The True Perplexity: Maimonides' Guide II<24

8 The TruePerplexity: The Guide of the Perplexed Part tt, Chapter z4 TZVI LANG ERM ANN f.,. i:l' c :la # tr $ f, :l THn incompatibility of the models used by professionalastronomers with the basic tenets of the Aristotelian world-view is the issue discussedby Maimonides in ii. z4 of the Guidc of thePerplexed.tOnthe one hand, the epicyclesand eccentrics employed by astronomersseem to violate the principle that the motion of the heavenly bodies be uniform, circular, and about a fixed centre. On the other hand, the results achieved through the use of these very devices are startlingly precise. This, Maimonides says,is the 'true perplexity'. In this paper I wish to look at three aspectsof this'true perplexity'. Both philosophers and astronomers had expressedthemselveson this problem, so I shall first sketch Maimonides' place among these thinkers. My second and main concern will be a comparison of the views e4pressed in the Guide with the rules laid down in the third chapter of the 'Laws Concerning the Basic Principles of the Torah', which forms the first section of the Mishneh Torah. I shall be particularly concerned with rwo questions: did Maimonides consider the true configuration ofthe heavensto be inscrutable?and can a close reading of both texts offer any clues about this true configuration? F'inally, I shall mention the views of some of Maimonides'followers on these questions. I The mathematical models presented by Ptolemy in his Almagest and the three-dimensional explanationsproffered in hisP/anetaryHypotheses t All quotations and page numbers come from the translation of the Guidc of the Perplnedby Shlomo Pines (Chicago, 1963). ]|rr60 Tzai Langermann The'True Perplexity' were criticized by medieval scientists and philosophers for having violated principles of Aristotelian natural philosophy., A number of prominent Spanishscholars,whose objectionswent hand in hand with the interest in that country in reaffirming the true Aristotelian doctrines,participatedin this criticism. Ibn Baija, perhapsthe founder of this trend, is known from Maimonides' remarks in Guide, ii. 24, to have written on this problem. The astronomer al-Bitrfjr, who himself developed an alternative system, albeit an unsatisfactory one, informs us that Ibn fufayl, the next great Spanish philosopher, also took an activeinterest in this issue.3Severaldetaileddiscoursesof Ibn Rushd, the greatest representativeof the Spanish school and Maimonides' contemporary, exist on this problem.a Maimonides tells us in the context of another astronomical discussion(ii. 9) that he read texts under the guidanceof some pupils of Ibn Baija. This fact and the space given to Ibn Baiia's views at the beginning of ii. z4 demonstrate Maimonides' connection to this Spanish school.sHowever, the subsequentdiscussionin ii. z4 shows that Maimonides' investigations went beyond what we know to have been the rangeofissues discussedby the Spanishschool.For example, by simply computing the planetary eccentricities in terms of terrestrial radii on the basis of the values found in al-Qablgr's Epistle Concerning theDistances,Maimonidesnoticed that the centres of the eccentric orbs of most of the planetslie betweenthe spheresof other planets(e.9.the centre of Jupiter's eccentric lies bet'weenVenus and Mercury' etc.)' and he was thus able to raise a strong obiection of his own to the Ptolemaic configuration.u Maimonides also brings in the necessity of positing intervening spheres,the existenceof which only raisesfurther problems regarding the location of their centres and their own proper motion. Maimonides has learned of these spheres from a treatise by 2 Pines deals briefly with this issue in his'Translator's Introduction, to the Guide, pp. lxiii, llai-l>o<ii, cix-cxi. Cf. also L. Gautier,'Une rdforme du systBmeastronomique de Ptoleom6e tent6e par les philosophes arabes du xtte sidcle',Journal asintique(r9og), pt. ii. 483-5ro; Juan Vernet, 'L'Astronomie dans I'Islam occidental', Archiaa intemationalesd.'histoireda scienees, r 6 (r 963), 225- 4c, esp. 235-7; and A. I. Sabra, .The Scientific Enterprise', in Bernard Lewis (ed.), The llorld olhlan (London, 1976), fit2oo, esp. r9r-2. The most recent treatment of this problem is Bernard R. Goldstein, 'The Status of Models in Ancient and Medieval Astronomy', Centaurus,z4 QgSo), r3z47. 3 Regarding Ibn Tufayl, see B. R. Goldstein, Al-Bitruji: On the Pineiples of Astronony,z vols. (New Haven, r97r), i. 6r. i The only study to date on Ibn Rushd's role in this problem (apart from brief discussions in the literature cited in n. z) is F. Carmody, 'The Planetary Theory of lbn Rushd', Osmi, ro (1952), 556-86. Carmody does not make use ofAverroes'summary of the Almagest, which survives only in Hebrew but in many copies (cf. M. Steinschneider, Die hebraeisehenUbenetzungender Mittelahers und dieJuden alsDolmexcher (Berlin, r 893), 546-9), nor the astronomical material found in the treatises on Aristotle's De Caelo and Maaplrysieaincluded in Rasa'il lbn Rushd (Hyderabad, r948). See also n. 47 below. 5 Note also Maimonides' high regard for the Spanish astronomer Jabir b. Aflah, mentioned in Guidc, ii. g. In fact, Maimonides editedJabir's astronomical treatise, as we arc informed by Ibn al-Q!fo-, Ta'nkh al-Hukand',ed.J. Lippert (Leipzig, r9o3),3r9. However, Jabir's criticisms of Ptolemy focused on various technical matters and not on the problem ofepicycles and eccentrics.Cf. R. P. Lorch,'The Astronomy ofJnbir ibn Aflah', Cmtaurus, rg (rg71,),85-ro7. 