquoModalismrdquo in a very specific sense it recognisesa specific but true reality of the objects whose numerical distinction is onlyldquorelationalrdquo33 Nevertheless Leontiusrsquo ldquoModalismrdquo too avoids the patristicparaconsistent logic with its famous equation ldquo1 = 3rdquo and the correspond-ing mathematical ideas with whom the modern thought became accustomedonly after Richard Dedekindrsquos and Georg Kantorrsquos theory of infinite sets34

7 Leontiusrsquo Theory of GraphsThe ldquonumbersrdquo defined through relation to each other are known in the

modern mathematics as graphs The very idea of the modern theory ofgraphs goes back directly to Leibnizrsquos geometria situs although Leibniz him-self saw its roots in some ldquoVeteresrdquo (scholars of Greek antiquity especiallyEuclid) and even Descartes35 According to the earliest of Leibnizrsquos formula-tions there are two different approaches in the mathematical analysis ldquo[hellip]je croy qursquoil nous faut encor une autre analyse proprement geometrique oulineaire qui nous exprime directement situm comme lrsquoAlgebre exprime mag-nitudinemrdquo36 In Leibnizrsquos geometria situs both modern theory of graphs and

Mittelalter Internationales Kolloquium in Sofia vom 8 bis 11 April 1999 unter der Schirmherrschaftder Socieacuteteacute internationale pour lrsquoeacutetude de la philosophie meacutedieacutevale Rencontres de PhilosophieMeacutedieacutevale 9 Turnhout Brepols 2000 41ndash85 here 54

32 For the whole context and especially the following quotation from Dionysius in Leontiuswhich is posed by him in a different context to distort its meaning see Perczel ldquoOnceAgainhelliprdquo Perczelrsquos interpretation of Leontius seems to me very plausible regardless of mysceptical attitude toward his interpretation of Dionysius

33 Both historical and modern recensions of the Modalist Triadology operate with theunique ndash classical ndash kind of numerical distinction See esp the logical analysis by Dani-ele Bertini ldquoUna difesa della trattazione modalista della Trinitagraverdquo in D Bertini G Sal-meri P Trianni eds La Trinitagrave Roma Edizione Nuova Cultura (forthcoming) and a lar-ger article published on-line as preprint ldquoChe cosa non va nel modalismordquo in Ela-borare lrsquoesperienza di Dio Atti del Convegno ldquoLa Trinitagraverdquo Roma 26ndash28 maggio 2009httpmondodomaniorgteologiabertini2011htm (accessed on 25 07 2015)

34 There is no so far a comprehensive study of the paraconsistent logic in the patristic Triad-ology but I have touched several related points in B Lourieacute ldquoThe Philosophy of Dionysiusthe Areopagite An Approachhelliprdquo

35 These references are given in Leibnizrsquos programme article De analysi situs (ca 1693) G HPertz ed Leibnizens gesammelte Werke aus den Handschriften der Koumlniglichen Bibliothek zu Han-over III Folge 5 Bd G I Gerhardt Leibnizens Mathematische Schriften II Abt Bd 1 HalleH W Schmidt 1858 178ndash185 For a detailed analysis of Leibnizrsquos historical context see VDe Risi Geometry and Monadology Leibnizrsquos ldquoAnalysis Situsrdquo and Philosophy of Space ScienceNetworks Historical Studies 33 Basel Boston Berlin Birkhaumluser 2007

36 Letter to Christian Huygens 8 September 1679 G H Pertz ed Leibnizens gesammelte WerkehellipIII Folge 2 Bd G I Gerhardt Leibnizens Mathematische Schriften I Abt Bd 2 Berlin AAsher amp Comp 1850 17ndash27 here 19 This is the first document marking the idea of thegeometria situs as already presented in Leibnizrsquos mind As it has been shown only recently

155

Basil Lourieacutetopology were still united37

The next and decisive step toward the theory of graphs was performedby Leonhard Euler in 1735 who kept in mind Leibnizrsquos idea (and called itldquoetiamnum admodum ignotaerdquo ndash ldquoalmost unknown howeverrdquo)38 Neverthe-less until Oswald Veblen in the 1930s the theory of graphs has never beenseparated from the topology as a self-standing mathematical discipline

In Leontiusrsquo example the ldquotoprdquo (or ldquouprdquo) and ldquobottomrdquo (or ldquodownrdquo) areclearly two vertices of a graph acting as two different positions in the spaceEven his example of a ten-cubit piece of wood is a demonstration of thepossibility of an arbitrary spatial organization introduced into a given spa-tial zone

A graph is by definition a representation of a set of objects where somepairs of objects are connected by links (called edges) and the interconnec-ted objects are represented by mathematical abstractions called verticesThus the graphs are pure representations of mutual relations and are thusidentical with the numbers in Leontiusrsquo second meaning

However neither three men nor the three persons of the Holy Trinity andthe two natures in Christ are related to a space in the ordinary sense of theword that is to a physical space And yet they too are vertices of graphsdrawn in what we call now after Peter Gaumlrdenfors ldquoconceptual spacesrdquo39

This is a late twentieth-century idea also preconceived by Leontius that aspatial representation of information is inherent to the humanity As Gaumlrden-fors wrote ldquoI will advocate a third form of representing information that isbased on using geometrical structures rather than symbols or connectionsbetween neurons Using these structures similarity relations can be modelledin a natural way The notion of similarity is crucial for the understanding ofmany cognitive phenomena I shall call my way of representing information

Leibniz did not stop developing his new mathematical discipline until his death in 1716 cfV De Risi Geometryhellip

37 One can additionally quote Leibniz from a recently published fragmentary text dated to1682 ldquoGeometria tractat de rerum magnitudine et figura Itaque duabus scientiis subordi-nata est uni de magnitudine in genere et magnitudinum comparatione sive aequalitate etratione alteri de rerum formis in genere sive de rerum similitudine et dissimilitudinerdquo VDe Risi Geometryhellip 623

38 L Euler ldquoSolutio problematis ad geometriam situs pertinentisrdquo Commentarii Academiae sci-entarum Petropolitanae 8 (1735) [published in 1741] 128ndash140 republished by L G du PasquierLeonhard Euleri Opera omnia Ser I vol 7 Commentationes algebraicae ad theoriam combinario-num et probabilitatum pertinentes Leipzig Teubner 1923 1ndash10 Cf reprint of du Pasquierrsquospublication English translation and a discussion in the context of the modern theory ofgraphs in H Fleischner Eulerian Graphs and Related Topics part 1 vol 1 Annals of DiscreteMathematics 45 Amsterdam Elsevier 1990

