The Transcendence of the Pythagorean Arithmetical Ontology in the Areopagitic Writings

Pay h h i c vaas {yurt 5, aA. Dis jira 199% è) THE TRANSCENDENCE OF THE PYTHAGOREAN ARITHMETICAL ONTOLOGY IN THE AREOPAGITIC WRITINGS By transcendence we mean neither the abolition, nor even a mere extension of Pythagorean ontology. What we really mean is its transfer and its natural assimilation within the Areopagitic works!, which however, indicates a serious and substantial difference from it. The Pythagorean ontological notions are correctly assimilated by the Areopagite according to their nature and order within the context of ontology and are kept together in a functional relation in the frame ofa universal ontology, while remaining remote in the sense of an essential morphological distinction, Although the Areopagitic ontology may inevitably echo Pythagoreanism, Platonism and above all Neoplatonism, the sequence of terms can only be considered as a matter of form, not of essence. Therefore, by referring to the transcendence of the Pythagorean arithmetical ontology in the Areopagitic writings, all we mean is not only that the former ontology is logically incorporated into them, as a union, but also that it is substantially differentiated as a distinction, and finally superceded by the latter. The Pythagorean arithetical ontology’, which clearly leads to an arithmetical consideration of the universe, uses as its fundamental ontological principle the first Pythagorean opposition, i.e. finite - infinite Grégas - Ustergov)?, whose existence is presumed everlasting’ — it has always been, existing in its own right. According to the Pythagoreans, the primordial being was invariable, unified and finite, i.e. indistinct, hence uncountable. This primordial being is identified with the number One, the initial unity or Monad. This One, then, which appears at the very beginning, the first to be applied (16 npürov äguoaëlév), attracts to itself the infinite and confers it a limit. The Pythagoreans categorically state, as is confirmed by Aristotle, that when the One (which was formed either out of planes, surface, seed or other untraceable substance) came into existence, immediately all 1. Cf. J.-P, MIGNE, Patrologia Graeca cursus completus (PG), val. 3, pp. De Divinis Nominibus, pp. 585-996. 1119-1122, especially 2. For the Pythagorean ontology, cf. CJ. DE VOGEL. Pythagoras and Early Pythagoreanism, Assen, Van Gorcum. 1966; 3. A. PHILIP, Pythagoras and Early Pythagoreanism, Toronto, 1966, and W. BURKERT, Lore and Science in Ancient Pythagoreanism, Cambridge, Mass, 1972, 3. Metaphysics, A 5, 986 a 15. 4. The term everlasting or sempiternal is used in the sense of ARISTOTLE, ibid., © 9, 1051 a 20; M 8. 1073 b 6; N3, 1091 a 12 and A 6, 1063 a 14; 33; 35. 5. {bid., N 3, 1091 a 14.

those parts of the infinite which were veryFane ro he One became attracted van bounded (elAxeto xai Enegalvero) byt e ini e. which een ben the bound to the pimordial finite being? This, of course, was a „on da which not only for the Pythagoreans, but also for the entire anciens bine nni a strongly connected with the void. Thus, the finite and in variable being(e PET ial being) is restricted by the void (the non-being) t at as i i This unlimited void, that sets the bound, intervenesinthe beginningMiche if O us erate ck gorean ontology and breaks up the inite eing — the Lane between its two parts. This invasion or interpolation is tradition anthropomorphically and metaphorically, as the resp late algo boundless void or the inhaling of the boundless (elonvon a ereathing an maintains that the universe performs some kind of respiration y that the Prine boundless void that surrounds it. More specifically, hehae nat dhe on goreans had claimed that the void exists and intro eri da ie he Wor on 5 aus > ne the infinite air. The world inhales the void whic things, as if it were what separates and distinguishes t ne Mi «ot actinguighes Nn remains true primarily in what concerns the numbers; for their nature. Through the inhaling of the boundless a continua! re; ; siì dad ° and the numbers are formed as separate entities. Thus, from t n mona Pythaporean formed and then the rest of the numbers follow in such a way that the gore i iverse constitutes a copy of natural numbers. That Pythagoreans a great ontological importance to numbers is an indisputableO dered dere i stituted the essential elements of the existing world. te entity with its own ontological content and properties that remair be discovered through research. Thus the Pythagorean ontology is an ote bains beings one, according to which the properties