CHAPTER XXXV
THE EARLY SCHOLASTICS: PETER ABELARD AND HUGH OF ST. VICTOR
Relation of scholastic theology to our theme—Character of Abelard’s learning—Incorrect statements of his views—The nature of the stars—Prediction of natural and contingent events—The Magi and the star—Demons and forces in nature—Magic and natural science—Hugh of St. Victor—Character of the Didascalicon—Meaning of Physica—The study of history—The two mathematics: astrology, natural and superstitious—The superlunar and sublunar worlds—Discussion of magic—Five sub-divisions of magic—De bestiis et aliis rebus.
Relation of scholastic theology to our theme.
The names of Peter Abelard, 1079-1142, and Hugh or Hugo of St. Victor, 1096-1141, have been coupled as those of the two men who perhaps more than any others were the founders of scholastic theology. Our investigation is not very closely or directly concerned with scholastic theology, which I hope to show did not so exclusively absorb the intellectual energy of the twelfth and thirteenth centuries as has sometimes been asserted. Our attention will be mainly devoted as heretofore to the pursuit of natural science during that period and the prominence both of experimental method and of magic in the same. But our investigation deals not only with magic and experimental science, but with their relation to Christian thought. It is therefore with interest that we turn to the works of these two early representatives of scholastic theology, and inquire what cognizance, if any, they take of the subjects in which we are especially interested. As we proceed into the later twelfth and thirteenth centuries in subsequent chapters, we shall also take occasion to note the utterances of other leading men of learning who speak largely from the theological standpoint, like John of Salisbury and Thomas Aquinas. Let us hasten to admit also that the scholastic method of instruction and writing made itself felt in natural science and medicine as well as in theology, as a number of our subsequent chapters will illustrate. In the present chapter we shall furthermore be brought again into contact with the topic of the Physiologus and Latin Bestiaries, owing to the fact that a treatise of this sort has been ascribed, although probably incorrectly, to Hugh of St. Victor.
Character of Abelard’s learning.
There is no more familiar, and possibly no more important, figure in the history of Latin learning during the twelfth century than Peter Abelard who flourished at its beginning. His career, as set forth in his own words, illustrates educational conditions in Gaul at that time. His brilliant success as a lecturer on logic and theology at Paris reveals the great medieval university of that city in embryo. His pioneer work, Sic et Non, set the fashion for the standard method of presentation employed in scholasticism. He was not, however, the only daring and original spirit of his time; his learned writings were almost entirely in those fields known as patristic and scholastic; and, as in the case of Sic et Non, consist chiefly in a repetition of the utterances of the fathers. This is especially true of his statements concerning astrology, the magi, and demons. To natural science he gave little or no attention. Nevertheless his intellectual prominence and future influence make it advisable to note what position he took upon these points.
Incorrect statements of his views.
Although not original, his views concerning the stars and their influences are the more essential to expose, because writers upon Abelard have misunderstood and consequently misinterpreted them. Joseph McCabe in his Life of Abelard,[1] for instance, asserts that Abelard calls mathematics diabolical in one of his works. And Charles Jourdain in his in some ways excellent[2] Dissertation sur l’état de la philosophie naturelle en occident et principalement en France pendant la première moitié du XIIe siècle, praises Abelard for what he regards as an admirable attack upon and criticism of astrology in his Expositio in Hexameron, saying, “It will be hard to find in the writers of a later age anything more discriminating on the errors of astrology.”[3] Jourdain apparently did not realize the extent to which Abelard was simply repeating the writers of an earlier age. However, Abelard’s presentation possesses a certain freshness and perhaps contains some original observations.
The nature of the stars.
In the passage in question[4] Abelard first discusses the nature of the stars. He says that it is no small question whether the planets are animated, as the philosophers think, and have spirits who control their motion, or whether they hold their unvarying course merely by the will and order of God. Philosophers do not hesitate to declare them rational, immortal, and impassive animals, and the Platonists call them not only gods but gods of gods, as being more excellent and having greater efficacy than the other stars. Moreover, Augustine says in his Handbook that he is uncertain whether to class the sun, moon, and stars with the angels. In his Retractions Augustine withdrew his earlier statement that this world is an animal, as Plato and other philosophers believe, not because he was sure it was false, but because he could not certainly prove it true either by reason or by the authority of divine scripture. Abelard does not venture to state an opinion of his own, but he at least has done little to refute a view of the nature of the heavenly bodies which is quite favorable to, and usually was accompanied by, astrology. Also he displays the wonted medieval respect for the opinions of the philosophers in general and the leaning of the twelfth century toward Plato in particular.