39 See esp his seminal monograph P Gaumlrdenfors Conceptual Spaces the Geometry of ThoughtCambridge MA MIT Press 2000 where the graphs in the conceptual spaces are discussedas well

156

Leontius of Byzantium and His ldquoTheory of Graphsrdquo against John Philoponusthe conceptual form since I believe that the essential aspects of concept form-ation are best described using this kind of representationrdquo40 Here the verywording such as ldquogeometrical structuresrdquo and ldquosimilarity relationsrdquo soundsvery Leibnizian [hellip]

Gaumlrdenfors shows that the conceptual spaces should be dealt with usingmathematical methods including the theory of graphs And the latter is thecase with Leontius his main innovation was not of course a spatial repres-entation of the problems discussed but in introducing a new and ldquorelationalrdquonotion of number which is nothing other than what we call now graphs ndash oras Leibniz would say not magnitudo but situs

So far historians of mathematics have not known of any precedent ofthe geometria situs before Leibniz However I would prefer to leave open thequestion whether Leontius himself discovered this new kind of mathemat-ical object or borrowed this idea from somebody else There are reasons tothink that we are still far from a complete understanding of the progress inphilosophy and scholarship achieved in the sixth-century Byzantium Nev-ertheless Leontiusrsquo mathematical innovation in the theological discussionwas produced out of the fear of logical inconsistency and more precisely inan attempt to avoid the recourse to the paraconsistent logic Thus in thisgeneral logical and theological inspiration Leontius was in accord with hisanti-Chalcedonian and Nestorian or crypto-Nestorian opponents and there-fore in disagreement with mainstream Byzantine patristic thought both Cap-padocian and Dionysian

8 An Intermezzo Forbidding the SingletonsThe primary purpose of the following discussion in the Solutio is to ex-

plain why the humanity of Christ does not form a separate subject besidethe Logos There was no explanation precirct-agrave-porter After having explainedhis own logical presuppositions (ch 1ndash2) and having discussed the inevit-able hermeneutical issues on some patristic sayings (ch 3 and 6) Leontius atfirst completes an initial outline of his doctrine with an explination ndash ratherobvious in such context ndash of why ldquothe unique composite naturerdquo of the anti-Chalcedonians is in fact not a nature but a hypostasis (ch 4 8317ndash84151925Bndash1928A) Then (ch 5 8416ndash858 1928BndashD) follows a curious exchange ndashespecially with respect to the history of science ndash about the possibility for theldquounique nature of Christrdquo to be simply the unique instantiation of a species(the sun being another such example) Leontius answers that such a thing hasto be properly called ldquohypostasisrdquo and not ldquonaturerdquo whereas the natures inChrist are different from each other This question by the Acephalus and the

40 P Gaumlrdenfors ldquoConceptual Spaces as a Framework for Knowledge Representationrdquo Mindand Matter 2 (2004) 9ndash27 here 10

157

Basil Lourieacuteresulting part of the Orthodoxrsquos answer is a locus communis of the polemicsaround the Chalcedon

The peculiarities of the species represented in unique objects had alreadybeen discussed by Aristotle (Metaphysics Z15 where the sun is mentionedamong such objects) but had never ceased to be under discussion Only theldquoold-fashionrdquo Neoplatonic tradition ndash those who were faithful to the Platonicview universalia ante res ndash accepted them without problems All others con-fronted difficulties41 especially dealing with the cases when more than oneinstantiation was thought to be theoretically impossible42

Leontius certainly surprises his readers ndash not only his direct oppon-ent(s) ndash with the claim that in a sharp contrast with the common opinionsuch things as the sun or heaven are not single in their species ldquoWhetheryou do not know oh my dear friend that the nature of the sun is the same asthat of the stars And that the heaven is the same as the others heavensrdquo43

Leontius had to be strongly motivated to make such a deviation from bothnormative cosmology44 and the standard logical textbooks of his epoch Sucha radical claim ndash that there is no uniquely instantiated natures at all ndash lookstoo excessive for a habitual philosophical ping-pong game on the margins ofthe theological discussion with the anti-Chalcedonians At first glance thiswas not an advantageous position to take within the discussion Thus onehas to conclude that Leontius needed such a claim for the logical consistencyof his system as a whole

In the philosophical traditions available to Leontius the claim that thereare no such things as species represented with unique individuals is a ratherrare thing Such a claim would be equivalent to the statement that even a

41 Cf P Adamson ldquoOne of a Kind Plotinus and Porphyry on Unique Instantiationrdquo in RChiaradonna G Galluzzo eds Universals in Ancient Philosophy Seminari e convegni 33 PisaEdizioni della Normale 2013 329ndash351 where the ancient authors discussed are not onlythose mentioned in the title

42 Cf R W Sharples ldquoAlexander of Aphrodisias on Universals Two Problematic TextsrdquoPhronesis 50 (2005) 43ndash55 Sharples discusses two kinds of universals in Alexander thosethat are in fact exemplified in many instances and those that only could to be exemplifiedin many instances

43 Ἀλλrsquo ἠγνόησας ὦ βέλτιστε ὅτι ἡ τοῦ ἡλίου φύσις ἡ αὐτή ἐστι τῇ τῶν ἄστρων Καὶ ὁ οὐρανὸςὁ αὐτὸς τοῖς λοιποῖς οὐρανοῖς (8419ndash20 1928B) The idea of plurality of heavens seems tome rather Jewish-Christian than Greek

44 In the normative (geocentric) cosmologies of antiquity the sun with its rotation aroundthe earth was sharply divided from the fixed stars However the sun as one of the starscould be conceived in the heliocentric system of Aristarchus of Samos (ca 310ndashca 230 BC)whose ideas are available to us (as most probably already to Leontius) through ArchimedesPsammites (Arenarius et dimensio circuli) another and especially probable source of Leontiusrsquoview would be Anaxagoras (5th cent BC) with his idea that ldquothe sun and the moon andall the stars are fiery stones [hellip]rdquo (apud Hippolytus Refutation of All Heresies 1816 P CurdAnaxagoras of Clazomenae Fragments and Testimonia A Text and Translation with Notes and EssaysPhoenix pre-Socratics 6 Phoenix Supplementary vol 64 Toronto University of TorontoPress 2007 95) cf Plato Phaedo 97b8ndash98c2 (ibid 101)

