Saadyah's second theory of creation in its relation to pythagoreanism and platonism

EFROS | e LD SAADYAH'S SECOND THEORY OF CREATION IN ITS RELATION TO PYTHAGOREANISM AND PLATONISM* Cui By ISRAEL EFROS The second of the thirteen cosmogonic theories, discussed by Saadyah in Amänät, ch. 1, namely that all things were created from eternal spiritual substances, is generally presented as a composite of atomism and Timaean Platonism, and hence corresponding, in its atomic aspect, to the second cosmogonic theory in Saadyah's Tafsir on Sefer Yesîtrah.: But here, as Malter notes, a difficulty arises. For in the Tafsir, the views are listed in the order of increasing acceptability, whereas here the order is that of decreasing acceptability; so that the view which is here next to the most reasonable ranks there as next to the Malter offers a solution, but there are other most repugnant. difficulties. First, atomism constitutes the ninth view in the Amänäl. Second, here a creator is assumed, whereas in the ninth view atomism dispenses with a deity. Third, it cannot be a presentation of Greek atomism which maintains that atoms have forms and sizes, nor of the Arabian type according to which atoms are indeed spaceless but continuously created. Fourth, Saadyah was too sharply discerning and too fond of piling up arguments and views, for the sake of the mere weight of numbers, to group together two such discrepant views as atomism and Platonism, a combination which is somewhat * Technical considerations necessitated the transliteration of Arabic quotations into Hebrew characters. 1 Sec J. Guttmann, Die Religionsphilosophie des Saadia, 45, n. 2; M. Lambert, Commentaire sur le Sefer Yesira par le Gaon Stadya de Fayyoum, 17, n. 3; MH. Malter, Life and Works of Sazdya Gaon, 203; M. Ventura, La Philosophie de Saadiz Gaon, 114, 117, n. 100. 3 Malter, l.c. Comp. D. Neumark, .Toledot ha-Pilosofiyyah be-Israel, II, 181-191. In: Louis Ginzberg jubilee volume-New York 1945,p.133-142

12) EFROS to Democritus that he reeven said to have wished a i ta RE a ls raine to burn En kat waite inte the details of the text, vai a follows the Timaeus, where, he says, Plato qua that the el sis of the world as moving from the point the m the line to the plane, and then to the various acne the line, wer m which God created all spheres. This Pea s theory of m,Ic ra his sources, fitted intoatoPlato' m mis and Platonis Ee word in a combination of res which Neumark ped. But where didiints? hich corporeal existence develoworl Quite find in the Timaeus that the d came fromLar it re w : Il soon see. $ : ary is true, as we sha ide » it asa o thematical points” is correct; but evidently ini ma ral phrase for atoms, or ite cre : a i urce,s for the ts te Di VAR. agrees on as of to that source, plier m sthe implicati : phrase he might have been led to a different source for the second view. es 4 Fa nc to show that this second try V nm, to à BA We age lee with some Platonic ee , ha Taf nts comme cal exegeti some light : er ‘a to identify this view with the eighth in the io i des Ela 1 In Metaph. 986al, meri a regni ofce all of th , the elements of numbers are Rd in Afelaph. 987a19, that number is the pri pari er ne (sce also 1080b18). The basis for this ari sine a Fe of the world is the correspondence of ee nia mber one, as is shown by the Pythagorean del The of = nt. povàs Btow éxovoa, a unit having position. ol a pol id’ a Thomas L. Heath, The Thirteen Books of Euctid's o entse I, 38. Elem . 4 Op. cit. 120, 154. Enrly Greek 1080b 20,32. See also John Burnet, ( ;E dad Metaph., arly S Simil ‘ . Taylor, Plato (N. Y., 19 36), 505. D AVR. yp 6 Sce .. Arist. àong e RE A imi hahrawal. Nidal, ed. Cureton, 270: oa o an mure en yy ieri 22, the equation is: point=1, plane =4, soli Jaw. a bar quid 122Np0 ‘D Abaupo ‘D num PAR 4 , h solid =8, 13] SAADYAH'S SECOND THEORY OF CREATION 135 implication that the point has minimum volume was-combated by Parmenides and Zeno, so that Plato came to regard the geometrical point as a “geometric al fiction,” and to speak of “indivisible lines”? which, according to A. E. Taylor,® means infinitely divisible lines; for a line is a continuum and will always break up‘ into lines, never into points. He defined the point merely as the “beginning of a line,” i. e. zero, and assigned the role of indivisible magnitude and the primary real of all things to the plane.’ Aristotle like Plato, and like Euclid in his second definition of a line, takes the point as “the boundary of a line," and regards the line as essent ially linear and hence does not consist of points but alway s of lines.“ The Arabian neo-Pythagorcans, the /khwän al-Saf a, blended these two distinct views, defining the point together with Plato as the beginning of a line, i. e. as non-magnitudina l, and at the same time, together with Pythagoras, as equivalent to the arithmetical one.” Among Jewish thinkers, we find the Platon ic-Aristotelian view dominant, but Gabirol, Abraham ibn Ezra, and Albo follow Pythagoras." thus following the Ikkwän al-Safa. See Dieterici, “Zahl und Maass nach den Arabischen Philosophen,” ZDMG 18 (1864), 694. ? Arist.ggAfetaph., 9922 20, $ Op. cit. 506. 9 Arist., De Gen. el Corr. 316a 30; De Coelo 298b 35. See also Heath, op. cit. 156, * Topics, 141b 20, 21. " Physics, 231a 24-26, 231b 15-16; Metaph. , 1016b 26. ® Dieterici, Ichwan Es-Safd, 292: Aysız vo em 55 on on nba Aupıbr 11998 Aynız vo qoñnbr bap Ade ambi bad ombre. But entirely in a Platonic mannat on p. 591: 559% jo «na in 01 Ans ba: 855K Duno. 5 The following references show the Platoni c-Aristotelian view na anpm opa non am ama ampan mani (45 Sana pres ‘25 mmorn 250) ipa nxp ¿e en ‘na 00998 9 nmaznm amzon) m bi at 0'937 09 ‘2 PP3 398 non MOI OR) op>anon 70 amoo nm Japon pon 13 MVD IWR SDR Rin pa nom 12 M on yy) nmpo 2300 1909 mor Rd ODIO DA 0'9901 1399 103 1305 PIA me Wisp IP n*bon AS mes jan omar ‘95 AT... pK Wenz ATP NN? (3.4 Sea pax “sd ody MI”) YT ¿(1 puo „wor AITIPIO 23219 KIT IpAZ DONI nun xd binanz no 93 piro... pon ame Pon mpatnaa ax 99 mob vanni wpa 345.289" ‘win 023 mondo) ponno ‘nds Sat ND 209 wann No +5 ANp IMD pI ea ono nea bo) BAD mam mebon vo 19 pm ,(45, 47, 48 mn spp mom

EFROS [4] her number is imThere was another controversy, as to whet Aristotle, the sie goreanism counts geometrical relations together with numbers and letters as elements of things; and Alexander Polyhistor epitomizes the Pythagorean view as a causal hierarchy: From numbers — points, from points — lines, from lines — planes, from planes — solids and then the four elements.2° Thus two distinct and opposing trends were blended under the name of Pythagoreanism, assuming points as non-magninumber, the Pythagoreanism as maintaining thatrocs — as maintaining ca Aver ;" ted -crea all things, is the first tances and I at the objects of mathematics are bodilessandsubs according to saac rsalia;* points are substances like univeagor reb. Shem-Tob,'? both the Pyth eans and the Platonists tudinal, transcendent, and corresponding to, yet apart from; numbers. According to Plato, numbers and the ‘‘mathematicals’’ — except the fictitious points — are eternal, whereas in the Pythagorcan view, presented by Shahrastani and Alexander Polyhistor, both numbers and points are created. We are now ready for the exegesis. garded number and magnitude as separable. reality of number One other issue. To the Pythagoreansin,, the ituting the and is the reality of the points residingintroducedconst y Hi hier a essence of, things. Plato however, ticals (rà pa9narch x) pari Being, and distinguished the “mathema grade te media inter an from number or Forms, giving them al and unchangeable,, differing from sensible things in being ctern Form itself is in each from Forms in being many alike while the Thes e ‚mathematicals case unique” (Arist. Metaph. 987b 12). not points, ns, are taken by Taylor‘? to be geometrical notio, but1. e.lines, planes, which are a “geometrical fiction” to ,Plato of ation separ this solids. And again a fusion took placetwoand dent scen tran nct disti number from geometrical notions as (43 wpbp ova) aan nies). For the Pythagorean view, see Gabirol, Fons 2. “The second view," Saadyah says, “is that the Creator of bodies has with Him eternal spiritual things from which He created these composite bodies.” From the sequel we learn that among these eternal spirituals are points; consequently the others must be numbers and letters, which Pythagoras, according to Shahrastani, included among the elements.” All these are spiritual in the sense of incorporeal. The assumption of points is un-Platonic, that of transcendence and, as in Saadyah's polemic, of unspatiality is un-Pythagorcan; yet it all passed, as we have seen, under the name of Pythagorcanism. One might take the spirituals as signifying mind, soul, and Ayle, all