16r the Harranian Thebit b. Qurra. The philosophically weak points of the accepted astronomical models came under aftack in Egypt as well as in Spain. In fact, the most comprehensive and biting attack on the Ptolemaic system known to us is Ibn al-Haytham's Doubts0n Ptolerqt.TIbn al-Haytham's doubts led him to brand the configuration presented in the Almagest x unequivocally false (bayila).8Ibn al-Haytham's arguments include very detailed analysis demonstrating how such Ptolemaic constructions as the equant and the lunar prosneuxi')violate the principles of natural philosophy and, in general, that the planetary motions are governed in the Ptolemaic system by imaginary points rather than by real bodies. Yet it seems significant that Ibn al-Haytham does not, for example, reiect epicycles per se; he proves the impossibility of the Ptolemaic features by working out in step-by-step fashion the consequencesof' say, the moon's epicycle moving exacdy as Ptolemy prescribes.to If indeed the epicycle by itself is a gross violation of the principles of natural philosophy, why should Ibn al-Haytham go to all that bother? We have recently discovered that Maimonides was hmiliar with at least one of Ibn al-Haytham's mathematicaltreatises." Nevertheless, neither Ibn al-Haytham nor the Doubtsare mentioned anywhere in the 6 B. R. Goldstein, review of Fuat Sezgin, Geschichteder arabisehmSchrifttms, vi' A strononi e,i n 1sri ,7r (r98o ),34I-2, at 342. 7 Ibn ai-Haytham,Al-Shukak'a!a Batlamyus,ed. A. I. Sabra and N. Shehaby(Cairo' oJ'theTenth rgTr). Cf. also S. Pines,'lbn al-Haytham's Critique of Ptolemy',Proceedings Iitemational Congras of rhe H*torv'ofscience in lrhaea ry62 (Paris' 1964),5a]- 5!' 01 Ibn al-Haytham,-whodid most of his work in Egypt, see A. I. Sabra,'Ibn al-Haytham', Dictionaryof ScientifcBiograply (New York, I97z)' vi. r89-zIo. 8 Ibn al-Haytham, Al-Shuknk, 34. e On the technical features and terminology of Ptolemaic astronomy see O. Pedersen, A Suruelt of the Almagest (Odense, tg74) nd O. Neugebauer, A Histom of Ancient M athematical A slronomy (Berlin-Heidelberg-New York' r 975). r0 Ibn al-Haytham, Al-Shttkuk, r 5-zo. rr T. Langermann,'The MathematicalWritings of Maimonides"JQR 75 (rS8+)' SZ65. r62 Tz,aiLangermann Guide,andthereis no evidenceto showthat Maimonidesknewof that work. II Maimonides ends his criticism of contemporary astronomical models with several observations. First, he notes that all this doesnot affectthe astronomer.For his purposeis not to tell us in which waythe spherestruly are,but to positan astronomical systemin which it would be possiblefor the motionsto be circular and uniform and to correspondto what is apprehendedthrough sight, regardlessof whether or not things are thusin fact.r2 Maimonides then makes a few remarks which strongly hint that the true state of affairs in the heavens is indeed beyond the power of human comprehension: 'to fatigue the minds with notions that cannot be grasped by them and for the grasp of which they have no instrument, is a defect in one's inborn disposition or some sort of temptation. Let us then stop at a point which is within our capacity.'r3 In sharp contrast to the doubts expressed'in Guifu ii. 24, both concerning the details of the Ptolemaic system and, in general, our ability to understand the configuration of the heavens, stand the descriptions found in the third chapter of the 'Laws Concerning the Basic Principles of the Torah'.la In the first five halakhot of this chapter, Maimonides does not limit himself to the facts that the orbs (galgalim)tsare 'pure and transparent like glassand crystal',r6and that t2 Guidc,3z6. 1 3lb id . 327. ra The astronomical material found in another part of the Mishneh Torah, 'Sanctification of the New Moon' (published in the translation of Solomon Gandz, New Haven, 1956) appertains strictly to the computational side of astronomy, and hence Maimonides' adherence therein to the Ptolemaic model cannot figure in the present discussion.For, as Maimonides explainsin Guide,ii.24,p.326, the discussionof the physical shape of the universe does not affect the working astronomer in his daily practice. See the English translation ofthe 'Laws Concerning the Basic Principles ofthe Torah' by Moses Hyamson, Mishneh Torah: The Book of Knowledge(Jerusalem, 196z), 34a-46a. However, the ffanslation of the passagesquoted in the following discussion are my own; I shall explain in the footnotes any significant points on which I disagree with Hyamsons's choice of words. 