On The Liberal Arts. A Compendium Of Texts.

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ON THE LIBERAL ARTS A COMPENDIUM OF TEXTS (c) 2013 Bart A. Mazzetti § 1 1. The liberal arts and their division according to St. Thomas Aquinas. Cf. Super Boethium De Trinitate by Thomas Aquinas. Aquinas. Questions 1-4, translated by Rose E. Brennan, S.H.N. (Herder, 1946) Questions 5-6, translated by Armand Maurer (Toronto, 1953), q. 5, art. 1, obj. 3, ad 3: 3. Again, philosophy is commonly divided into seven liberal arts, which include neither  natural nor divine science, but only rational and mathematical science. Hence natural and divine should not be called parts of speculative science. <…> Reply to 3. The seven liberal arts do not adequately divide theoretical philosophy; but, as Hugh of St. Victor says, seven arts are grouped together (leaving out certain other ones),  because those who wanted to learn philosophy were first instructed in them. And the reason why they are divided into the trivium and quadrivium is that “they are as it were paths ( viae) viae) introducing the quick mind to the secrets of philosophy.” This is also in harmony with the Philosopher’s statement in the  Metaphysics that we must investigate the method of scientific thinking before the sciences themselves. And the Commentator says in the same place that  before all the other sciences a person should learn logic, which teaches the method of all the sciences; and the trivium concerns logic. The Philosopher also says in the  Ethics that the young can know mathematics but not physics, because it requires experience. So we are given to understand that after logic we should learn mathematics, which the quadrivium concerns. These, then, are like paths leading the mind to the other philosophical disciplines. We may add that among the other sciences these are called arts because they involve not only knowledge but also a work that is directly a product of reason itself; for example,  producing a composition, syllogism or discourse, numbering, measuring, composing melodies ( formare melodias melodias)),1 and reckoning the course of the stars. Other sciences (such as divine and natural science) either do not involve a work produced  but only knowledge, and so we cannot call call them arts, because, as the  Metaphysics says, art is “producti “productive ve reason”; reason”; or they involve involve some bodily activity, activity, as in the case of medicine, medicine, alchemy, and other sciences of this kind. These latter, then, cannot be called liberal arts  because such activity belongs to man on the side of his nature in which he is not free, namely, on the side of his body. And although moral science is directed to action, still that action is not the act of the science but rather of virtue, as is clear in the  Ethics.  Ethics. So we cannot call moral science an art; but rather in these actions virtue takes the place of art. Thus, as Augustine says, the ancients defined virtue as the art of noble and well-ordered living. Cf. idem (tr. B.A.M.): PS3 QU5 AR1 AG3  praeterea, communiter dividitur philosophia in Furthermore, philosophy is commonly divided septem artes liberales, inter quas neque naturalis into seven liberal arts, among which neither naneque divina continetur, sed sola rationalis et tural philosophy nor divine science is contained, mathematica.  but only rational and and mathematical science. 1 On the correct interpretation of this expression, see further below. 2 1. The liberal arts and their division according to St. Thomas Aquinas. Cf. Super Boethium De Trinitate by Thomas Aquinas. Aquinas. Questions 1-4, translated by Rose E. Brennan, S.H.N. (Herder, 1946) Questions 5-6, translated by Armand Maurer (Toronto, 1953), q. 5, art. 1, obj. 3, ad 3: 3. Again, philosophy is commonly divided into seven liberal arts, which include neither  natural nor divine science, but only rational and mathematical science. Hence natural and divine should not be called parts of speculative science. <…> Reply to 3. The seven liberal arts do not adequately divide theoretical philosophy; but, as Hugh of St. Victor says, seven arts are grouped together (leaving out certain other ones),  because those who wanted to learn philosophy were first instructed in them. And the reason why they are divided into the trivium and quadrivium is that “they are as it were paths ( viae) viae) introducing the quick mind to the secrets of philosophy.” This is also in harmony with the Philosopher’s statement in the  Metaphysics that we must investigate the method of scientific thinking before the sciences themselves. And the Commentator says in the same place that  before all the other sciences a person should learn logic, which teaches the method of all the sciences; and the trivium concerns logic. The Philosopher also says in the  Ethics that the young can know mathematics but not physics, because it requires experience. So we are given to understand that after logic we should learn mathematics, which