of which the Jkhwan al-Safä call spiritual, or the substantiae es, et quantilus quae subsistet in Vitae 11 22: Numerus resoluilur in untlal a sunt unitates quie scilicel aci| substantia resolvitur in puncta, el punct ibn Ezra on Ex. 26:6 wr nn 73de ham Abra in materia quie est substantia; WT pr MIN 121 Op. cit, 269. » Diogenes Laertius, VIII, 25: *Apxñv uèr arkvrwr povada. tx de rs povados Gbpraror Övada ws Gv vAny Tf povads árriw övrı Lroorfjvat. tx dè rs povados Kal rijs doploror dvados rots apiWpobs, Ex dé rav dpWyar Ta onpeta. tx dì robrwv ràs ypaupas, dE Oy rà trireda oxpuara. &x Öl rap Emrédwv ra oreped oxuara. Ex dè robrwr rà alo0nrà awuara, dv koi rá grouxeïa elvas rérrapa. Comp. Arist., Afetiph, 1080b 20. MINKE 329 arın sapa ban 9919 ame WIT! 72237 077 N99) aps MNT 093 Woo "nce ANN abo pann ab Abo, Ikkarim ch. 10 n dywwa . "a Map, 1090a 20-35; 1099b 5. Sce also 937b 25-28. Comp. however a Op. cit, 269. Gomperz, Greek Thinkers, 1 104. » Dieterici, Ichwan, 3: nino Ayema ami powder... uma ami in bppdba pode jo nwo Auema ami bibi “drab... boybn yo. See also Palqera's Hi-mebakkesh, 107: 011371 ‘> ovina 0270 Ding ON ys07 01377 Yaw 19 vorn vanm by han baza vnnm quam pan mista pan 59 on 0D ou 15 Shahrastani, op. cit. 267. 16 Horten, Die Metaphysik des Averroes, 44, 45, 49, 121. + Quoted by Wolfson, Crescas, 395. 137 beings, or even in some hicrarchical form, was ascribed to the Pythagoreans. Thus Shahrastani in his exposition of Pythato manent or transcendent. Accordinbeg numb ers — not separab sa to gs thin real d goreans “suppose h real things consist ; numbers, however, but numbers of whic number separable assume whereas the Platonists, “who makee... and similarly with the that it both exists and is separabl ” Here too the Platonic spatial magnitudes of mathematics.ncnt ome contention was grafted upon its oppo . Shahrastani princip eo o moya wie KON... navnoa. SAADYAH'S SECOND THEORY OF CREATION 1 = cit. $14. Cf. J. Burnet, Greek Philosophy, 1 314-318. tini

EFROS [7] SAADYAH'S SECOND THEORY OF CREATION 139 spirituales of Gabirol in Fons Vitae, II, 24, quae sunt natura are composed of lines, and lines of points,” and he might also mention the Mutazilite view that “body is composed of atoms, i.e. points.” It would seem then that Israeli identifies points accepted mind, soul, nature, and hyle, corresponding, though not number but only numbered (iyo>my), to the first four elemental numbers. Still, numbers and letters are more analogous to points; and we shall see that, like Shahrastani, Saadyah himself in the Tafsir and also Gabirol in Fons Vilae group together these three elements. The Zkhwän al-Safa speak of with atoms; in fact he ascribes the point-theory to the atomist Democritus. But this ascription is erroneous, for Democritus maintained that bodies cannot be composed of points which el tres animae et intelligentia. Such an interpretation would not differ essentially, for Pythagoras, according to Shahrastani, points, as well as of line and plane, as Spy and ‘om, which terms are epistemological equivalents of the metaphysical “spiritual.” o “The adherents of this view,” Saadyah continues, “imagine that the Creator assembled from amongst them (i. e. from amongst the spirituals) tiny points which are the indivisible parts.” These are not atoms for reasons given above, but geometrical points which Euclid and Aristotle defined as indivisible. Gabirol, in Fons Vitae, 11, 16, cautions against confusing the point with the atom, the former being a part of the body only accidentaliter, nec naluraliler, nec essentialiter, whereas the latter is part of the body’s essence. Isaac Israeli too, in Sefer Yesodot, 43, differentiates between them; although, at first blush, the opposite scems to be true. He states that an opponent of his Empedoclean theory of elements might cite “the sage Democritus” who said that “body is composed of planes, planes oo on 190 PTT TINA enni nadir mbhan, Shahrastani, op. cit., 268-269, in his presentation of Pythagoreanism speaks of mind, soul and nature as elements embodying numbers 2, 3, 4 respectively, and also of the hyle as sensor mnt. The Ikhwär however (see Dieterici in ZD MG, XVIII, 693, cited supra n. 6) make the kyle correspond to 4, and are followed by Palgera, op. cit., 105. 