as well as the relations among cannot be expressed by any other means than ratios of natura un cr | uri sn music. The numbers |, 2, 3 and 4 which once they are summe! / give the pare tetractys or the decade — became the basis of Pythagorcan onto he Pure ontological terms of which are: identity, otherness, rest an me i 7 se ro a Alexandria? asserts after Plato®. They also are incorporated an transe nded in the Areopagitic writings®, this being considered not as a logica consegue ee pu as different modes of a free communication, relationship and reference (o) he st per substantial One. The One represents Being. It is the progenitor and foun crane universe. From this very One, through a natural split, resulted number wo, which represented the straight line. From number two number three, whic Tepes tec the triangle, the simplest plane figure. From number three comes m mere di identified with the tetrahedron, the simplest solid body. Pythagoreans be von Ê the discreteness of the universe, out of which counting emerged. Num THE TRANSCENDENCE OF THE PYTHAGOREA N ONTOLOGY 27 closely related to the form (idea), according to a major strand of Greek thought. To count things together means that they belon g to the same form. Co-counting Presuposes close relation, and this is the etymo logical meaning of the number. The word is relate d to the root art: close relation; and ratis: a raft, intert wined Pieces of wood. Thus the original meaning leads us to the concept of a morphologically formed entity and this is the reason why the numbe r (dqu@6c) can be subsumed under the Greek terms /ogos and idea. Everything that is not a number has for the Pythagoreans a subordinate meaning. However, as every number is finite, the bound constitutes a characteristic of numbers and hence of all things. Whatever lacks bound and appears as infinite constitutes the defective element of reality, out of which, according to Philolaus?®, Jalsity, disha rmony, absurdity and envy derive. Thus the Pythagoreans compared infinity with matter, which cannot undergo either counting or specification, and has no limit. In this way the concept of matter as a senseless and unspecified element was introd uced: an element that refutes every specification or reason and is considered as the source of every ontological and ethical defect. Diogenes Laertius, in his valuable compendium!!, mainta ins that Pytha goras and the Pythagoreans considered the monad as the beginning of all things. From the monad resulted, or rather was created, the indefi nite dyad. All other numbers were considered to have derived from the mona d and the infinite dyad. From numbers resulted the points and from them, the lines. From the lines came the plane figures, from them the solid bodies and finall y the perceptible bodies, which consisted of four elements: Fire, Water, Earth and Air, that is the tetractys in nature, which was considered sacred and the source of eternal nature. These elements change. Through this process of changing the World becomes animated, intelligible and spheroidal, which in its kernel holds the spheroid and inhabited earth. Although Pythagoreans identified God with the Monad ~ the One - they have not left any indication of ever reaching a clear concept therof. By the same analogy according to which the soul mainta ins, within the human being, its moving cause, God was considered as the movin g cause of the universe, being symbolically presented as the Monad. Thus, next to the monad, i.e. in the burning kernel (16 év 1@ xévrow 70g), the Pythagorea ns placed the metaphysical Monad God. Since all numbers are referred to the monad , from which they come, by the same token the incorporeal and sempiternal ontological elements, which are registered with numbers, are referred to a primor dial ontological principle, which was symbolically represented by the monad, depri ved of generation (fig oùx Eon Yéveotg). This monad, then, is identified with the Pythagorean God and its existence is considered as the cause (the moving force) mony of the universe. of order, summetry and har- -— 6. Physics, IV 6, 213 b 23-26. u . 7. CE About Geometricals, vol. 4, Definitions (Heiberg). 8. Sophist, 254 d - 256 b. 9. De divinis nominibus, PG 3, IX, 909 b - 918 a. 10. Cf. fr. 11 H. DIELS - W. KRANZ, Die Fragme nte der Vorsokratiker, Weidmansche Verlags buchhundlung. 1952, p. 412. The notion of infinite, negative since the Pythagorcans, became positive only with Plotins. 11. Cf DIOGENES LAERTIUS, VIII 25, in H. S. LONG (ed.), The Lives ofthe Philosophers, Oxford Classical Texts, Oxford, 1964 (also in Loeb Classica l Library).