158

Leontius of Byzantium and His ldquoTheory of Graphsrdquo against John Philoponusunique instantiation of a nature is impossible if this nature would be taken-off There is only instance a saying ascribed to Alexander of Aphrodisias(2ndndash early 3rd century) whose literal sense is like that45 However Alexan-der was much more known by his apparently opposite statements namelythat the unique objects such as the sun do not need to have anything com-mon above them46 We have neither the need nor the possibility of goingdeeper into understanding the views of Alexander or those ascribed to himWe have to retain from this survey that Leontiusrsquo rejection of natures withunique individuals was indeed a radical move away from the backdrop ofsixth-century Aristotelism although this was probably not entirely unique

Now we know especially thanks to David Lewis that the assumption ofthe classes having only one element (so-called singletons) leads to the para-dox within any consistent logic So far there is no way to either define theclass or the set without referring to the idea of the plurality of its elementsor to provide a good logical foundation for the prohibition of singletons Le-ontius had he lived in our epoch would face the same problem as DavidLewis the existence of modern mathematics which is based on the modernset theories The latter all without exception (including the NF theory byQuine although Quine himself thought otherwise) do allow the existence ofsingletons but in this way the mathematics reveals its problems with the lo-gical consistency Lewis has joked that it is certainly somebody else not hewho would bring to the mathematicians this news He personally was con-vinced that the paradox would be resolved in the future ldquoSingletons andtherefore all classes are profoundly mysterious Mysteries are an onerous

45 Quaestio XIa διὸ ἀναιρουμένῳ μὲν ἑνὶ τῶν ὑπὸ τὸ κοινὸν οὐ συναναιρεῖται τὸ κοινὸν διότιἐστὶν ἐν πλείοσιν εἰ δrsquoἀναιρεθείη τὸ κοινόν οὐδrsquo ἂν τῶν ὑπὸ τὸ κοινὸν εἴη τι οἷς τὸ εἶναι ἐντῷ ἐκεῖνο ἔχειν ἐν αὐτοῖς (ldquoTherefore doing away with one of the items under the commonitem does not do away with the common item as well because it exists in many But if thecommon item should be done away with there would not exist any of the items under thecommon item since their being lies in having that [common item] in themrdquo) I Bruns Alex-andri Aphrodisiensis Praeter commentaria Scripta minora Qaestiones De Fato De Mixtione Supple-mentum Aristotelicum vol II pars II Berlin G Reimer 1892 2117ndash20 tr M M TweedaleldquoAlexander of Aphrodisiasrsquo Views on Universalsrdquo Phronesis 29 (1984) 279ndash303 here 289 ThisMartin M Tweedalersquos article was considered until now as the most exhaustive collection ofthe data relevant to its title

46 See esp but not uniquely Simplicius (early 6th century) Commentary on the Categories 8513Kalbfleisch ἀλλὰ κοινὸν φησίν οὐδὲν εἶναι δύναται χωρὶς ἀτόμου ἄτομον δὲ ἔστιν χωρὶςκοινοῦ οἷον ἥλιος καὶ σελήνη καὶ κόσμος (ldquoBut he [Alexander] says that the common itemcan be nothing apart from the individual but the individual exists apart from the com-mon item for example the sun the moon and the universerdquo) quoted and translated byTweedale ldquoAlexander of Aphrodisiasrsquohelliprdquo 283 As to the interpretation of the apparent con-tradictions within the works attributed to Alexander it continues to be in the focus of adiscussion Cf first of all the same paper by Tweedale and then among others SharplesldquoAlexander of Aphrodisias on Universalshelliprdquo and Ch Helmig Forms and Concepts ConceptFormation in the Platonic Tradition Commentaria in Aristotelem Graeca et Byzantina Quellenund Studien 5 Berlin Boston De Gruyter 2012 161ndash164

159

Basil Lourieacuteburden [hellip] And so I have to say gritting my teeth that somehow I know nothow we do understand what it means to speak of singletonsrdquo47

The mathematics Leontius knew was still working without the set theo-ries Thus Leontiusrsquo condition was easier than that of Lewis he could simplyreject the singletons as he did What remained after this procedure is aconsistent theory of universals albeit a bit overloaded with the necessity ofseeking for an appropriate common to any apparently unique individual ofa species

It is interesting to note that although Leontiusrsquo theory which belongs tothe domains of philosophy and logic was obviously inspired by his theolo-gical thought Lewisrsquo research led to the same point ndash acknowledgement ofat least an apparent incompatibility of the singletons with logical consist-ency ndash out of his repulsion for what he has called ldquotheologyrdquo48 In fact bothof them were acting out of their common repulsion for what we call nowldquointensional entitiesrdquo49 In the case of Lewis as well as with his direct pre-decessors Quine and Leśniewski the intensional entities were rejected outof philosophical nominalism The attitude of Leontius was somewhat similarbut different and it could be easily ndash but unjustly ndash confused with nominal-ism and so needs to be approached after some preliminary explanations

9 Moderate Realism and Its Problems of ConsistencyAs is well known50 the mainstream in the understanding of the univer-

sals throughout the whole ldquoByzantine Millenniumrdquo was the so-called moder-ate realism universalia in rebus ndash and thus neither ante res nor post res This

47 D Lewis Parts of Classes Oxford Blackwell 1991 29ndash59 quoted 57 59 The correspondingideas of this book were rewritten in a more succinct way and with further elaboration inhis 1993 paper reprinted with some corrections once more as D Lewis ldquoMathematics ismegethologyrdquo in idem Papers in philosophical logic Cambridge studies in philosophy Cam-bridge Cambridge University Press 1998 203ndash229 Lewis criticizes among others Quinersquosattempt of excluding singletons from his own theory of sets which is according to Lewisincomplete and therefore unsuccessful Cf esp W V O Quine Set Theory and Its Logic Reved Cambridge MA London The Belknap Press 1969 31ndash34 The complete and consecutiveexclusion of the singletons (as something different from their elements) is a feature of analternative to the modern set theory the mereology of Stanisław Leśniewski first proposedby him in 1916 cf R Urbaniak Leśniewskirsquos Systems of Logic and Foundations of MathematicsTrends in Logic 37 Cham etc Springer 2014 113ndash114

48 Cf ldquoMust set theory rest on theology ndash Cantor thought sordquo (Lewis ldquoMathematics is me-gethologyrdquo 215)