15 I consistently translate galgal as'orb', a technical term ofmedieval astronomy; the Arabic equivalent is falak. Similarly, I render kadur as'sphere', a term common to astronomy and geometry; the Arabic equivalent is Aara. 16 The Hebrew is sapir, which Hyamson translates as 'sapphire'. Maimonides states clearly that the heavensare transparent. It is true that sapphire is 'often used in a general The 'TruePerPlexi4t' r63 the planetaryorbs are arranged'like the layersof an onion'. In the which he calls'small refersto epicycles, fourth halakhahhespecifrcally orbs': the earthareroundlike a sphereandthe earth All theseorbswhich encompass is suspendedin the middle.Someof the starshavesmallorbswhich are fixed the earth.Rather,a smallorb insideof them,andthoseorbsdo not encompass orb. in the large,encompassing earth] is fixed which doesnot encompass [the It is clear that in this halakhah specifically, and in the chapter in general, Maimonides is speaking not of the computational models, which are much more complicated, but of the physical configuration of the heavens. In the next halakhah,Maimonides revealsmore details: there are eighteen 'encompassing orbs' and eight small, non-encompassing orbs. This is a very acceptable count, both for epicyclic and nonepicyclic orbs, according to Ptolemaic theory.t7Furthermore, in the sense so as to include all corundum ofgem quality regardlessofcolour. Hence clear and colourlesscorundum is known as white sapphire or'leucosapphire'. Such stoneshave occasionally been cut as lenses for microscopes, being recommended for such use by their high refractivity, weak dispersion and great hardness' (F. W. Rudler, 'Sapphire', Bitannica, rfih edn., n<iv (Cambridge, ryr r), zoz). However, it seems to Encyelopaed.ia me that in current usage, sapphire refers to a coloured stone. Sa'adya Gaon translates the biblical sapir (Exod. z8: r8) as maha, synonymous with ballir and meaning a transparent stone or crystal. Cf. J. Kafih, PerusheRabbenuSa'adya Gann 'al ha-Torah (Jerusalem,ry64), n, and Ibn Manzlr, Lisan al-Arab, xr' (Beirut, 1956),zgg.l feel that Maimonides :usessapir in accordance with the translation of Sa'adya; so also Shemuel ha-Nagid, 'heavens as clear (tehorim) as sapirim' (Y. Cana'ani, Ozar Lashon ha-'Iorit, xii (Jerusalem, tgTz), s.a. sapir). Abraham b. Ezra (commentary to Exod. z8: g) disagrees with Sa'adya, claiming that sapir is a red stone. r? The commentator (ad loc. cit. in the various printings of the Mishneh Torah with commentaries) writes: 'This is their reckoning. The moon has three orbs and these are their names: al-janzahar (node) and al-ma'il (inclined) and bharij al-markaz (eccentric). Mercury also has three orbs and they are al-mumalhthal (parecliptic) and al-mudir (turning) and kharij al-markaz. This makes six. Each of the five remaining planets has two orbs, muma.thtlta.land khdrij al-marhaz. This makes sixteen. The eighth orb, in which are the remaining, fixed stars, and the ninth orb. This makes eighteen.'Note that the commentator gives the names in Arabic. The eight epicycles are: two apiece for Mercury and Venus (the extra epicycle is needed to help account for the planet's latitude), and one each lor the moon, Mars, Jupiter, and Saturn. Note the commentator's remark: 'The later astronomers say that the sun has no falak tadotr (epicyclic orb).' Note in particular tiat eccentric orbs are included in this list. It would seem. however. that Maimonides wishes to exclude eccentrics, since he says, 'the earth is suspended in the middle (ez.aa')'; compare his unequivocal statement elsewhere in the Mishneh Torah that the planetary deferents xi. r 3; p. encompassthe world, but the earth is not at their centre (emza')'Sanctification', 45 in Gandz's translation; note that here eccentrics are allowed, since computations only r65 Tzai Langermann The 'TruePer\lexity' same halakhah, Maimonides states that we can infer the 'way of encompassing'of the orbs, that is, whether they encompassor, as in the case of epicycles,do not encompass,the earth from the proper motions of the stars,their latitudinal crossings,and their apogeesand perigees. willing there to stop the discussionby pleading that man can never know these things, there seemsno reasonnot to do so in the chapter which we are now examining. In this connectionit would be illuminating to look at an interesting passagefrom Maimonides' Comment(ulto theMishnah ('Erutsim,i. 5). At issue is the irrationality of rr. Maimonides writes: 'You ought to know that the ratio of the diameter of the circle to its circumferenceis unknown, nor will it ever be possibleto expressit precisely.This is not due to any shortcoming of knowledge on our part' as the ignorant think. Rather, this matter is unknown due to its nature, and its discoverywill never be attained.'22In my opinion, Maimonides' iibe here at 'the ignorant' may be aimed at those who are less than circumspect in listing all sorts of wonders which are claimed to be beyond human comprehension.In the caseof 7T)we aredealingwith a particular mathematicalproperty. Human understanding,Maimonides would claim, certainly has its limits, but these should be investigated more rigorously.The notion of inscrutabilityhas its preciseplace and ought not be invoked indiscriminately.'z3 It seems clear to me, then, that Maimonides does regard the true configurationof the heavensas somethinghumanly attainable'He may have had tactical reasons in the Guifu for making the situation appear to be hopeless,as Pines once suggested:'The contradictionbetween astronomyand physicsservedhis purpose.It provesaccordingto him, the limitations of human knowledge: man is unable to give a satisfactoryscientific account of the world of the spheres.'24 It was in fact true that at the time of Maimonides no one had offered ft4 And from the motion of the starsand the knowledgeof the measureof their revolutionin eachday and eachhour, and their passagefrom southto north and from north to south, and from their height abovethe earth and their nearness, thenumberof all theseorbs,the formof theirmotion,andtheirway of encompassing, is