Prediction of natural and contingent events.
Abelard next comes to the problem of the influence of the stars upon this earth and man. He grants that the stars control heat and cold, drought and moisture; he accepts the astrological division of the heavens into houses, in certain ones of which each planet exerts its maximum of force; and he believes that men skilled in knowledge of the stars can by astronomy predict much concerning the future of things having natural causes. Astronomical observations to his mind are very valuable not only in agriculture but in medicine, and he mentions that Moses himself is believed to have been very skilful in this science of the Egyptians. It is only to the attempt to predict contingentia as distinguished from naturalia that he objects. By contingentia he seems to mean events in which chance and divine providence or human choice and free will are involved. He gives as a proof that astrologers cannot predict such events the fact that, while they will foretell to you what other persons will do, they refuse to tell you openly which of two courses you yourself will pursue for fear that you may prove them wrong by wilfully doing the contrary to what they predict. Or, if an astrologer is able to predict such “contingent events,” it must be because the devil has assisted him, and hence Abelard declares that he who promises anyone certitude concerning “contingent happenings” by means of “astronomy” is to be considered not so much astronomicus as diabolicus. This is the nearest approach that I have been able to find in Abelard’s writings to McCabe’s assertion that he once called mathematics diabolical. But possibly I have overlooked some other passage where Abelard calls mathematica, in the sense of divination, diabolical.[5] In any case Abelard rejects astrology only in part and accepts it with certain qualifications. His attitude is about the average one of his own time and of ages preceding and following.
The Magi and the star.
Abelard speaks of the Magi and the star of Bethlehem in a sermon for Epiphany.[6] This familiar theme, as we have seen, had often occupied the pens of the church fathers, so that Abelard has nothing new to say. On the contrary, he exhausts neither the authorities nor the subject in the passages which he selects for repetition. His first point is that the Magi were fittingly the first of the Gentiles to become Christian converts because they before had been the masters of the greatest error, condemned by law with soothsayers to death, and indebted for their “nefarious and execrable doctrine” to demons. In short, Abelard identifies them with magicians and takes that word in the worst sense. He is aware, however, that some identify them not with sorcerers (malefici) but with astronomers. He repeats the legend from the spurious homily of Chrysostom which we have already recounted[7] of how the magi had for generations watched for the star, warned by the writing of Seth which they possessed, and how the star finally appeared in the form of a little child with a cross above it and spake with them. He also states that they were called magici in their tongue because they glorified God in silence, without appearing to note that this is contrary to his previous use of magi in an evil sense. Abelard believes that a new star announced the birth of Christ, the heavenly king, although he grants that comets, which we read of as announcing the deaths of earthly sovereigns, are not new stars. He also discusses without satisfactory results the question why this new star was seen only by the Magi.
Demons and forces in nature.
In a chapter “On the Suggestions of Demons” in his Ethica seu Scito te ipsum,[8] Abelard attempts to a certain extent a natural explanation of the tempting of men by demons and the arousing of lust and other evil passions within us. In this he perhaps makes his closest approach to the standpoint of natural science, although he is simply repeating an idea found already in Augustine and other church fathers. In plants and seeds and trees and stones, Abelard explains, there reside many forces adapted to arouse or calm our passions. The demons, owing to their subtle ingenuity and their long experience with the natures of things, are acquainted with all these occult properties and make use of them for their own evil ends. Thus they sometimes, by divine permission, send men into trances or give remedies to those making supplications to them, “and often when such cease to feel pain, they are believed to be cured.” Abelard also mentions the marvels which the demons worked in Egypt in opposition to Moses by means of Pharaoh’s magicians.
Magic and natural science.