Neoplatonism is the last philosophical system of antiquity which imme” diately precedes the Areopagitic writings. Besides rational) Wopns ices in order to seek the ultim aerate ate , irratione means i an d practices also used some irrational increased aware ad » ith, introspection, > love, trance and such as enlightenment, faith, ness!?. Due to this it has often been believed that Neoplatonism is devoid of scientific accuracy; thus a distinction between rational and rand phi Othe CONE: ine SY: is considera sideration leads to a serious misunderstandi This became necessary. See irrati i s not attributed to the infrastructure is oeT he Pp fuer that philosophy term irrational i and explici icit form of knowledge, but to its biectives, objectives. The Heren as a systematic re logies as îand analog i philosophy ilos I tends; to |use images, symbols Neoplatonic effective means of expression in its effort to acquire wider perspective and pro c thod i reactions does,$ by no |means, imply that it uses irrationa voke emotional of thinking. In the Areopagitic writings one also finds analogica! and me i on n an & anc eliverance!*, salvation irrational experiences, like love, ecs tasy, i zeal, faith, i irrati but the basic method of thinking remains strictly rational, taking into account the reason of truth in comparing things of different qualities and in using ; a outof the cleares i comess ou n dealing with i the analogy which finest rule of truth’? 15 or in picture!®. Finally, and very significantly, it stresses that one must know all natural rings Me Use € these writings, Ire of 1 cordi to right reason 17, *. AA pprominent feature things according F i i an p “ I qualitative Platonic 1 in the m ore and analogies, of symbols, pictures tonie sense, than in the quantitative Aristotelian one, is obvious. However there exists a noticeable transcendence of human reason by tight reason, Nalso i ne very close relation, which leads to their union within the context of Areopag ae | | ntology. Dionysius strongly maintains!? that the primordial ontological principle È not divisible and dual, self-contradictory and differentiated, but simple, single am | unified. It is impossible that two contradictory origins of beings co-exist. „maken no sense to say that two diametrically opposed things come into existences tor one single source. Hence, we can not accept any dyad but only the mona ve oh principle. He therefore introduces the first ontological pair union - disti an (Evwais - Suéxovats) for the Absolute and the pair unions - distinctions cin p ua ) in the relative, built or created «world» and uses three main Mustratione 7 or ci to explain these concepts. From this first pair numbers are natural y orme through distinction and discreteness. Although Dionisius’s ontology remains NW close to Neoplatonism, he does not accept the theory of emanation, but constan Ny speaks of creation. His consideration of the summum bonum does not seem to partially ethical, but entirely ontological. 12, PLOTINUS, Enn.. VI,9, 10. u 889 13. De divinis nominibus, PG 3, IV, pp. 693 b - 736 bi also VII, pp. 865 b - 873 à and VIII, pp. 88° :-897 €. | 14, fbid., PG 3, 1, 1, p. 588 b: ratà tov ainov tig ddnBelag hóyov. 15. ibid., PG 3, 11,1, p. 640 a: boreg ted xavova wökkotov bAnBelas. | 16. Ibid., PG 3, IV, IV, p. 700: natä tov airôv ths êugavoûs elxóvog Aöyov. 