known.'8 Though the remarks found in the Guidemay reflect Maimonides' most mature ponderings on this subject, it seemsto me to be beyond any doubt that at the time he wrote the Mishneh Torah, Maimonides was well aware of the problematic state of contemporaryastronomy.For example, in his famous letter to the rabbis of southern France, Maimonides remarks that in his youth he read all there was to be found on the subiect of astrology,r"and it is, of course,impossible(at least for the serious medieval scholar) to become expert in astrology without a thorough knowledgeof astronomicaltheory. Indeed, it seems very reasonableto presume that Maimonides learned of the criticisms voiced by Spanish scholars while still in his native country.20 Now there is no question that Maimonides, in the Mishneh Torah, does claim that certain matterslie beyondhuman understandingwhen he feels compelled to do so. Thus Maimonides concludes his discussion of fate and free will in the fifth chapter of the Hilkhot Teshuaa(Laws of repentance)with the statementthat man can never understand the meaning of 'God's knowledge'.'' The particular issue discussedin that chapter, it seemsto me, is of far more importance than the description of the details of the heavens.If Maimonides is are involved;cf. xi. r7 (Gandz, 46) and alson. r4 below).We shall return to this point at t hc e n d o f s e c . i i ; s e e also n . 3 7 . r8 l{yamson's translationof nettiyahas declinationis unacceptable;thc referenceis to the latitudinal crossingsof the ecliptic, not of the equator re A. Marx, 'The Correspondence between the Rabbis of Southern France and Mai m o n i d e sa b o u t A s tr o lo g y' HUCA , 3 Qg z6 ) ,3 ;g - 7 o , e sp . 3r8, 35r. 20 This is my impression, based upon Maimonides' remarks in Guide, ii. g, concerninghis personalcontactswith Andalusiansinvolvedwith astronomicalproblems. 2r This proclamation of inscrutabilityexposedMaimonides to a strong attack on the part of Rabad ('Laws of Repentance', Ioc. cit.). Cf. also I. Twersky, Rabad of Posquiires (Ca m b r i d g e ,M a s s . , r 9 6 z) , z8 o - r . 22 See the edition and Heb. translation by Rabbi J. Kafih (Jerusalem, 1963), ii. o8. ' 23 By way of example only I shall cite Abraham b. Ezra's short commentary to Exod' z3: zo (ed. A. Weiser,Jerusalem,1976, ii.3o5). Ibn Ezra lists here quite a number of phenomena whose inscrutability is strongly implied and sometimes explicitly stated. Among these are some matters of astronomy which agree with Maimonides' observationsin Guidc, ii. I9-in Ibn Ezra's words, 'why one place on the orb is full of stars and another is not, some are big and some are small, some are white [and some] red, and all fofthis] in one orb'. Yet alongside this lbn Ezra lists the known irrationality of the square root of two, and the differences of opinion regarding this. I do not mean to imply that Maimonides'criticism is aimed at Ibn Ezra, (ln fact, I find thesetwo thinkers quite close on some basic issues concerning what may be called the Jewish attitude towards science, and I hope to develop this in some future paper.) I am sure that it would not prove difficult to find quite a few examples of wholesale invocation of human inscrutability among Maimonides' contemporaries, both Muslim and Jewish. 2+ S. Pines, 'Maimonides', Dictionary of Scientifc Biograpiy, ix (New York' r974' 2732, tt 3c..See, however, my remarks towards the end of n. 25. r66 ft7 Tzai Langermann The 'TruePerpbxity' an acceptablesolution. Nevertheless,I regard Maimonides'remarks at the end of ii. z4-'lt is possible that someone else may find a demonstration by means ofwhich the true reality of what is obscure for me will become clear for him'25-not as rhetoric, but as a statement that the problem of the true configuration of the heavens, however difficult, may after all admit of a solution. Hence, on this particular point, there need not be any contradiction between the Guide and the Mishneh Torah. A very interestingapproachto the problem ofthe scrutabilityofthe heavens was taken by the anonymous commentator to the 'Basic Principles', someone who was rather knowledgeablein the field of astronomy.26Commenting on the beginning of the third halakhah, 'None of the orbs is either light or heary', he writes: In other words, Maimonides' conclusion-'All that Aristotle says about that which is beneath the sphere of the moon is in accordance with reasoning . . . However, regarding all that is in the heavens,man graspsbut a small measureof what is mathematical'28-refersto our inability to understand the nature of the 'fifth element' of which the heavensare formed, and not to any inability to comprehend the threedimensionallayout of the celestialspheres. Close inspection of Guide, ii. r9 will bolster this claim' Here Maimonides distinguishes between two unsolved features of the heavens:there is no clear relationship between the velocitiesof the spheres,the direction of their motions, the number of spheresassigned to each star, and their ordering; and it can be shown-either on the basis of different transparencies (Alfarabi) or on the principles of motion and rest (Maimonides himself)-that the matters and forms of stars and spheres differ from one another.'e Now the first feature is patently a problem in astronomy-and here I include the issue of the physical configuration-and in this connection I have found no