Evidently then Abelard believes both in the existence of demons and of occult virtues in nature by which marvels may be worked. Magic avails itself both of demonic and natural forces. The demons are more thoroughly acquainted with the secrets of nature than are men. But this does not prove that scientific research is necessarily diabolical or that anyone devoting himself to investigation of nature is giving himself over to demons. The inevitable conclusion is rather that if men will practice the same long experimentation and will exercise the same “subtle ingenuity” as the demons have, there is nothing to prevent them, too, from becoming at last thoroughly acquainted with the natural powers of things. Also magic, since it avails itself of natural forces, is akin to natural science, while natural science may hope some day to rival both the knowledge of the demons and the marvels of magic. Abelard does not go on to draw any of these conclusions, but other medieval writers were to do so before very long.
Hugh of St. Victor.
Upon Hugh of St. Victor Vincent of Beauvais in the century following looked back as “illustrious in religion and knowledge of literature” and as “second to no one of his time in skill in the seven liberal arts.”[9] Hugh was Abelard’s younger contemporary, born almost twenty years later in Saxony in 1096 but dying a year before Abelard in 1141. His uncle, the bishop of Halberstadt, had preceded him at Paris as a student under William of Champeaux. When Hugh, as an Augustinian canon, reached the monastery of St. Victor at Paris, William had ceased to teach and become a bishop. Hugh was himself chosen head of the school in 1133. He is famous as a mystic, but also composed exegetical and dogmatic works, and is noted for his classification of the sciences. Edward Myers well observes in this connection: “Historians of philosophy are now coming to see that it betrays a lack of psychological imagination to be unable to figure the subjective coexistence of Aristotelian dialectics with mysticism of the Victorine or Bernardine type—and even their compenetration. Speculative thought was not, and could not be, isolated from religious life lived with such intensity as it was in the middle ages, when that speculative thought was active everywhere, in every profession, in every degree of the social scale.”[10] Later, in the case of St. Hildegard of Bingen, we shall meet an even more striking combination of mysticism and natural science.
Character of the Didascalicon.
Of Hugh’s writings we shall be chiefly concerned with the Didascalicon, or Eruditio didascalica,[11] a brief work whose six books occupy some seventy columns in Migne’s Patrologia. It is especially devoted, as its first chapter clearly states, to instructing the student what to read and how to read. On the whole, especially for its early twelfth century date, it is a clear, systematic, and sensible treatise, which shows that medieval men were wider readers than has often been supposed and that they had some sound ideas on how to study. In order to have a basis for systematic study, Hugh describes and classifies the various arts and sciences, mechanical and liberal, theoretical and practical. He is possibly influenced in his definitions and derivations by Isidore’s Etymologies, although he seldom if ever acknowledges the debt, whereas he cites Boethius a number of times, but at least his classification and arrangement of material are quite different from Isidore’s. In this description and classification, and indeed throughout the treatise, Hugh seems to display no little originality of thought and arrangement—once he tells us of his own methods of study[12]—although his facts and details are mostly familiar ones from ancient authors and although he of course embodies generally accepted notions such as the trivium and quadrivium.
Meaning of physica.
To the four subjects of the quadrivium he adds physica or physiologia,[13] which he says “considers and investigates the causes of things in their effects and their effects in their causes.” He quotes from Vergil’s Georgics, (II, 479-)
“Whence earthquakes come, what force disturbs the deep,
Virtues of herbs, the minds and wraths of brutes,
All kinds of fruits, of reptiles, too, and gems.”
Thus Physica is more inclusive than the modern science of Physics, while Hugh evidently does not employ it in the specific sense of the art of medicine, of which the word physica was sometimes used in the medieval period. Hugh goes on to say that Physica is sometimes still more broadly interpreted to designate natural philosophy in contrast to logical and ethical philosophy. His quotation from the Georgics also causes one to reflect on the prominent part played in natural science from before Vergil to after Hugh by the semi-human characteristics ascribed to animals and the occult virtues ascribed to herbs and gems.
The study of history.
Hugh’s attitude to history is interesting to note in passing. In his classification of the sciences he does not assign it a distinct place as he does to economics and politics, but he shows his inchoate sense of the importance of the history of science and of thought by attempting a list of the founders of the various arts and sciences.[14] In this connection he adopts the theory of the origin of the Etruscans at present in favor with scholars, that they came from Lydia. He regards the study of Biblical or sacred history as the first essential for a theologian, who should learn history from beginning to end before he proceeds to doctrine and allegory.[15] Four essential points to note in studying history in Hugh’s opinion are the person, the event, the time, and the place.
The two mathematics: astrology, natural and superstitious.