49 For this notion and its value in patristics cf B Lourieacute ldquoThe Philosophy of Dionysiushelliprdquo89ndash92

50 Especially after a series of studies by Linos Benakis See his summarising article Λ Γ Μπενά-κης ldquoΤὸ πρό βλη μα τῶν γενικῶν ἐννοιῶν καὶ ὁ ἐννοιολογικὸς ρεαλισμὸς τῶν Βυζαντινῶν[1978ndash1979]rdquo in idem Βυζαντινὴ Φιλο σο φία Κείμενα καὶ Μελέτες Athens Παρουσία 2002107ndash136 as well as several others reprinted in the same volume

160

Leontius of Byzantium and His ldquoTheory of Graphsrdquo against John Philoponusattitude however is the most difficult from a logical point of view The clas-sical logic does allow without problems both the strong realism of the Pla-tonics (ante res) and nominalism and the latter was not by chance so dearto the hearts of Leśniewski Quine David Lewis as well as many other mod-ern philosophers Moderate realism leads to problems with the logical con-sistency which either need to be accepted as such or taken as the impetusto look for a workaround This is why I suppose concepts of this sort areso unpopular among modern philosophers who prefer either Platonism ornominalism

Basically the problem is the following what is an individual togetherwith its universal given that the latter exists in some way within this indi-vidual If we consider a species as having a plurality of instantiations thenthere is a chance to evade the question with respect to a connection (but ofwhat sort51) between this given individual and all others within the speciesIf we discuss a singleton even this loophole is closed

We are dealing with a paraconsistent statement having the same type asthat of the Russell set (ldquoset of all setsrdquo) namely of the lack of self-identityX ne X The Russell set includes all sets and so includes itself and thereforeis not identical to itself

(1) existx((x isin x)f and (x isin x))

The same is true about the singleton of a species which exists in rebus52

Such an individual contains nothing but itself (because there is no Platonicidea accompanying it but having existence of its own) but moreover it con-tains its species (although we do not discuss in what way it is contained)Extensionally it possesses self-identity but intensionally it does not Onecan write for an individual x which is the unique member of the singletonset x

(2) forallx((x = x) and (x = x))

One can see from this that paraconsistency follows from the acknow-ledgement of intensional entities without allowing to them separate (anteres) existence

The left part of the conjunction (2) represents the nominalist attitudewhereas its right part the strong realist (Platonic) attitude and only their51 Cf Lewisrsquo discussion of the ldquoLasso hypothesisrdquo invented ndash and rejected ndash by himself Lewis

Parts of Classes 42ndash4552 Here and below I omit the reservations for excluding the ontological commitment because

they are rather self-evident (we can easily substitute for ldquoexistencerdquo something like ldquoexist-ence in some possibleimpossible world(s)rdquo etc) and although necessary for an exhaustivelogical discussion are excessive in the case of the problems discussed within the frameworkof the ldquoapplied philosophyrdquo of Byzantine dogmatics All these problems were considered inrelation to our unique real world although this world itself was somewhat different fromthe world where the most of modern philosophers livehellip

161

Basil Lourieacuteparaconsistent conjunction results in the moderate realism of the universaliain rebus

If we do not accept nominalism this intensional ldquoadditionrdquo to its self-identity has some ontological weight ndash it is an existing intensional entityTherefore ontologically the individual of a singleton contains itself as a classcontaining an individual but at the same time it is contained itself and there-fore differs from itself as the containing one The above statement first writ-ten for the Russell set is applicable to any singleton given that the universaliado exist in rebus

The ldquomysteryrdquo of the singleton as David Lewis coined it consists in itsparaconsistency ndash tolerated in the ldquonaiumlverdquo set theory by Cantor53 passed un-discussed by Zermelo and Fraenkel and unsuccessfully attacked by QuineThe singleton is equal to itself but is also more than itself it contains itselfbut is also contained by itself The singleton is a member of itself and is nota member of itself ndash precisely in the same manner as the Russell set Thisunderstanding of the singleton the naiumlve and ZF set theories share with themainstream of Byzantine ontology54 ndash but not with Leontius of Byzantium

Leontius does not allow the paraconsistent conjunction (2) but he doesnot subscribe to the nominalist formula x equiv x either He does not allowsingletons at all For him the species exist if and only if they are instantiatedin plurality of individuals Thus he avoids both paraconsistency and nom-inalism He managed to find out a workaround We have already seen thatLeontiusrsquo original idea was lying in the field of mathematics he inventedgraphs to become able to construct a consistent and original ontology

10 Unreality of the Division between the Two Natures in ChristLeontius explains his original Christological ideas only in the last two

chapters of the Solutio (chs 7 and 8) Before this he was mostly con-cerned with his original ideas in logic numerology and ontology In the lastchapters he shows what purpose this newly created philosophical doctrineserves

At first the Acephalus formulates the main argument known from theArbiter of Philoponus (esp its ch 7 preserved in Greek) It is very friendlytoward the Chalcedonians and was indeed elaborated in the perspective of

53 On some of Cantorrsquos paraconsistent intuitions as well as recent proposals of paraconsist-ent set theories sее W Carnielli M E Coniglio ldquoParaconsistent set theory by predicatingon consistencyrdquo Journal of Logic and Computation advanced access published 09 07 2013doi101093logcomext020 For different ways open to ldquorehabilitationrdquo of the ldquonaiumlverdquo settheory sее A Weir ldquoNaiumlve Set Theory Is Innocentrdquo Mind 107 (1998) 763ndash798 esp 792ndash793

54 Sее above section 4 on Eulogius of Alexandria and after him the Christology of the de-fenders of icons in the ninth century

162

Leontius of Byzantium and His ldquoTheory of Graphsrdquo against John Philoponusthe union (which failed at the Council of 553)55 your unique but compositehypostasis is the same thing as our unique but composite nature (8615ndash251929Dndash1932A) Some phrases here are of special interest however ldquoWe tooconsider the (two) natures only in thought (Τὰς φύσεις μόνῃ τῇ ἐπινοίᾳ καὶἡμεῖς θεωροῦμεν)rdquo given that the concrete and the real one is one resultingfrom the two nature of Christ ldquoin the same manner you understand the (two)hypostases in thought and unify them into the unique hypostasis [hellip] (Ὧι γὰρλόγῳ ὑμεῖς τὰς ὑποστάσεις τῇ ἐπινοίᾳ λαμβάνοντες καὶ ταύτας ἑνώσαντες εἰςμίαν ὑπόστασιν αὐτὰς συντίθετε [hellip])rdquo (8915ndash18 1929D)