unambiguous statement that the matter is inscrutable. Maimonides' comment is: 'Now if fuistotle had been able-as he thought-to give us the cause for the differences between the motions of the spheresso that these should be in accordance with the order of the positions of the spheres with regard to one another, this would have been extraordinary.'3o However, regarding the second feature (called by Maimonides 'the existence of the stars'), Maimonides is explicit: 'no one would be able to find a cause particularizing it other than the purpose of one who purposes'." In sum, Maimonides' general purpose in raising doubts about our understanding of the celestial regions is clearly aimed at attacking the underpinnings of the doctrine of the eternity of the world. However, it seemsto me that in the context of these arguments, Maimonides takes It is clear from the words of the philosophersthat the matter(golem)of rhe heavensis not like the matterof the four elementsnor what is composedfrom them. The true natureof the matter of the heavenswas not known to them. Therefore it is said of them that they are not light and not heavy and [have]no tastenor smell,becauseall theseaccidentsare belowthe orb ofthe moon, and of that whose essenceis not known, the nature is not known either.2? 2s In a discussion of the incompatibility of the Ptolemaic slstem with Aristotelian physics published some zo years ago, Pines wrote: 'It can even be maintained that the thoroughly skeptical position was, for the reasons he [Maimonides] gave, the only consistent and logical one. Yet it seemsto me that such agnosticism would stulti$ all that Maimonides set out to accomplish in t\e Guide, and would also be quite irreconcilable with his general views, expressed in quite different contexts, on man's highest destination and man's knowledge'. ('Translator's Introduction', Guide,p. cxi). Pines has since moved away from this view and now emphasizesthe limitations which the Guid.e places on the capacity of the human mind to understand celestial affairs. Cf. 'The Limitations of Human Knowledge according to al-Fertb\ ibn Beija, and Maimonides', in I. Twersky (ed.), Studia in Med.inal Jeoish History and Literature (Cambridge, Mass.London, ry79), 8z-rog, esp. on 93: 'in contradistinction to that theory [or lbn Beija], Maimonides is of the opinion that no scientific certainty can be achieved with regard to obfects that are outside the sublunar world'. 26 Cf. n. r4. It is significant that in his commentary to the fifth halahhah,'Greek scholars wrote many books . , .' he writes: 'This science is the science of astronomy (tekhunah)and in Arabic it is called 'ilm al-hay'ah.' 'Ilm al-hay'ah is used for astronomy in general, but it also is the specific connotation ofthat branch ofastronomy which deals with the configuration of the heavens.Cf. David Pingree, "Ilm al-Hay'ah' , EnEclopaedia of hlam, znd edn., iii (Leiden, r 97 r), r r 35-8. Maimonides continuesat the end of the fifth halahhah: 'this is the science of the computation of seasonsand signs ltequfot umazalot, a phrase commonly used to denote astronomy].' In this context,'computation' must refer to the calculations which demonstrate (in the medieval view) the planetary distances, the existence and sizes of the epirycles, etc. 27 Jonathan b. Joseph of Ruzhany, in his own commentary to this hahkhah (Yeshu'ah be-Yisrael (Frankfurt, ryzo), rcpr. in vol. i of Po'al ha-Shem (Bnei Brak, ry6g\, z), correctly points out that the remarks of the anonymous commentator are motivated by Guid.e, ii. 24. To my knowledge, the only other writer to refer to the two seemingly contradictory texts is the great modern historian of astronomy, Otto Neugebauer, in 'The Astronomy of Maimonides and its Sources',HUCA zz Qg4g), 3zz-69, esp. 336. After discussing the obiections raised in the Guide, Neugebauer states without further comment:'No such doubts are voiced in the Mishneh Torah (completed Ir47). The Ptolemaic arrangements of the planets is accepted without restriction.' zB Guitle,3z6. This remark, in my view, does not imply that man's ability is limited to tie computation of the planetary motions since, as I maintain, the 'Basic Principles' clearly presents a physical description. As I commented in n. 26, the physical descriptions also are inferred from mathematical data. rr lbid. 'o lbid. 3og. " Ibid.3o8-9. r68 r69 Tnsi Langermann The 'TruePerplexity' care to distinguishbetweenthose aspectsof the problem which indeed do not admit of solution-these belong ultimately to the realm of metaphysics-and those which, however elusive they may seem at present, may someday yield their secrets to human inquiry. This second class, I contend, includes the physical configuration of the heavens. This view nonvithstanding,there remains the need to square some of the details of the presentation of the ,MishnehTorahwith the specific criticisms found in the Guid,e.My claim is as follows. When writing the Mishneh Torah, Maimonides knew of the difficulties elaborated in the Guide. There was no known solution to these problems, and (I emphasize)Maimonides did not intend to offer any new cosmologyin the Mishneh Torah. However, basing himself upon the minimal demands of the principles of natural science on the one hand, and the irrefutable evidence of mathematical astronomy on the other, Maimonides was confident enough of the general scheme of any correct cosmology to offer the descriptions found in the 'Basic Principles'. A careful reading of Guide,ii. z4 revealsthat Maimonides may not have reiected epicyclesout of hand. The first obfection to epicycles, that the epicycle 'rolls and changesits place completely',3' applies only ifthe revolution of the epicycle takes place about a centre other than the centre of the orb which carries the epicycle (known also as the deferent)-in other words, if eccentricityof some sort (including an equant or rotating deferentcentre,one must assume)is positedaswell. Ifthe epicyclerevolvesabout the centre ofthe deferent,no such rolling would occur. There then follow two objectionsaimed specificallyat the epicycles, but these, I emphasize,are brought in the name of Ibn Baiia. These obiections are:.