In discussing the quadrivium Hugh explains the significance of the terms, mathematica, astronomia, and astrologia. Mathematica, in which the first letter “t” has the aspirate, denotes sound doctrine and the science of abstract quantity, and embraces within itself the four subjects of the quadrivium. In other words it denotes mathematics in our sense of the word. But matesis, spelled without the aspirate, signifies that superstitious vanity which places the fate of man under the constellations.[16] Hugh thus allows for the common use since the time of the Roman Empire of the word mathematicus for an astrologer, and the frequent use of mathematica in the sense of the Greek word mantike or divination. He correctly states the Greek derivation of astrology and astronomy and employs those words in just about their modern sense. Astrology considers the stars in order to determine the nativity, death, and certain other events. For Hugh, however, it is not wholly a superstition, but “partly natural science, partly a superstition,” since he believes that the condition of the human body as well as of other bodies depends upon the constellations, and that sickness and health as well as storms or fair weather, fertility and sterility, can be predicted from the stars, but that it is superstitious to assert their control over contingent events and acts of free will,—the same distinction as that made by Abelard.
The superlunar and sublunar worlds.
In an earlier discussion of the universe above and beneath the moon[17] Hugh had further emphasized the superiority of the heavenly bodies and their power over earthly life and nature. He distinguished three kinds of beings: God the Creator (solus naturae genitor et artifex) who alone is without beginning or end and truly eternal, the bodies of the superlunar world which have a beginning but no end and are called perpetual and divine, and sublunar and terrestrial things which have both a beginning and an end. The mathematicians call the superlunar world nature, and the sublunar world the work of nature, because all life and growth in it comes “through invisible channels from the superior bodies.” They also call the upper world time, because of the movements of the heavenly bodies in it determining time, and the lower world temporal, because it is moved according to the superior motions. They further call the superlunar world Elysium on account of its perpetual light and peace, while they call the other Infernum because of its confusion and constant fluctuation. Hugh adds that he has touched upon these points in order to show man that, in so far as he shares in this world of change, he is like it, subject to necessity, while in so far as he is immortal he is related to the Godhead.
Discussion of magic.
Hugh’s brief, but clear and pithy, account of magic occurs in the closing chapter of his sixth and last book,[18] and seems to be rather in the nature of an addendum. It is, indeed, missing from the Didascalicon in some of the earliest manuscripts[19] and is found separately in the same collection of manuscripts, so that possibly it is not by Hugh. At any rate, magic is treated by itself apart from his previous description and classification of the arts and sciences and listing of their founders. The definition of magic makes it clear why it is thus segregated: “Magic is not included in philosophy, but is a distinct subject, false in its professions, mistress of all iniquity and malice, deceiving concerning the truth and truly doing harm; it seduces souls from divine religion, promotes the worship of demons, engenders corruption of morals, and impels the minds of its followers to every crime and abomination.” Hugh had prefaced this definition by much the usual meager history of the origin of magic to be found in Isidore and other writers, but his definition proper seems rather original in its form and in a way admirable in its attitude. The ancient classical feeling that magic was evil and the Christian prejudice against it as the work of demons still play a large part in his summary of the subject, but to these two points that magic is hostile to Christianity or irreligious, and that it is improper, immoral, and criminal, he adds the other two points that it is not a part of philosophy—in other words, it is unscientific, and that it is more or less untrue and unreal. Or these four points may be reduced to two: since law, religion, and learning unite in condemning magic, it is unsocial in every respect; and it is more or less untrue, unreal, and unscientific.
Five subdivisions of magic.
Hugh’s list of various forbidden and occult arts which are sub-divisions of magic is somewhat similar to that of Isidore, but he classifies and groups them logically under five main heads in a way which appears to be partly his own, and which was followed by other subsequent writers, such as Roger Bacon. His first three main heads all deal with arts of divination. Mantike divides as usual into necromancy, geomancy, hydromancy, aerimancy, and pyromancy. Under mathematica are listed aruspicina, or the observation of hours (horae) or of entrails (hara); augury, or observation of birds; and horoscopia, or the observation of nativities. The third main head, sortilegia, deals with divination by lots. The fourth main head, maleficia, with which magic has already been twice identified in the chapter, is now described by Hugh as “the performance of evil deeds by incantations to demons, or by ligatures or any other accursed kind of remedies with the co-operation and instruction of demons.”[20] Fifth and last come praestigia, in which “by phantastic illusions concerning the transformation of objects the human senses are deceived by demoniacal art.”[21]
De bestiis et aliis rebus.