the quadrivium concerns. These, then, are like paths leading the mind to the other philosophical disciplines. We may add that among the other sciences these are called arts because they involve not only knowledge but also a work that is directly a product of reason itself; for example,  producing a composition, syllogism or discourse, numbering, measuring, composing melodies ( formare melodias melodias)),1 and reckoning the course of the stars. Other sciences (such as divine and natural science) either do not involve a work produced  but only knowledge, and so we cannot call call them arts, because, as the  Metaphysics says, art is “producti “productive ve reason”; reason”; or they involve involve some bodily activity, activity, as in the case of medicine, medicine, alchemy, and other sciences of this kind. These latter, then, cannot be called liberal arts  because such activity belongs to man on the side of his nature in which he is not free, namely, on the side of his body. And although moral science is directed to action, still that action is not the act of the science but rather of virtue, as is clear in the  Ethics.  Ethics. So we cannot call moral science an art; but rather in these actions virtue takes the place of art. Thus, as Augustine says, the ancients defined virtue as the art of noble and well-ordered living. Cf. idem (tr. B.A.M.): PS3 QU5 AR1 AG3  praeterea, communiter dividitur philosophia in Furthermore, philosophy is commonly divided septem artes liberales, inter quas neque naturalis into seven liberal arts, among which neither naneque divina continetur, sed sola rationalis et tural philosophy nor divine science is contained, mathematica.  but only rational and and mathematical science. 1 On the correct interpretation of this expression, see further below. 2 ergo ergo natura naturalis lis et divina divina non debuer debuerunt unt poni poni  partes speculativae. speculativae. Therefore, Therefore, natural natural philosoph philosophy y and divine divine science ought not to be put down as parts of speculative science. PS3 QU5 AR1 RA3 ad tertium dicendum quod septem liberales artes To the third it must be said that the seven liberal non sufficienter dividunt philosophiam theory- arts do not adequately divide theoretical philocam, sed ideo, ut dicit hugo de sancto victore in sophy, but then, as Hugh of St. Victor says in iii sui didascali didascalicon, con, praetermis praetermissis sis quibusda quibusdam m the third book of his  Didascalicon,  Didascalicon, setting aside aliis septem connumera connumerantur, ntur, quia his primum primum certain other arts, seven are numbered together  erudieban erudiebantur, tur, qui philosop philosophiam hiam discere discere volevole-  because those who wanted to learn philosophy  bant, were first instructed in them, et ideo distinguuntur in trivium et quadrivium, eo quod his quasi quibusdam viis vivax animus ad secreta philosophiae introeat. and so they they are distin distingui guishe shed d into into a trivi trivium um [“three roads” or ways] and a quadrivium [“four  roads” or ways] because they are, as it were, certain “roads” by means of which the lively  soul might enter into into the secrets of philosophy philosophy . et hoc etiam consonat verbis philosophi qui dicit And this agrees with the words of the Philoin ii metaphysicae quod modus scientiae debet sopher, who states in the second book of the quaeri ante scientias;  Metaphysics that the method of a science ought to be sought before the sciences; et commentator ibidem dicit quod logicam, quae docet modum omnium scientiarum, debet quis addiscere ante omnes alias scientias, ad quam  pertinet trivium. and the Commentator says the same thing, that logi logic, c, whic which h teac teache hess the the meth method od of all all the the sciences, ought to be learned before all the other  sciences, to which the trivium pertains. dicit etiam in vi ethicorum quod mathematica He also says in the sixth book of the  Ethics that  potest sciri a pueris, non autem physica, quae mathematics can be learned by boys, but not experimentum requirit.  physics, which requires requires experience. et sic datur intelligi quod post logicam consequente quenterr debet debet mathem mathemati atica ca addis addisci, ci, ad quam quam  pertinet quadrivium; quadrivium; And in this way one is given to understand that mathematics ought to be learned after logic, to which the quadrivium pertains. et ita his quasi quibusdam viis praeparatur animus ad alias philosophicas disciplinas. And so by these, as it were, “certain roads”, the soul is prepared for the other philosophical disciplines. vel ideo hae inter ceteras scientias artes dicuntur, tur, quia quia non solum solum habent habent cognit cognition ionem, em, sed opus aliquod, quod est immediate ipsius rationis, ut constructionem, syllogismum, 2 vel orationem formare, Then again, among the rest of the sciences these are called called arts arts becaus becausee they they involv involvee not not only only knowledge, but some work that belongs immediately to reason itself, as to form a construction,2 a syllogism, or a speech; 2 2 Correcting Busa’s  syllogismi and adding punctuation in order to give a reading supplying a work to each of the arts of the trivium. That is, to put together a sentence, inasmuch as the right construction of the sentence is the goal of the art of grammar. 