One can see that so far the Acephalus still does not grasp the differencebetween the particular nature in its Leontian understanding and the hypo-stasis Thus he understands ldquofrom two naturesrdquo (a common slogan of thetwo sides of the conflict over the Chalcedon) in the Chalcedonian termino-logy as equivalent to ldquofrom two hypostasesrdquo Moreover he accepts that thetwo natures of Christ before the union existed ldquoonly in thoughtrdquo This canbe understood in either a traditional (for both anti-Chalcedonians and neo-Chalcedonians) way that the two natures of Christ before union could be dis-cussed only in a speculative manner or in a properly Philoponian way thatthese natures are per se abstractions without any self-standing existence Wewill see that Leontius (ldquothe Orthodoxrdquo) will perceive the term τῇ ἐπινοίᾳ inthe latter sense56

In his response Leontius defines two different kinds of ἐπίνοια (8626ndash8710 quoted below 8626ndash876 1932AB)

Τὴν ἐπίνοιαν οἱ Πατέρες καὶ ὁ ἀλη- The Fathers and the true reasoning defined twoθὴς λόγος διτ τὴν ἀπεφήναντο εἶναι different kinds of epinoia According to theἩ μὲν γὰρ οἷον ἐπέννοιά τίς ἐστι first one it is something like (analytical) re-καὶ ἐπενθύμησις τὴν ὁλοσχερῆ καὶ flection57 which unfolds and clarifies for con-ἀδι άρ θρω τον τῶν πραγμάτων ἐξα- templation and knowledge the wholeness andπλοῦσά τε καὶ δια σα φοῦ σα θεωρίαν non-com po siteness of real things whose beingκαὶ γνῶσιν ὡς τὸ τῇ αἰσθή σει δόξαν seems to the sensual apperception to be simpleεἶναι ἁπλοῦν τῇ πολυπραγμο σύνῃ but with (the help of) the inquisitiveness of theτοῦ νοῦ πολυμερές τε καὶ ποικίλον intellect is reve aled to be ma ni fold and diversi-ἀναφαί νεσ θαι fied

ἡ δὲ ἀνάπλασμα διανοίας τυγχάνει According to the second meaning it is the ima-

55 Sее for all details U M Lang John Philoponus and the Controversies over Chalcedon in the SixthCentury A Study and Translation of the ldquoArbiterrdquo Spicilegium Sacrum Lovaniense Eacutetudes etdocuments fasc 47 Leuven Peeters 2001

56 Unfortunately I had no access to the complete text of the monograph by Antonio Orbe Laepinoia Algunos preliminares histoacutericos de la distincioacuten κατrsquo ἐπίνοιαν (En torno a la Filosofiacutea deLeoncio Bizantino) Roma Pontificia Universitas Gregoriana 1955

57 On the pair of synonymic words ἐπέννοια and ἐπενθύμησις precisely in our text sее G WH Lampe A Patristic Greek Lexicon Oxford Clarendon Press 1961 514 svv The first of thetwo is lacking from the LiddellndashScott dictionary

163

Basil Lourieacuteκατὰ συμπλο κὴν αἰσθήσεώς τε καὶ gination58 which combining the (data of) sen-φαντασίας ἐκ τῶν ὄντων τὰ μηδα- sual (apperception) and the fantasy constructsμῶς ὄντα συντιθεῖσα καὶ εἶναι δο- from the existing things what can never existξάζου σα τοιαύτη δέ ἐστιν ἡ τῶν ἱπ- but believes them to be exi st i ng such are theποκενταύ ρων καὶ Σειρήνων καὶ τῶν mythical creatures like hippocentaurs or Sirensτοιούτων μυθοπλαστία [hellip] [hellip]

The epinoia of the second kind takes some parts of the really existingthings and composes albeit only in the mind and the words (ἐν τῇ διανοίᾳκαὶ τοῖς λόγοις) something new which has neither hypostasis nor essence(τὰ μηδαμῶς ἐν ὑποστάσει καὶ οὐσίᾳ θεωρούμενα)

Then the Orthodox becomes able to proceed to the salient questionldquoThus which one of these two kinds of epinoia do you mean oh excellentone when you consider the two naturesrdquo (8711ndash12 1932B Κατὰ ποίαν τοί-νυν ὦ θαυμάσιε τῶν ἐπινοιῶν τούτων θεωρίαν τὰς δύο φύσεις λαμβάνεις)Of course the second alternative would lead to an arbitrary fantasy if notdirectly to the idolatry (8714ndash17 1932BC) But the first one is not much bet-ter ldquoIf (you mean) the first kind (of epinoia) you would define the Christ asbeing a gathering of objects of contemplation but not as coming together ofthe (two) natures because such is the nature of the things that are contem-plated only by epinoiardquo (8711ndash14 1932BC Εἰ μὲν οὖν κατὰ τὴν πρώτην θεω-ρημάτων ἄθροισμα ἀλλrsquo οὐ φύσεων σύνοδον τὸν Χριστὸν εἶναι ὁρίσῃ τοιάυτηγὰρ ἡ φύσις τῶν ἐπινοίᾳ μόνῃ θεωρητῶν)

We have to retain from there this clear definition of epinoia in whatevermeaning as something that is related to mental constructs outside thereality

What follows is a critic of Monophysitism but not only for ldquomixingrdquo thetwo natures into one but also for denying their existence whatsoever ldquoBe-cause from the very fact of understanding the natures only with epinoia itfollows for them to be nonexistent and non-being or demolished and disap-pearedrdquo (885ndash7 1932D Αὐτὸ μὲν οὖν τὸ τῇ ἐπινοίᾳ μόνῃ τὰς φύσεις γνωρί-ζειν τὸ ἀνύπαρκτον αὐτῶν καὶ ἀνούσιον ἢ τὸ συγκεχυμένον καὶ ἠφανισμέ-νον κατασκευάζει)

Leontiusrsquo own teaching ndash that he of course ascribes to ldquoour Fathersrdquo ndashis that not the natures themselves but only their division in Christ is to beapprehended by the epinoia in the first meaning of the term59 Thus heconsiders the division of the natures in Christ as not only understandablethrough an analytical procedure but also existing only in our mind

58 The meaning of the idiom ἀνάπλασμα διανοίας is precisely that ldquoimaginationrdquo59 8717ndash19 1932C ὅπότε οἱ θεσπέσιοι ἡμῶν Πατέρες οὐ τὰς φύσεις τῇ ἐπινοίᾳ εἶναι ὡρίσαντο

ἀλλὰ τὴν διαίρεσιν τούτων κατὰ τὴν πρώτην ἐπίνοιαν ἐξειλήφασιν

164

Leontius of Byzantium and His ldquoTheory of Graphsrdquo against John Philoponus11 Unreality of ldquoThreerdquo in the Holy Trinity