Among the doubtful and spurious works ascribed to Hugh is a bestiary in four books,[22] in which various birds and beasts are described, and spiritual and moral applications are made from them. At least this is the character of the first part of the treatise; towards the close it becomes simply a glossary of all sorts of natural objects. Physiologus is often cited for the natural properties of birds and beasts, but as we have already dealt with the problem of the Physiologus in an earlier chapter, and as we shall sufficiently deal with the properties and natures ascribed to animals in the middle ages in describing the treatment of them by various encyclopedists like Thomas of Cantimpré, Bartholomew of England, and Albertus Magnus, we are at present mainly interested in some other features of the treatise before us. It is often illustrated with illuminations of birds and animals in the manuscripts and was originally intended to be so, as the prologue on the hawk and dove by its monkish author to a noble convert, Raynerus, makes evident. “Wishing to satisfy the petitions of your desire, I decided to paint the dove whose ‘wings are covered with silver, and her feathers with yellow gold,’ and to edify minds by painting, in order that what the simple mind can scarcely grasp by the eye of the intellect, it might at least discern with the carnal eye, and vision perceive what hearing could scarcely comprehend. However, I wished not only to depict the dove graphically but to describe it in words and to explain the painting by writing, so that he whom the simplicity of the picture did not please might at least be pleased by the morality of Scripture.” Indeed, the work is often entitled The Gilded Dove in the manuscripts. The treatise is manifestly of a religious and popular rather than scientific character. One interesting passage states that a monk should not practice medicine because “a doctor sometimes sees things which are not decent to see,” and “touches what it is improper for the religious to touch.” Furthermore, a physician “speaks of uncertain matters by means of experiments, but experience is deceitful and so often errs. But this is not fitting for a monk that he should speak aught but the truth.”[23] It is rather surprising to find free will attributed to the wild beasts, who are said to wander about at their will.[24] This passage, however, is simply copied from Isidore.[25]
[1] J. McCabe, Peter Abelard, New York, 1901.
[2] Especially considering its date, Paris, 1838.
[3] Ibid., p. 119.
[4] Cousin, Opera hactenus seorsim edita (1849-1859), I, 647-9.
[5] I have, however, searched for such in vain.
[6] Migne, PL 178, 409-17.
[7] See above, chapter 20, page 474.
[8] Cap. 4, in Migne, PL 178, 647.
[9] Speculum doctrinale (1472?), XVIII, 62, “Hugo Parisiensis sancti victoris canonicus religione et literarum scientia clarus et in VII liberalium artium peritia nulli sui temporis secundus fuit.”
[10] CE “Hugh of St. Victor,” where is also given a good bibliography of works on Hugh’s theology, philosophy, psychology, and pedagogy.
[11] I have employed the text in Migne PL vol. 176, cols. 739-812. It should be noted, however, that B. Hauréau, Les Œuvres de Hugues de Saint-Victor, Essai critique, nouvelle edition, Paris, 1886, demonstrated that there should be only six books of the Didascalicon instead of seven as in this edition and that of 1648. This will not affect our investigation, as we shall make no use of the seventh book, but we shall have later to discuss whether a passage on magic belongs at the close of the sixth book or not. There appears to be a somewhat general impression that the edition of 1648 is the earliest edition of Hugh’s works, but the British Museum has an undated incunabulum of the “Didascolon” numbered IB. 859, fol. 254.
Vincent of Beauvais in the thirteenth century speaks of the “Didascolon” as in five books (Speculum doctrinale, XVIII, 62) but is probably mistaken. The MSS seem uniformly to divide the work into a prologue and six books, as in the following at Oxford:
New College 144, 11th (sic) century, folio bene exaratus et servatus, fols. 105-43, “Incipit prologus in Didascalicon.”
Jesus College 35, 12th century, fol. 26-
St. John’s 98, 14th century, fol. 123-
Corpus Christi 223, 15th century, fol. 73-
I have not noted what MSS of the Didascalicon there are in the British Museum. The following MSS elsewhere may be worth listing as of early date:
Grenoble 246, 12th century, fols. 99-133.