3 numerare, mensurare, melodias formare et cursus siderum computare. to number, to measure, to form melodies, and to reckon the course of the stars. aliae vero scientiae vel non habent opus, sed cognitionem tantum, sicut scientia divina et naturalis; But the other sciences do not involve a work,  but knowledge alone, as in divine science and natural philosophy. unde nomen artis habere non possunt, cum ars dica dicatu turr rati ratio o facti factiva va,, ut dici dicitu turr in vi meta meta- physicae. For this reason they cannot have the name of  art, since art is called “productive reason”, as is said in the sixth book of the  Metaphysics.  Metaphysics. vel vel habe habent nt opus opus corp corpor oral ale, e, sicu sicutt medi medici cina na,, alchimia et aliae huiusmodi. Or they involve a bodily work, as medicine, alchemy and others of the sort. unde non possunt dici artes liberales, quia sunt hominis huiusmodi actus ex parte illa, qua non est liber, scilicet ex parte corporis. And so they cannot be called liberal arts because they belong to man on the side of that by which he is not free, namely, on the part of his  body. scientia vero moralis, quamvis sit propter operationem, tamen illa operatio non est actus scienti entiae ae,, sed sed magi magiss virt virtut utis is,, ut pate patett in libr libro o ethicorum. And moral science, although it exists for the sake of activity, still, that activity is not the act of the science but rather of virtue, as is clear in the Ethics the Ethics.. unde unde non non pote potest st dici dici ars, ars, sed sed magi magiss in illi illiss operationibus se habet virtus loco artis. So one cannot call moral science an art, but rather in these activities virtue takes the place of  art. et ideo veteres diffinierunt virtutem esse artem  bene recteque vivendi, ut augustinus dicit in iv de civitate dei. And this is why the ancients defined virtue as the art of living well and rightly, as Augustine says in Book IV of the City of God . Cf. St. Thomas Aquinas, Summa Theol ., ., Ia-IIae, q. 57, art. 3, ad 3 (tr. English Dominican Dominican Fathers): QU57 AR3 RA3 ad tert tertiu ium m dice dicend ndum um quod quod etia etiam m in ipsi ipsiss speculabilibus est aliquid per modum cuiusdam operis, puta opus constructionis aut syllogismi aut orationis congruae aut opus numerandi vel mensurandi.2 To the third third it must be said said that even even in speculative matters there is something by way of a certain work, for instance, a work of a construction, or of a syllogism, or of a fitting speech, or  a work of numbering or measuring. 2 I have corrected Busa’s text here, which reads, construct constructio io syllogism syllogismii aut orationis orationis congruae congruae , etc. A ‘construction’ is the work produced by the art of grammar, a syllogism, the work of  logic, and a fitting speech, the work of rhetoric. et ideo quicumque ad huiusmodi opera rationis And so whatever speculative habits are ordered habitu habituss specu speculat lativi ivi ordina ordinantu ntur, r, dicun dicuntur tur per  to works of reason of this sort, they are called quandam similitudinem artes, sed liberales; arts by a certain likeness, but liberal ones. 4 ad differentiam illarum artium quae ordinantur  ad opera per corpus exercita, quae sunt quodammodo serviles, inquantum corpus serviliter subditur animae, et homo secundum animam est liber. This is to distinguish them from the arts that are ordered to works performed by the body, which are somewhat servile because the body is sub ject to the soul in a servile manner, but man in regard to his soul is free. illae vero scientiae quae ad nullum huiusmodi opus ordinantur, simpliciter scientiae dicuntur, non autem artes. But sciences that are not ordered to a work of  this sort are called sciences simply, and not arts. nec oportet, si liberales liberales artes sunt nobiliores nobiliores,,  Nor is it necessary, if the liberal arts are nobler, quod magis eis conveniat ratio artis. that the definition of art belong more to them. Cf. St. Thomas Aquinas, Summa Theol ., ., IIa-IIae, q. 47, art. 2, ad 3 (tr. B.A.M.): QU47 AR2 RA3 ad tertiu tertium m dicend dicendum um quod quod omnis omnis applic applicati atio o To the third it must be said that every applirationis rationis rectae ad aliquid aliquid factibile pertinet pertinet ad cation of right reason to something makeable arte artem. m. sed sed ad prud pruden enti tiam am non non pert pertin inet et nisi nisi  pertains to art. But nothing pertains to prudence applicatio rationis rectae ad ea de quibus est except an application of right reason to those consilium. things about which there