17. Ibid. PG 3, IV, XI, p. 708 b: béov eldévar xatà tov dgfdv Adyov. THE TRANSCENDENCE OF THE PYTHAGOR EAN ONTOLOGY 29 The transcendence of the Pythagorean arithm etical ontologyof the finite and the infinite by the circular and bilateral Areopagitic ontology of union and distinction can be summarized in the following four main points: (a) The dualism of the ontological principle of the Pythagorea ns, which derives from the contradiction existing within the first Pythagorean ontological pair of finite - infinite and is transcended by the unity and simplicity of the unitary, undivided, non - contradictory, bilateral and circular Arcopagiti c ontological pair: union - distinction. (b) The appearance of the material element, which the Pythagoreans identified with the indefinite dyad by presenting the One too as matter, In turn it expresses the irrational as well as the evil, even in Plato and Aristotle, and is transcended by the Areopagitic acceptance of the ex nihilo2! creation of matter and its property of goodness”? in a saltus fidei manner. Hence a different essential consideration of the void as a complementary form of the Being and not as non-Being. (c) The arithmocentric reductionism of the Pythagorea ns, which has already collapsed together with their unrevised ontology, accor ding to which there is a reduction of Geometry (hence Cosmology) to Arithmetic, is neither transcended by the inversion of Pythagorean reductionism, as carried out by Plato® , towards a geometry, nor by the presentation of a new arithmetical ontology? in an effort towards the unification of number and form (tôéa) within the concept of formal or ideal number, as in the Platonic Parmenides, that was transmitted to the Neoplatonists?. All the above are transcended, taking into account the arithmetical as much as the geometrical ontology”®, Both depict equally well reality within the frame of the circular, bilateral and universal ontology of union and distinction of Dionysius, (it unifies them and distinguishes betwe en them without making the one necessarily reducible to the other). And (d) The nonexistence of a God, master and creator of the universe (God’s Ruling - Creation) according to the Pythagoreans. However, the identification of God, through a simple logical process and natural reduction, with the indefinite, non-sp ecific One, i.e. the metaphysical monad next to the burning kernel, which all numbers refer to, and which is not transcended even through the identification of the One with the abstract concept of — —__—___ 18. Ibid., PG 3, IV, XXI, p.921 6,92) 4.2. 19. /bid.: aan yao dväg ot Apyri, povas à’ Fata náons duddag dayr. 20. fbid., PG 3, 11, IV, p. 641 bi also in U, V, p. 644 4 and II, VI, p. 644 b. 21, V. LOSSKY, Essai sur ta thelogie mystiqu e de l'Eglise d'Orient, Paris, Aubicr, 1944; cf. mainly Chap, V; also in English translation 1957 and in reprint 1970. 22. Op. cit, PG 3, IV, XXVIII, P. 729 a: àAA' oùbé tO NOAWÜgUVMTON... “Ev On 1 xaxôv, @s quo, xa 6 Tin... “AdMag te, RÓS h Dan Karóv: 23. K. POPPER, The Open Society and Its Enemies . London, Routledge and Kegan Paul, 1945: cf. Chap. 6 Note 9(2) and Addendum 1957; also Conjectures and Refutations, London and New York, Routledge, 19895, pp. 75-93, 24. Parmenides, 127 b - 135 c: 137 - 160 band 165 b - 166 c; also Philebus, 14 € + 19 h. 25. PLOTINUS, Enn. VI, 6, 15 and VI, 9 (About Numbers), 26. De divinis nominibus, PG 3, V, VI, pp. 820 d - 821 a. 27. Ibid., PG3, V, VII, p. 821 a, 821 b: “AdAG nat èv Tf SAN t@v Av quos Raves ol tiie xa fxaotov Gbaews Adyar ovverAnppévor eloi xaté Hiav dovyyutov Evaov.

the summum bonum? and its relation to the theory of emanation?’ propounded by Plato and the Neoplatonics. However the above process is transcended through the acceptance, by the slatus fidei, of the entire thearchy - God's ruling (tiv GAnv Oeagxlav)?®: (i) as Monad or Oneness, (ii) as Triad or Trinity, (iii) as the Cause of beings, (iv) as Wise and Benevolent and (v) as loving mankind — as asserted in the ontology and the theology of Dionysius. (Athens) Andreas PAPAMICHALOPOULOS 29. Timaeus, 41 d; cf, PLOTINUS, Enn., V, 1,8 and V, 2, 1, 28. Symposium, 211 a and Republic, VI, 508 e 1 - 509 b 10; cf. PROCLUS, The Elements of Theology, 13. 30. Op. cit, PG 3,1, IV, pp. 589d - 592 a.