23 Sce supra, n. 22. from AYpy Ronn LL Dieter, Ichwän, 293-294. Aoprde nin qu Dip:sn.wands... Soc also Kilab Ikhwdn wd eri nb nde vn Arypybn Aupıba 199 ad ati nb vo al-Safa, redacted by Ahmad ibn ‘Abd Allah (Bombay, 1887), 1 53-54, where mention is made of nuo Som 55 ‚Arypy Aupa "pp nuo “py 53 ¿py ñomn Yom oo! om, For the meaning of am sce Goichon, Lexique de la langue philosophique d'Ibn Sind, 442. Sce also Dieterici in ZDMG cited supra, n. 6. % Arist., Metaph., 1016b 26. are only extremities of lines. That it is the Pythagorean points that Israeli has in mind, and that, far from identifying them | with atoms, he really separates them, is shown by the fact that he combats first the point-theory, and only on p. 49 he turns to the Mutazilite doctrine and there he raises the question whether the atoms are spatial, a question that does not occur in his argument against “Democritus.” The expression” atoms i.e. points" is therefore his opponents’ contention, not his own. Thus a distinction was made between points and atoms, and we should not confuse them in the interpretation of our text. . “And He made out of them,” Saadyah continues, “a straight line and then He cut that line into two halves.” Here, where scholars note a change of source and the beginning of the parallel to Plato's Timaeus, we really discern the unity of design anda coherence with the first part. In Timaens 36b 5, there is no mention of a line but of a fabric woven out of the soul-stuff the Same and the Other. of Why does Saadyah speak of a line? cause the nature of this creative act is different from that of the Timaeus. The Timaean band of soul-stulf is regarded as cosmic matter; whereas Saadyah, unlike Plato, begins with the point which can only yield a line, i. e. length. The same reason accounts for the next divergence: the Timacan band is split _lengthwise; Saadyah does not say “lengthwise”, for such a division is impossible in a mathematical fine. Then the two halves were fastened, one across the other like the Ar. Lam-Alif or the letter K.” This is also found in the Timaeus as well as in the second part of Parmenides' poem, the * See Ingeborg Hammer Jensen, “Demokrit und Platon,” Archiv f. Gesch. der Philosophie, XXIII (Berlin, 1910), 105. ” Sec Guttmann, op. cil., 46, n. 2.

EFROS part which is Pythagorcan.* But here it has for its additional purpose to generate a plane by the intersection of the lines. “Then He cut (Ar. sonyop Tibbon 13) them from their point of fastening and He made out of one of them the all-surrounding sphere, and out of the other — the smaller spheres.” In the Timaeus, the Demiurgus bent cach band around into a circle. The word ‘cut’, in Saadyah's text, seems pointless. Tibbon mistook the meaning of the Ar. xonyup which means here ‘he made «them cross’ (r. perhaps: konyops). The same expression in a similar context is used in the Tafsir, where it undoubtedly has this meaning. The Timaeus now proceeds to discuss the genesis of diverse subjects until 47E where the discovery of “necessity” in the paradise of reason compels the author to begin his account anew. The notion of space is introduced, and then we are told how God formed the four elements “by giving them a distinct configuration, by means of shapes and numbers” (53B). Here the number-theory makes its appearance. From half-square triangles there was formed the cube whichis the appropriate form of the earth-corpuscle, and from “half-triangles” there came into being the tetrahedron (fire), the octahedron (air), and the icasohedron (water). The dodecahedron was reserved "for the whole, adorning it with constellations.” This is Pythagorean,?? but it does not begin back enough, not, of course with the point which Plato regards as a “geometrical fiction,” not even with the line which he does posit in Laws 894a as an px, but with the plane whichis his cosmic unit, thusignoring the lirst three cosmogonic steps in the Pythagorean account, summarized, as stated, by Alexander Polyhistor. Saadyah's statement about the geometrical construction of the four elements does not constitute a revision or a second account, but flows entirely along Pythagorean lines from his previous statements. + [9] SAADYAH’S SECOND THEORY OF CREATION 141 According to him, God formed “out of those spiritual parts” (i. e. the points) a conic form, an octahedron, a dodecahedron, an icasohedron and created from these forms fire, earth, air, and water respectively. The geometrical forms of these elements do not agree entirely with those of Timaeus, but the Zkhwän al-Safä also had a different arrangement. 