(a) the motion of the epicyclebelongs to none of the three allowable categoriesof motion-namely, towards, away from, and about the centre of the world; (&)the motion of the epicycle is not about'some immobile thing'. The remaining obiections apply to eccentricity, and here, interestingly enough, Maimonides takes credit himself for pointing out the impossibilities:'It was by me that attentionwas drawn to this point.'33 These difficulties concern the location of the eccentres,which, as we noted earlier, was indeed an original observationof Maimonides, and the difficulty connected with the treatise of Thabit, also noted above.3a Now we note that in the Mishneh Torah epicyclesare mentioned, but eccentricitynot. How then, however,would Maimonides deal with the obiectionsto epicyclesbrought in the name of Ibn Bajfa?It is a fact that the epicycle has at least two motions. Its revolution about its own centre is the causefor criticisms such as those of Ibn Bajia. However, the epicycle as a whole also moves around the fixed earth with a motion which, if we assume no eccentricity, should raise no difficulties. In short, the fact that the epicycle is fixed within an orb which has a perfectly legitimate motion of its own about the earth mitigates to a large degree the obiectionablefeaturesof the epicycle'smotion about its own centre, if it does not completelyremove those obiections. Profiat Duran, relying upon Levi b. Gerson, understands the discussion in the Cuid,e along these lines, and this without any referenceto theMishneh Torah.ln his commentaryto Cuide,ii. 24, we read: 32 Guide, 323. x Ibid. . . . but ratherhe wishesto explainthat it is impossibleto do without an immobilebody about which it shall move,even if the body moveson a that the lowestof thembe immobile.As thousandbodies,sinceit is necessary proof [wenote]that a manmoveson a ship,andit moves,but sincethewateris immobile,it is correct to saythat the man is movingon an immobilething, namelythe water.So explainedRabbiLevi of blessedmemory;eventhough tlre epicyclemoveson the orb while it [the orb] is in motion,sincethe greatorb movesabout a fixed thing, the epicyclemovesaboutan immobilething.3s In answer to Maimonides' question, 'Furthermore, how can one conceivethe retrogradationof a star, togetherwith its other motions, without assumingthe existenceof an epicycle?"t',we can now simply say that one does use epicycles.If eccentricityis eliminateid,and if we accept Levi b. Gerson's view that what counts is that ultimately, whateverother motions it may have,the epicycledoes move about an immobile centre, we are not troubled by Maimonides' second question, viz. 'How can one imagine a rolling motion in the heavensor We thus arrive at an a motion about a centre which is not immobile?'37 3+ That the objectionbasedupon the treatiseofThabit is aimed at eccentricswe learn from Maimonides'introductory statement(Guide,3z4): 'in all casesin which one of the Nvo spheresis inside the other and adheresto it on everyside, while the centersofthe two are different'. Epicycles do not fulfil the first of the two conditions. rs Efodi on Cuide, loc. cit. (Ileb.). See the l{ebrew edition of the Guide with commentaries(New York, t946), 5o. r7 Ibid. 36 Guide, 326. 170 Tzoi Langermann essentialdifference between Maimonides and the Spanish school.38 Ibn Rushd, for instance, does not limit his concern to the elimination of the difficulties of the Ptolemaic system. He is rather interested in restoring Aristotle's own model, which, in his incomplete understanding,3ewas comprised of concentric earth-centred sphereswhose poles do not all lie on the same line. As a result of the combined motions of these spheres, a spiral (lawlabfl motion ensueswhich, it is hoped, will account for the observed motion of the star or planet'4o Maimonides, on the other hand, is not necessarily interested in rediscovering, as it were, the Aristotelian cosmology, for as he says several times in the Guide, astronomy in the time of Aristotle was relatively underdeveloped.n'Maimonides' attitude thus seems to be closer to that of Ibn al-Haytham, in that he hopes that some configuration, not necessarilythat of Aristode, will be found that can satisfy the constraints of natural philosophy. A significant difficulty with the explanations which I suggest is the fact that in the Mishneh Torah, as noted above, Maimonides gives a specific number for the epicycles and 'encompassing orbs', as if he knows more than just the type of configuration found in the true cosmolory. Though eccentric orbs are not specifically mentioned, Maimonides' count