The most revealing of Leontiusrsquo triadological passages is found in a longexplanation about two kinds of difference the purely mental one by epinoiaand the real one which he calls ldquoby energyrdquo (ch 7 passim with repetitions inch 8) There is no need to collect all the relevant formulations by Leontiusbecause all of them repeat the same idea

The natures themselves exist not ldquoby epinoiardquo as said the Acephalus butldquoby energyrdquo (in reality) however the difference between them is only ldquobyepinoiardquo the Fathers ldquo[hellip] demonstrated the natures as being and called ac-cording to the energy whereas the division between them they understoodby epinoia (8722ndash23 1932C [hellip] τῇ μὲν ἐνεργείᾳ τὰς φύσεις εἶναί τε καὶ καλε-ῖσθαι ἀπεφήναντο τὴν δὲ τούτων διαίρεσιν κατrsquo ἐπίνοιαν ἔλαβον)

The division ldquoby energyrdquo would produce difference between the hypo-stases and this is why ndash Leontius here continues to answer the initial ques-tion of the Acephalus ndash we do not say that Christ is produced from the twohypostases (8810ndash21 1933AB) ldquo[hellip] the division by energy implies and estab-lishes hypostases whereas the division by epinoia does not entail the numberof hypostasesrdquo (8819ndash21 1933B [hellip] τῆς κατrsquo ἐνέργειαν διαιρέσεως τὰς ὑπο-στάσεις ἐχούσης τε καὶ τιθεμένης ἡ κατrsquo ἐπίνοιαν διαίρεσις τὸν τῶν ὑποστά-σεων ἀριθμὸν οὐ παρα δέχεται)60 ndash Let us notice the mention of number hereLeontius demonstrates that Christ is not divisible into two hypostases andso the notion of number here is the ordinary one

Immediately after the sentence just quoted Leontius continues taking anexample from the Holy Trinity (8821ndash24 1933B)

Ὡς γὰρ τὸ κατrsquo ἐπίνοιαν μεῖζον ἐπί When it is said by epinoia ldquogreaterrdquo concerningτε Πατρὸς καὶ Υἱοῦ τῇ τοῦ αἰτίου the Father and the Son [John 1428] because ofλεγόμενον φύσει τὸ τῇ φύ σει με- being the cause by nature61 nothing greaterῖζον οὐ συνεισάγει οὕτω τὸ κατrsquo is co-introduced to the nature In the sameἐπί νοιαν διαιρετὸν τὸ κατrsquo ἐνέρ- manner the division by epinoia would never co-γειαν οὐ συνεισάξει ποτὲ καὶ διὰ introduce the division by energy and there-τοῦτο οὐδὲ τὰς ὑποστάσεις fore (never co-introduce) the hypostases

One question would be in order here in what manner then do the hypo-stases of the Holy Trinity differ from each other by epinoia or by energy ndash oreven somehow else Leontius does not give us any explicit answer neitherdoes he provide any third kind of division The division could be either realby energy like that between three men or by epinoia as between the two60 Leontius elaborates further on the topic but either repeats himself or repeats the standard

anti-Nestorian argumentation of his epoch Cf in the same ch 7 8913ndash908 1933Dndash1936Cch 8 9530ndash9613 1944Dndash1945A

61 Leontius alludes to the common patristic understanding of John 1428 as pointing out thatthe Father is the ldquocauserdquo within the divine nature that is the principle of the μοναρχία inthe Holy Trinity

165

Basil Lourieacutenatures of Christ but also ndash let us recall what was said by Leontius in ch 2 ndashbetween ten cubits within a ten cubit piece of wood62 and as we now areforced to acknowledge between the three hypostases of the divine nature

I admit that now I am trying to carry through what Leontius himself leftunarticulated Indeed had he said that the three hypostases of the Holy Trin-ity differ only by epinoia he would face charge of Sabellianism He would alsohave had a hard time explaining his original theory of graphs

Leontius defends the unity of the conceptual apparatus used in bothldquotheologyrdquo and ldquoœconomyrdquo and so we would expect from him an explana-tion of why he describes the three divine hypostases in conformity with hisown definition of particular natures but still calls them hypostases In hislanguage where the particular natures differ from each other as the verticesof a graph whereas the hypostases differ from each other as enumerablethings divided ldquoby energyrdquo the notion of hypostasis was tacitly changing itsmeaning when applied to the Holy Trinity Leontiusrsquo escaping from the para-consistency of patristic thought cost him inconsistency in his own usage ofa key term hypostasis

Leontius left too many loose ends after having changed his mind fromthe Christology of CNE to that of the Solutio The building of his dogmaticswas left with no chance to be completed

12 ChristologyWe still have not quoted the famous Christological passage of ch 8 but

our analysis of Leontiusrsquo philosophy and logic is accomplished We still needhowever to learn more about his theology This is why ch 8 will be especiallyimportant to us Mostly this final chapter contains various repetitions ofearlier statements or the trivia of such polemics but among them there areimportant theological applications of the logical and ontological principlesformulated earlier

Leontius revisits his initial problem with which he had started the wholediscussion in the very beginning of his treatise how to understand the hu-man individuality of Christ Now it has already been explained that in lo-gical categories it is a particular nature in Leontiusrsquo specific understandingof this notion Thus it is time to explain it in a more theological way

The larger context is as follows Leontius needs to explain why his under-standing of the human individuality in Christ does not lead him to acknow-ledge Jesus as a human hypostasis (as the Nestorians do) However he turns62 This example must be understood in the context of Leontiusrsquo ldquogeometricalrdquo approach Thus

the cubits here are geometrically different (within a graph) and the whole example is notto be confounded with the unity of money in the bank account (the famous comparisonexplaining the indiscernibility of quantum objects invented by Erwin Schroumldinger in the1950s) cf S French D Krause Identity in Physics A Historical Philosophical and Formal Ana-lysis Oxford Clarendon Press 2006 142ndash143 159 220 370ndash371

166

Leontius of Byzantium and His ldquoTheory of Graphsrdquo against John Philoponusout to be unable to exclude the pre-existence of Christrsquos humanity on a purelytheoretical level albeit he of course excludes it as a fact Marcel Richardwas still too moderate when saying about this statement of Leontius thatldquo[crsquo]eacutetait jouer avec le feurdquo63