is counsel. et huiu huiusm smod odii sunt sunt in quib quibus us non non sunt sunt viae viae determinatae perveniendi ad finem; ut dicitur in iii ethic.. And of this sort are the things in which there are no determinate roads for arriving at the end, as is said in the third book of the Ethics the  Ethics.. quia igitur ratio speculativa quaedam facit, Therefore, Therefore, because because speculativ speculativee reason reason makes something,  puta syllogismum, propositionem propositionem et alia huiusmodi, in quibus proceditur secundum certas et determinatas vias; inde est quod respectu horum  potest salvari ratio artis, non autem ratio prudentiae. for instan instance, ce, a syllog syllogism ism,, a propos propositi ition, on, and other things of this sort, in which it proceeds accord according ing to certai certain n and determ determina inate te roads roads,, thence it is that with respect to these things it can preserve the character of art, but not the character of prudence. et ideo ideo inveni invenitu turr aliqua aliqua ars specu speculat lativ iva, a, non autem aliqua prudentia. And so a speculative art is found, but not [a speculative] prudence. Cf. St. Thomas Aquinas, In Aquinas, In I Meta., Meta., lect. 3, n. 8 (tr. B.A.M.): LB1LC-3N.-8 et notandum, quod hoc potest dupliciter intelligi. But one must note that this can be understood in two ways. uno uno modo modo quod quod hoc hoc quod quod dici dicitu turr haec haec sola sola demonstret in genere omnem scientiam speculativam. In one way the expression only this may indicate every speculative science in genus. 5 et tunc verum est quod solum hoc genus scientiarum propter seipsum quaeritur. And then it is true that only this genus of the sciences are sought on account of themselves. unde et illae solae artes liberales dicuntur, quae ad sciendum ordinantur: And this is why only those arts are called liberal which are ordered to knowing: illae vero quae ordinantur ad aliquam utilitatem  but those that are ordered to some benefit that is  per actionem habendam, dicuntur mechanicae had by action are called “mechanic” or “sersive serviles. vile”. Cf. Commentary on the Metaphysics of Aristotle by Thomas Aquinas, translated by John P. Rowan (Chicago, 1961), Book VII, lect. 2, n. 1303 (slightly rev. B.A.M.): lib. 7 l. 2 n. 34 1303. Et ideo in disciplinis oportet procedere ex In matters of learning, then, it is necessary to minus notis secundum naturam ad magis nota,  proceed from things which are less known by et hoc opus est, idest necessarium est hoc fa- nature to those which are more known. “And cere sicut in actibus hoc est in actibus vel one’s task is” the same here, i.e., it is necessary  potentiis activis, in quibus ex bonis uniuscuius- to act in the same way here, “as in practical que, idest ex his quae sunt bona isti et illi, fiunt matters,” i.e., in the arts and active potencies, ea quae totaliter sunt, idest universaliter bona, in which we go “from things which are good et per consequens unicuique bona. for each individual,” i.e., from things which are good for this person and for that person, so as to reach those things which “are” totally good, or universally good, and therefore good for  each individual. Militaris enim pervenit ad victoriam totius exercitus, quae est quoddam bonum commune ex singularibus victoriis huius et illius. For the military art attains the victory of the whole army, which is a certain common good, from the victories of this and of that particular  man. Et similiter aedificativa ex compositione horum lapidum et illorum, pervenit ad constitutionem totius domus. And similarly the art of building by combining  particular stones succeeds in constructing a whole house. Et similiter oportet in speculativis, ex his quae sunt notiora ipsi, scilicet addiscenti, pervenire oportet ad ea quae sunt naturae nota, quae etiam fiunt ultimo ipsi addiscenti nota. And so too in speculative matters we must proceed from those things which are more knowable to oneself, namely, to the one learning, in order to reach those which are knowable by nature, which also finally become known to the one learning. § 6 2. Matters pertaining to the liberal arts according to three Medieval Schoolmen. (a) The liberal arts according to Hugh of St Victor: Cf. The Didascalicon of Hugh of St. Victor: A Medieval Guide to the Arts. Translated from the Latin with an introduction and notes by Jerome Taylor (New York, 1961), Book III, chap. 3, pp. 86-87: Chapter Three: Which Arts Are Principally to Be read  Out of all the sciences above named, however, the ancients, in their studies, especially selected seven to be mastered by those who were to be educated. These seven they considered so to excel all the rest in usefulness that anyone who had been thoroughly schooled in them might afterward come to a know- [86-87] ledge of the others by his own inquiry and effort rather than by listening to a teacher. For these, one might say, constitute the best instruments, by which the way is prepared for the mind’s complete knowledge of philosophic truth. Therefore they are called by the name of tri vium and quadrivium, because by them, as  by certain ways (viae), a quick mind enters into the secret places of wisdom. (b) On the meaning of liberalis. Cf. Peter of Auvergne, In VIII Politic.2 L. 1. 