of the 'encompassing orbs' fits a scheme which allows eccentrics; and indeed, eccentric orbs do encompassthe earth. Though it appearsthat the phrase in the fourth halabhah,'the earth is 3s The essential difference between Maimonides and Ibn Rushd was ioted by Pines in his Dictionary of Scientif.c Biography article (n. z4 above) and in his 'Translator's Introduction', p. cx. $ It is highly doubtful that any medieval astronomef understood iust how the -model of Eudoxus accepted (with modifications) by Aristode really worked. homocentric It was only in the rgth cent. that the Italian astronomer G. Schiaperelli worked o1t Eudoxus' iystem, showing that this arrangement is an ingenious way ofproducing the type of curve desired, but simply cannot be made to fit the observational data in most cases. Cf. Neugebauer, History of Ancient Mathematical Astronomy (see n. 9 above), ii.677-fu. Goldstein observes (Al-BitruiI, vol. i, p' ix) that al-Bitrtir, far from reviving Eudoxus'"models, 'does not even draw attention to the relevant passagesin Aristotle's works'. Ibn Rushd, however, does refer to these passages'in his Great Commentary to Aristotle's Meiaphysica (Tafsir Ma ba'da at-Tahi'a), ed. M. Bouyges, vol. iii (Beirut, r948), r657 ff.). -ob Rushd', 57o-2. Carmody suggests(57t n. z4) thatthe.Kitab alb".tiody,'Ibn Iqtisn 'perhaps' refers to the commentary of Theon of Alexandria of the Almagat' ln fibi, ittii is the Arabic title of Ptolemy's own PlanetaryHlpotheses.Cf . SezgSn,Geschichte d,erarahischenSchriftuns, vi. 94-5. at Guide, ii. 24, p. 326: 'For in his [Aristotle'sl time mathematics had not been brought to perfection.'-Guide, ii. rg, p. 3o8: 'However' as I have let you know, the scienie of aitronomy was not in his [Aristotle'sl time what it is today.' The 'True Perplexity' r7r ( suspended in the middle', excludes eccentricity, there may be some ambiguity as to whether the intention is that the earth is at the centre of { a// the orbs, or perhaps just at the centre of the universe. In any event, eliminating eccentrics would leave a serious gap in astronomical theory.n2We can only suggest that this state of affairs reflects the dilemma with which Maimonides was faced. He openly proclaims the L existence of epicycles, since, as we have seen, the philosophical problems entailed by these devices are not insurmountable. However, the epicycles were placed by astronomers in eccentric orbits, and on this point Maimonides is less open; he does not mention eccentrics' but he may not necessarilyexclude them either. 5 III The question of the scrutability of the heavens and the challenge of finding the true configuration generated agreat deal ofinterest among Maimonides' successors. F'or example, Solomon Corcos, in an unpublished commentary to Book II, chapter 9 of Isaac Israeli's Yesod 'Olam,where an alternate configuration of the heavensis the topic of a short discussion,a3wrote as follows: 'One should really be surprised at this author [i.e. Isaac Israeli]. How did he include it all in one chapter? It requires a large book all to itself in order to understand the profundity of the issue.'no Some scholars attempted new cosmologiesof their own. These have for the most part not been subiected to modern analyses.We would like now to sketch the views of some of these thinkers."s Joseph Albo took the remarks of the Guidr to imply that the principles of the astronorner and those of the natural philosopher are In Book [V, chapter z of his'Iqqarim, their difference irreconcilable.a6 a2 See n. r7 above.I cannot help wonderingwhether Maimonides may have had in mind a system wherein epicycles are embedded in concentric spheres,whose axes are inclined to the axis of diily rotation. This is sheer speculation, and I do not know if, theoretically, such a system could overcome the difficulties cited in n. 34' 43 Al-Bitrtil is not mentioned by name, but it seems likely that he is the astronomer whose views are discussed. See Goldstein,,4l-Bitrujl' i. 43. { The manuscript I consultedwas Munich z6r, fo. rga.I wish to thank the Institute of Microfilmed Hebrew Manuscripts in Jerusalem for their co-operation' +s OnJewish reaction to the alternative models of al-Bitrtji, see Goldstein,ll-Bilrujl' i. 4o-4. i Aibo refers specifically to Guidc, ii. 24, in connection with Maimonides' observation that theientres ofthe eccentric orbs lie above the orb ofthe moon. To this 172 TzzsiLangermann of opinion is developedinto a paradigm for the sort of disagreement which becauseit depends ultimately on opposing basic assumptions cannot be decided by reason alone. In the following chapter, Albo (the explicitly states: human mind is not adequateto know this, any more than it is able to explain the causesof the heavenlymotions without doing violence to the theories of physics'.