Probably Leontius did not explicitly contradict any authoritative text ofhis epoch but he did certainly contradict the mainstream (among the neo-Chalcedonians) theological intuition which in the 580s resulted in Eulogiusof Alexandriarsquos (paraconsistent) statement that the conjunction of a naturewith the individual characteristics of an individual still does not form a hypo-stasis There would be no Jesus without the divine Logos who accepted theindividual characteristics of Jesus and thus became ndash but only the Logos him-self now called Jesus ndash one of the individuals of the human common natureJesus is simply the name of the Logos as a hypostasis of the human nature inthe same manner as the Son is the name of the same Logos as a hypostasis ofthe divine nature The one and unique hypostasis of the Logos thus becamecommon to the two natures at once and acquired the individual character-istics (idioms) as an individual of each of the two natures I recalled theseexplanations of Nicephorus of Constantinople and Theodore the Studite tofacilitate our tracing of Leontiusrsquo attempts to avoid these (paraconsistent)Christological conclusions

Leontius approaches the problem of the pre-existence of Christrsquos human-ity from the analogy of the resurrection of the dead (9424ndash9518 1941Dndash1944B) This example allows him to conclude that ldquofrom this it is shown thatit is acceptable for a hypostasis to be produced out of the previously exist-ing things without (their) change even if it is not completely applicable toChrist because he is not created beforehandrdquo64 It is worth noting that Le-ontius considers the resurrected bodies as being materially identical to thedead ones and so he is following the line of Gregory of Nyssa rather thanthe Origenistic line of Philoponus or Eutychius of Constantinople65

Then Leontius proceeds to the issue that turns out to be the touchstoneof his Christology (9519ndash30 1944CD)66

Τὸ δέ τινας λέγειν διὰ τὸ μὴ προδια- As to the fact that some say because theπεπλάσθαι μηδὲ προϋφεστᾶναι τὴν Lordrsquos humanity was not formed or did notτοῦ Κυρίου ἀνθρωπό τη τα μηδὲ τε- exist beforehand and because it was not as-λείαν προσειλῆφθαι ἀλλrsquo ἐν τῷ Λόγῳ sumed already complete but has its being in

63 М Richard ldquoLeacuteoncehelliprdquo 6064 9432ndash34 1944A Ἐξ ὧν δείκνυται ὅτι καὶ ἐκ προϋφεστώτων πραγμάτων ὑπόστασιν γενέσθαι

ἀτρέπτως ἐνδέχεται εἰ καὶ ὅλως ἐπὶ Χριστοῦ τοῦτο οὐ δίδοται ὅτι οὐ προδιαπέπλασθαι65 Cf B Lourieacute ldquoJohn Philoponus on the Bodily Resurrectionrdquo В М Лурье ldquoИдентичность

человеческой личности по Иоанну Филопонуhelliprdquo66 I mostly owe my English translation below to Brian Daley ldquoThe Origenism of Leontius of

Byzantiumrdquo Journal of Theological Studies N S 27 (1976) 333ndash369 here 338

167

Basil Lourieacuteὑποστῆναι διὰ τοῦτο μίαν ὑπόστα- the Logos therefore they make one hypostasisσιν ἀμφοτέρων ποιεῖν τὸ μέν τι ἀλη- of both ndash part of this is true and part is notθὲς τὸ δὲ οὐκ ἀληθὲς ὂν τυγχανει We too grant that (his humanity) did not pre-Τὸ μὲν γὰρ μὴ προϋφεστᾶναι μηδὲ exist was not formed first but we do not at allπρο διαπεπλάσθαι καὶ ἡμεῖς δώσομεν grant that one therefore makes one hypostasisτὸ δὲ διὰ τοῦτο μίαν ὑπόστασιν ποιεῖν of both as if it were not permitted for thingsὡς οὐκ ἐγχωροῦν ἄλλως οὐδὲ δυνα- to be otherwise or as if it were impossible forτὸν Θεῷ καὶ τελείῳ ἀνθρώπῳ οὕτως God to be united even with a complete manἑνωθῆναι οὐκέτι δώσομεν Τί γάρ in this way But why Is there any import-Οὕτως ἢ ἐκείνως ἔχον τι πλέον ἔσται ance for God whether the union would be inΘεῷ εἰς ἕνωσιν Οὔτε γὰρ ὁ χρόνος τῆς this way or another In fact the unique Christἑνώσεως ἢ ὁ τόπος ἢ τὸ ἀτελὲς τοῦ σώ- is made not by the time or the place of theματος ἀλλrsquo αὐτὸς ὁ τῆς ἑνώσεως τρό- union or by the imperfection of the body67 butπος τὸν ἕνα Χριστὸν πεποίηκεν Οὐ by the very mode (tropos) of union We rejectτοίνυν διὰ τὸ ἀδύνατον ἀλλὰ διὰ τὸ the prior formation [ie of Christrsquos humanity]μὴ πρέπειν ψιλήν ποτε καὶ ἄνευ θεό- not because it was impossible but because itτητος εἶναι τὴν τοῦ Κυρίου ἀνθρωπό- was not fitting that the humanity of the Lordτητα τὴν προδιάπλασιν ἐκβάλλομεν should once have been alone and without his

divinity

Thus the particular human nature of Jesus according Leontius existedindependently of the fact of the incarnation even though its creation wassynchronised with the moment of incarnation

Of course even in the case of the ldquoprior formationrdquo of Christrsquos humanitythe principle forbidding any φύσις ἀνυπόστατος68 would not be broken Thisparticular nature of Jesus would use for its temporary being without divinitysome other hypostasis than that of the Logos that is a human hypostasis ndashfor instance of some Mr X let us say In Leontiusrsquo approach this would notcause a problem with the identity of the humanity of the further Jesus withthat of Mr X the unity of subject would be guaranteed by the human particu-lar nature that was at first ἐνυπόστατος in Mr X then in the Logos viz JesusIt is needless to say that such a thought experiment would render quite a dif-ferent result in the classical perspective of the Byzantine (neo-Chalcedonian)patristics here the humanity of Mr X would be inseparable from the hypo-stasis of Mr X because no such things as particular natures which are differ-ent from the hypostases exist

Leontiusrsquo treatment of the humanity of Christ makes it a separate subjectwithin the uni que Christ and so is really crypto-Nestorian from any ldquoneo-Chalcedonianrdquo point of view

67 ldquoImperfectionrdquo in the sense that the incarnation took place at the very moment of concep-tion unlike the alternative scenario ndash considered by Leontius as theoretically acceptable ndashas if it took place when Jesus grew up that is when his body became ldquoperfectrdquo Cf discus-sion above in ch 8 and the standard mode of speaking about growing of the human body