1 (tr. B.A.M.): 1266. —Deinde cum dicit “quod quidem” Prosequitur. Et primo declarat in universali in quibus erudiendi sunt, quoniam in utilibus et liberalibus. 1266. Then when he says Which indeed  He continues. And first he declares universally in what they are to be instructed, since [they are to be instructed] in [both] useful and liberal things. Secundo cum dicit “Sunt autem quator”, magis determinate declarat quae sint illa. Second, when he says  Now there are four , he declares more determinately what they are. Circa primum primo ostendit quod in utilibus et liberalibus sunt erudiendi. With respect to the first, he first shows in what they are to be instructed in both useful and liberal things. Secundo cum dicit, “Sunt etiam quaedam”, declarat usque ad quid et cuius gratia. Second, when he says, There are also certain things, he even declares for what and for the sake of which [they are to be instructed]. Et circa primum est intelligendum quod homo liber est, qui est suipsius causa et in ratione causae moventis et in ratione finis, sicut dictum est  prius. And with respect to the first, one must understand that that man is free who exists for his own sake in both the character of a moving cause and in the character of an end, as has been stated earlier. In ratione quidem moventis, quando ab illo per  quod est homo et quod est principale in eo, puta ab intellectu, movetur praeiudicando et ordinando modum et rationem agendi. In the character of a mover, when by that through which he is a man and which is principle in him, for instance, by the intellect, he is moved by prejudging and ordering the manner  and reason for acting. 2 Being a continuation of St. Thomas’ commentary on the Politics. Cf. Pol . VIII, 1-3. 7 In ratione autem finis cum movetur ad bonum et finem ipsius secundum illud idem quod princi pale est in eo secundum intellectum; In the character of an end when he is moved to the good and the end with respect to the very thing which is principal in him according to understanding; et tanto magis liber est secundum naturam, quanto magis natus est moveri ab eo quod principalissimum est in eo et ad finem et bonum eius secundum illud idem. and to the extent that he is more free according to nature, to that extent he is naturally apt to be moved by that which is principal in him toward his end and good according to the same thing. Homo autem servus dicitur qui non est natus But that man is called a slave who, by reason of  moveri propter indispositionem materia ab an indisposition of matter, is not naturally apt to intellectu proprio per quem determinatur, sed ab  be moved by his own understanding through intellectu et ratione alterius; which he is determined, but by the understanding and reason of another man; nec etiam operatur sui gratia, sed gratia illius alterius. nor is he employed for his own sake, but for the sake of that other man. Et quanto minus natus est moveri a se et magis And to the extent that he is less naturally apt to ab alio et ad finem alterius, tanto magis servus  be moved by himself and more by another and est. for the end of another, to that extent he is more a slave. Ad hoc autem quod movetur ab alio et agat ad finem alterius, requiritur robur corporale. But for one to be moved by another and to act for the end of another, bodily strength is required. Et hoc rationabiliter accidit; quia ubi deficit virtus intellectus et formae, excedit virtus corporis et materiae. And this happens reasonably, seeing that, where the power of the intellect and of the form falls short, the power of the body and of the matter  exceeds. Et propter hoc dixit Aristoteles in primo huius, quod vigentes intellectu, etsi deficiant corpore sunt naturaliter aliorum domini: robusti autem corpore, deficientes intellectu, sunt naturaliter  servi. And for this reason Aristotle says in the first  book that those strong in understanding, even if  weak in body, are by nature masters of other  men: but the strong in body but lacking in understanding are by nature slaves. 1267. —Et secundum hoc scientia libera vel 1267. And in this respect a science was called liberalis dicta est ab antiquis secundum quam  free or liberal  by the ancients insofar as [by it] a homo per se disponitur secundum intellectum ad man is disposed  per se according to the underfinem proprium. standing toward his proper end. Illa autem secundum quam disponitur in ordine ad bonum corporis per se et ad bona exteriora, servilis, quia ordinatur ad bonum eius secundum hoc quod debet servire in homine, ut mechanice, quia moechari1 facit quodammodo intellectum circa ea quae non sunt propria sibi secundum quod huiusmodi. 