+7In his next sentence he goes even further, claiming that even some terrestrial phenomenaare beyond the comprehensionof the human intellect. Levi b. Gerson took a very different position. The investigationof the heavenlyphenomenademandsboth the mathematicalexpertiseof the astronomerand the masteryof physicswhich belongsto the natural philosopher. Levi statesthat both of these will be utilized in his own astronomicaltreatise;in that sametreatise,models alternativeto those of Ptolemy are discussed,and complicated models of Levi's own invention are proposed. Levi would thus not seem to hold that the nature of the heavensis inscrutable.a8 The approach taken by Profiat Duran inhis fleshn ha-Efo7+'tlooks to be in line with the views expressedin his commentary to the Guide. In chapter 3 Duran demonstrates the necessity of positing either epicycles or eccentres.At the end of this chapter he opts for the epicyclic model for the sun, againstacceptedpractice from Ptolemy onwards, Eventhoughall the mastersof astronomyhavechosenthe eccentricmodel (tekhunah) for the sunoverthe epicyclicmodel,due to its simplicity,I, in this treatise,choosethe epicyclicmodelfor the sun so that the modelsof the sun and the moon shall be the same,and you will not be confusedby an eccentricity for the sun,nor for the moon,sihcethe epicyclicmodelis easier and simplerfor the moon,and thereis no placein it [the lunar model]for eccentricity-thisis true for the timesof conjunctionand opposition, i.e. the molad,withwhich the intentionand fulfilment[of this treatiselie].s" are added, in this chapter and the next, difliculties associatedwith epicyclesand other astronomical matters not discussed in the Guide. See Joseph hlbo, Sefer ha-'lqqarim (Book ofprinciples), ed. and trans. L Husik (Philadelphia,r93o), iv. r7-r8. r lbid. +8The astronomicalwork of [,evi b. Gerson has been the subiect of intensive and fruitful research by B. R. Goldstein; see his TheAstronomicalTablesof Lni hen Gerson, Transactions of the Connecticut Academy of Arts and Sciences,xlv (Hamden, Conn., rg74), and the literature cited thcrein. The first chapter of Levi's Astrononty(actually pt. i, bk. 5 of his Warsof theLord) was translatedby Goldstein in'The Statusof Modcls', (s een . z a b o v e ) ,r 4 5 - 7 . +e I consulted MS Parma 8oo (2776), fos. rol-33. n) Ibid. fo. lo3&. Maimonides (Guide, ii. tr, pp. 273-$ is aware rhat the eccentric The'TruePerplexiryr' r73 Duran is apparentlyreviving the simple lunar model of Hipparchus, which may be satisfactoryfor the syzygiesbut is not so for other points of the lunar orbit. We recall that when calculationsalone are involved, as in the presentcase,Maimonides himself has no obiectionsto all the complications of the complete Ptolemaic lunar model. It would bc foolish to say anything more on the subject until this interesting treatisehas been thoroughly studied. JosephNahmias is the author of a book known in English asLight oJ' the World,slan original attempt at an astronomicalsystembasedupon correct principles.A thorough study ofthis treatiseis perhapsthe chief desideratumfor the history of Jewish astronomy.We must therefore limit ourselvesagain to some preliminary observationsmade on the basis of the author's introduction. Nalrmias seesastronomyas being forced to accept one oftwo unsavourydevicesin order to account for (contrary motion', the planetary motions: epicyclesand eccentres,or and eccentres Epicycles is, in opposite directions. that circular motion are rejected out of hand, and Natrmias will do the best he can (philosophically and mathematically)with the principle of contrary motion. We observe that the latter does not figure among the objections raised by Maimonides in Cuide, ii. 24, and in the 'Basic Principles', iii. z, it is explicitly statedthat some of the orbs turn from west to east and some from east to west. Contrary motion does figure prominently in the objections of the Spanish school.s2 In the courseof his introduction, Nahmiasexpressesastonishmentat Maimonides' remarks in Guide, ii. 24, on the impossibility of explaining the planetary motion without recourse to epicycles or eccentres.Natrmiascredits al-Bitrfii with reviving the investigationof the true principles, something which stands to al-Bitrtjr's credit despite the technical shortcomingsof his work. model was chosen for the sun for reasonsof economy,and Duran must haveknown this too. In the light of Duran's remarks on the Guide, I suggestthat physical-philosophical motivations lay behind Duran's choice of the epicyclic model' in addition to the proclaimed simplicity of t}re system. sr The treatisewas written in Arabic (Nir al-Alam) and rendered into Hebrew by an unknown translator.I consulted the Hebrew version, Bodley 2778. Cf. Steinschneider, H ebraeisth en 0 benet:ungen, 5g7-8. s2 Carmody, 'lbn Rushd', 562. l{owever, in his commentary to the Metaphysica (cited in n. 3g), r673-5, Ibn Rushd appearswilling to accept some type of contrary motion, spurred, in part, by contemporaryideas on the trepidation of the equinoxes' There is need for a thorough study ofthe views oflbn Rushd on mattersastronomical. See also Goldstein,l/-,Bilruji, i. 67. 1 74 Tzai Langermann CO NCLUSI O N Maimonides, like many of his contemporaries,was concerned with the philosophical weaknesses of the Ptolemaic system; in this he was influenced by the Spanish school of criticism, but differed considerably from it. Though it may seem from Guidc, ii. 24 that epicycles and eccentrics are unacceptable, and that in fact the true configuration of the heavensis beyond human comprehension, a careful reading of that chapter in conjunction with the relevant portion of the Mishneh Torah suggeststhat Maimonides did indeed have some idea of what the true configuration would be, and that in this configuration epicycles are allowed. The problems raised in Guide, ii. 24, were a matter of continued interest among Maimonides' successorsand evoked quite different responses.