68 CNE I 1 quoted in footnote 22 above

168

Leontius of Byzantium and His ldquoTheory of Graphsrdquo against John PhiloponusNow we are in position to summarise the Christological doctrine of Leon-

tius For this purpose we have to recall Leontiusrsquo ldquotheory of graphsrdquo as wasused by him to create an original understanding of the notion of particularnature

The doctrine of Leontius could be summarised in these three points1) The humanity of Jesus does not exist and never existed as a numeric-

ally distinct separate entity This is why both open Nestorianism andTheodore of Mopsuestiarsquos Christology are unacceptable

2) It does exist since the incarnation ndash and could exist before incarnationbut actually did not ndash as a numerically distinct position within the com-mon nature of the humankind which is a particular human natureThis is an original idea of Leontius himself and exists in his Solutio only

3) The humanity of Jesus is not the common nature of the humankind ndashpace the whole consensus of the Chalcedonian theologians including Le-ontius himself in CNE

It is tempting to suppose that Leontiusrsquo ldquotheory of graphsrdquo was designed tosupply a rational model for the Origenistic Henas At least its Christologicaland Triadological applications would fit the theology of the Protoctist Origen-ism and I sympathise with Istvaacuten Perczelrsquos idea that Leontius belonged tothat group69

13 John Philoponus behind the ScenesIt was only Richard Cross who asked himself what happened to Leon-

tius between CNE and the Solutio but his answer was ldquoIt is not clear why LBchanged his mind [hellip]rdquo70 Given that the time span when the Solutio could havebeen written is to be expanded up to the epoch of the Council of 553 and es-pecially with reference to the preceeding Christological discussions we cantake a fresh look at the already known polemical parallels between the Arbiterby Philoponus (esp its ch 7) and Leontius of Byzantium

Philoponus was trying to present ldquothe unique naturerdquo of the Severians asthe same thing as ldquothe unique hypostasisrdquo of the (neo-)Chalcedonians Theidea of the humanity of Christ as a particular nature was in the core of hisargumentation There are some other polemical parallels with the Solutioone of them being already reviewed by Uwe Lang71 This is Philoponusrsquo ar-gumentation against those Chalcedonians who deduce their ldquounique hypo-stasisrdquo from the fact that the humanity of Christ did not exist prior to the in-carnation To the contrary Philoponus himself deduces from the same fact69 I Perczel ldquoOnce Againhelliprdquo70 R Cross ldquoIndividual Natureshelliprdquo 25071 U M Lang John Philoponushellip 70ndash72

169

Basil LourieacuteChristrsquos ldquounique naturerdquo Leontius as we have just seen denies the argu-mentation of both sides because he does not allow as a derivative of this factanything featuring the mode of the union (ὁ τῆς ἑνώσεως τρόπος) in ChristIt appears then that it was Leontius who wrote after Philoponus and not viceversa (pace Lang) But anyway this is a secondary detail

The main project of Philoponus on the eve of 553 was a reinterpretationof the Chalcedonian ldquounique hypostasisrdquo as a particular nature which wouldopen the way to allow the official Church under Justinian to adopt the ba-sic assumptions of Severian Christology We see the Chalcedonian positionthat there is no such thing as a particular nature which is not identical tothe hypostasis staggered precisely in the middle of the sixth century This isthe historical context in which Leontiusrsquo change of mind would seem mostnatural ndash especially if he did really keep his Origenistic skeleton in the closet

This is why I would consider the Solutio to be a response provoked by achallenge of John Philoponus

170

a DPhil from the University of Oxford (1997) and a Dr theol habil fromHumboldt University Berlin (2011) His research interests lie in late ancienttheology and philosophy as well as modern theology Major publications in-clude Human Nature in Gregory of Nyssa (2000) Theology as Science in Nineteenth-Century Germany (2013) and Individuality in Late Antiquity (ed with A Tor-rance 2014)Joseacute Mariacutea Nieva is an Associate Professor of Ancient Philosophy at the De-partment of Philosophy of the University of Tucumaacuten (Argentina) He isthe autor of Ver en el no-ver Ensayo criacutetico sobre el De Mystica Theologia de Di-onisio Areopagita (Tucumaacuten EUNT 2010) and of several articles concerningDionysius the Areopagite and other Platonic and Neoplatonic thinkersFilip Ivanović was born in Podgorica (Montenegro) in 1986 He earned hisPhD from the Department of Philosophy and Religious Studies of the Nor-wegian University of Science and Technology in Trondheim with a thesisentitled Love Beauty Deification The Erotic-Aesthetic Soteriology of Dionysius theAreopagite and Maximus the Confessor As for previous education he holds BAand MA degrees from the Department of Philosophy of the University of Bo-logna Among his publications are the edited volume Dionysius the Areopagitebetween Orthodoxy and Heresy (2011) and the monograph Symbol and Icon Di-onysius the Areopagite and the Iconoclastic Crisis (2010) as well as several otherjournal articles and book chapters As organizer or speaker he participatedat over twenty international conferences and symposia in Argentina UKGreece Spain Israel etc In 2010 he was a guest fellow at the Centre forthe Study of Antiquity and Christianity of the University of Aarhus and in2013 he spent a semester in Athens as a fellow of the Onassis Foundationwith affiliation to the Norwegian Institute and the National Hellenic ResearchFoundation He is a member of a number of professional and academic associ-ations including Socieacuteteacute Internationale pour lrsquoEacutetude de la PhilosophieMeacutedieacutevale In-ternational Society for Neoplatonic Studies and Association Internationale drsquoEacutetudesPatristiques His areas of interest include Greek and Byzantine philosophypatristics and Christian studiesBasil Lourieacute b 1962 PhD (2002) and Dr habil (2008) in Philosophy (StPetersburg State University) the Editor-in-Chief of Scrinium A Journal of Patro-logy Critical Hagiography and Church History Senior Research Fellow of the StPetersburg State University of Aerospace InstrumentationVladimir Cvetković PhD is an independent researcher based in GoumlttingenGermany Germany He is also a non-residential research fellow of the In-stitute of Philosophy and Social Theory of the University of Belgrade Ser-bia Previously he conducted research and taught at the universities of Aar-hus (Denmark) St Andrews (UK) Oslo (Norway) Belgrade and Nis (Serbia)His research interests include Patristics and Byzantine tradition especiallyGregory of Nyssa and Maximus the Confessor as well as Modern Orthodox

469