BN 13334, 12th century, fol. 52-, de arte didascalica, is probably our treatise, although the catalogue names no author.
BN 15256, 13th century, fol. 128-.
Still other MSS will be mentioned in a subsequent note.
[12] Didasc. VI, 3.
[13] Ibid., II, 17.
[14] Didasc. III, 2.
[15] Ibid., VI, 3.
[16] A similar distinction will be found in the Glosses on the Timaeus of William of Conches (Cousin, Ouvrages inédits d’Abélard, 1836, p. 649), one of Hugh’s contemporaries of whom we shall presently treat. A little later in the twelfth century John of Salisbury (Polycraticus, II, 18) makes the distinction between the two mateses or mathematics lie rather in the quantity of the penultimate vowel “e”. In the thirteenth century Albertus Magnus (Commentary on Matthew, II, 1) also distinguished between the two varieties of mathematics according to the length of the “e” in “mathesis”; but he did not regard the second variety as necessarily superstitious, but as divination from the stars which might be either good or bad, like Hugh’s astrologia.
Roger Bacon mentioned both methods of distinction between the true and false mathematics; but statements in his different works are not in agreement as to which case it is in which the “e” is long or short. In the Opus Maius (Bridges, I, 239 and note) and Opus Tertium (caps. 9 and 65) he states that the vowel is short in the true mathematics and long in the superstitious variety; but in other writings he took the opposite view and declared that “all the Latins” were wrong in thinking otherwise (see Bridges, I, 239 note; Steele (1920) viii).
In a twelfth century MS at Munich (CLM 19488, pp. 17-23) a treatise or perhaps an excerpt from some longer work, entitled De differentiis vocabulorum, opens with the words, “Scire facit mathesis et divinare mathesis.” Roger Bacon says (Steele, 1920, p. 3), “Set glomerelli nescientes Grecum ... ex magna sua ignorancia vulgaverunt hos versus falsos:
Scire facit matesis, set divinare mathesis;
Philosophi matesim, magici dixere mathesim.”
[17] Didascalicon, I, 7.
[18] Didasc. VI, 15 (Migne PL 176, 810-12).
[19] BN nouv. acq. 1429, 12th century, fols. iv-23, and CLM 2572, written between 1182 and 1199; both end with the thirteenth chapter of Book VI, or at col. 809 in Migne. St. John’s 98, 14th century, fol. 145v, also ends at this point. Jesus College 35, 12th century, is mutilated at the close.
Other early MSS, however, include the passage on magic in the Didascalicon, and end the sixth book with the closing words of the account of magic, “Hydromancy first came from the Persians”: see Vitry-le-François 19, 12th century, fols. 1-46; Mazarine 717, 13th century, #9, closing at fol. 97v.
The passage on magic is also cited as Hugh’s by Robert Kilwardby, archbishop of Canterbury 1272-1279, in his work on the division of the sciences, cap. 67: MSS are Balliol 3; Merton 261.
In Cortona 35, 15th century, fol. 203, the Didascalicon in six books is first followed by a brief passage, Divisio philosophie continentium, which is perhaps simply the fourteenth chapter of the sixth book as printed in Migne, and then at fol. 224 by the passage concerning magic and its subdivisions.
The account of magic also occurs in MSS which do not contain the Didascalicon, for instance, Vatic. Palat. Lat. 841, 13th century, fol. 139r, “Magice artis quinque sunt species....”
[20] “Malefici sunt qui per incantationes daemonicas sive ligaturas vel alia quaecunque exsecrabilia remediorum genera cooperatione daemonum atque instructu nefanda perficiunt.”
[21] “Praestigia sunt quando per phantasticas illusiones circa rerum immutationem sensibus humanis arte daemoniaca illuditur.”
[22] Migne, PL 177, 13-164, “Hugo Raynero suo salutem. Desiderii tui petitionibus, charissime, satisfacere cupiens....”
[23] I, 45. “De incertis per experimenta loquitur, sed experimentum est fallax, ideo saepe fallitur. Sed hoc religioso non expedit ut alia quam vera loquatur.”
[24] II, prologus. “Ferae appellantur eo quod naturali utantur libertate et desiderio suo ferantur. Sunt enim liberae eorum voluntates et huc atque illuc vagantur et quo animus duxerit eo feruntur.”
[25] Etymologiarum, XII, ii, 2.