3. Thus the second view is not a composite of atomism and Timaeanism, but Pythagoreanism as it was understood about the time of Saadyah. Now what relation does this view bear to any of the views in the Tafsir? Hitherto scholars thought that the doctrine of the Sefer Yesirah or the eighth view of the Tafsir was disregarded in the Amänät-enumeration of the cosmogonic theories, either because Saadyah did not take the Sefer Yesirah-view seriously (Guttmann), or because he deals here with views which are either positively true or positively wrong but not with those which are just tolerable (Malter), or because he did not reject this view as he did the others (Neumark).# But if our interpretation of the second Amänätview is correct, it becomes identical with the eighth view of the Tafsir, i. e. the stand-point of the Sefer Yesirah. They are both Pythagorean. True, in the Amänät the spiritual substances are viewed as eternal, whereas in the 7ufsir they are created, but, as Saadyah himself states in the seventh view of the Tafsir, the anteriority of numbers and geometrical figures is acceptable if rÉarded only in a potential sense, objectionable if taken in an actual sense. Hence, in the Amänät, in the list of objectionable cosmogonies, he gives the view with its objectionable Platonic feature which includes actual anteriority and eternity, whereas in the Tafs?r, presenting it as the Abrahamitic view, he » Dieterici, Ichwan, 439: anna o Anaioda Absnodn busonbn fooddm Anobx 14 Senna Souder RADASDA mucbn gambi 13 Tada dore om orbpa 14 Tbe baron RADAR mobs Aunohda 14 Probe born AAVADON muoba 3 Sce Burnet, op. cit., 187, 40030 Apnp 129 "fin vi Faboba Soudan AADAD finyap pray). This does not » Lambert, op. cit., 83: nahbAnı var p Aopnod aus bn DBS RIK TDD agree, as Dieterici notes, with Euclid's Elements. XIII, XIV, XV. ‘by Nagya ROYAN JO eni Anyanoı ohhh vamp Alapio Rows con ARS 1 neoojo) bros buon RSya Rasys Apunpoi fya. See also n. 33. # Taylor, op. cit., 458 n. 1; Burnet, op. cit., 292 ff. Sec Dieterici, Die Lehre vom Weltseele, 3; Propadeutsk, 30, 129. Palgera, Reshit Hokmah, 43, speaks of Euclid as a Pythagorean. “na opr. » Guttmann, op. cit., 26; Malter, op. cit., 204; Neumark, op. cit, 191.

EFROS carefully specifies that numbers and letters are not to be taken as abstract and separable, but, that is, in the originally Pythagorean conception. The various cosmogonic steps of the Amanat are reproduced in the Tafsir as follows: “He (the adherent of this view) does not posit them (the 10 numbers and the 22 letters) as pure and separated. He maintains that He created the air and deposited there these 32 things. According to him, the air consists of distinct particles which number traverses (so Lambert. Barzillai however: "200% mann). And when it moved forward according to straight and oblique lines, it generated figures.’ In this account, the “air” is a monotheistic adaptation of the Pythagorcan-Platonic receptacle or xwpa. The distinct particles are the points. Number traverses (or cuts) them, because each point is a numerical one. The straight and oblique lines, like the Lam-Alif of the Amänät, make the planes. In another passage in the Tafsir, Saadyah says: ‘Thus when He drew in the air straight lines in circles, triangles, and squares, * and also traced oblique lines in circles, triangles, and squares, there came into being, out of the bending and crossing of one line over the other, plane and solid figures.® The bending and : crossing is reminiscent of the bending and crossing of lines to , form spheres which we have noted in the Amänäl. Gabirol also identified the point-theory, or the second view of the Amánát, with the cighth of the Tafsir, which is the| theory of the Sefer Yesirah; for in Fons Vitae, 11, 21, after. stating the gist of his teaching that quantity subsisting in sub- : stance is a conjunction of unities, which he explains in the sequel as being points, he remarks with unmistakable reference to the cighth view of the Tafsir: ac per noc dictum est illud, quod composilio mundi non eventt nist ex lineamento numeri et litterarum in aere. n Lambert, op. cît., 10: sind pos nus Sip’ none App Agno ay? odo im Sy Nava and aim ipa hayon Add ende ADR pe TN te Abb ata ay TN ebeoos nina Alnyını Ab'pnoo od. See supra n. 29. The Heb. version in Barzillai’s commentary on the Sefer Ye,irah, 272: espino) inpbm man 2 won inonm.