1 But that insofar as he is disposed  per se in an order to a good of the body and to an exterior  good, [a science was called]  servile, since it is ordered to his good with respect to what ought to serve in man, as in mechanics, because in some way it makes the understanding adulterate1 about those things which are not proper to it insofar as they are of this sort. For an explanation of this usage, see m y note. 8 Et inter liberas illa libera est maxime quae immediate disponit intellectum ad finem optimum; And among the free that is most free which immediately disposes the understanding to the best end;  puta illa in cuius operatione consistit felicitas: for instance, that in whose activity happiness consists: illa autem quae mediate disponit intellectum ad  but that which in a mediate way disposes the ipsum, minus; understanding to itself, less so; sicut scientiae posteriores in quibus scire contingit ordinare ad scire in superiori, quamvis contigat ipsum quarere propter seipsum. as the sciences which come after in which knowing happens to order knowing [something] to the superior ones, although it happens to be sought on its own account. Et illa minime liberalis est inter speculativas, in qua minime quaeritur scire propter se, et quae  per plura media ordinatur ad bonum hominis ultimum. And that is least liberal among the speculative sciences in which knowledge is least sought on its own account, and which is ordered through many intermediates to the last good of man. Similiter inter servas illa magis serva est in qua Likewise among slaves that man is more a slave magis deprimitur intellectus seu ratio circa ulti- in whom the understanding or reason is more ora et magis extranea ab homine secundum  burdened about things more remote from and quod homo; more extraneous to man insofar as he is man; sicut illa quae ordinatur ad bona exteriora magis  just as that man which is ordered to an exterior  quam illa quae ordinatur ad bonum corporis. good is more [a slave] than the one ordered to a good of the body. Quamvis autem liberali maxime non contingat  Now, although the most liberal do not happen to uti male quantum ad usum per se ipsius,  be badly used inasmuch as to their use  per se  posterioribus tamen etiam minus liberalibus itself, still, those coming after are also less liquantum etiam ad usum earum per se contigit.  beral inasmuch as to their use it happens per se. Sicut circa finem ultimum hominis simpliciter  Just as about the last end of man it happens non contingit male se habere; simply not to have itself badly; his autem quae sunt ad ipsum, contingit quandoque male uti.  but the things which are for themselves sometimes happen to be used badly; Et hoc contingit quando per considerationem vel exercitium in eis retrahitur aliquis, vel a fine, vel ab his quae propinquiora sunt fini; And this comes about when by consideration or  exercise in them one is withdrawn either from the end or from the things that are closer to the end; sicut contingit per considerationem in aliqua scientia posteriori respectu alicuius minus sci bilis retrahitur aliquis a consideratione in prima respectu maxime scibilis. as happens by the consideration in any posterior  science with respect to any less knowable things someone is withdrawn from a consideration in the first thing with respect to the most knowable. N.B. On Peter’s use of the verb moechari in connection with the mechanical art, cf. the following: 9 Cf. The Didascalicon of Hugh of St. Victor: A Medieval Guide to the Arts, op.cit ., Book I, chap. 9, pp. 55-56: Among these works, the human work, because it is not [55-56] nature but only imitative of  nature, is fitly called mechanical, that is adulterate, just as a skeleton key is called a “mechanical” key. 64 64 Hugh associates “mechanical” with the Greek  moi)/xoj , Latin moechus, adulterer, rather  than with mhxane,3 machine. Cf. Martin of Laon Scholia graecarum glossarum (M. L. W. Laistner, ed. “Notes on Greek from the Lectures of a Ninth Century Monastery Teacher,”  Bulletin of the John Rylands Library , VII [1922-3], 439): “‘Moechus’ means adulterer, a man who secretly pollutes the marriage bed of another. From ‘moechus’ we call ‘mechanical art’ any object which is clever and most delicate and which, in its making or operation, is beyond detection, so that beholders find their power of vision stolen from them when they cannot penetrate the ingenuity of the thing.” Martin of Laon was a pupil of John the Scot and a teacher of Remigius of Auxerre, with whose works Hugh shows familiarity elsewhere in the  Didascalicon. Sallust  Bellum Jugurthinum XII.iii, uses the term claves adulterinae; see n. 48, for direct quotation of this work. Cf. also idem, Book II, chap. 20, p. 75: These sciences are called mechanical, that is, adulterate, because their concern is with the artificer’s product, which borrows its form from nature. Similarly, the other seven are called liberal either because they require minds which are liberal, that is, liberated and practiced (for these sciences pursue subtle inquiries into the causes of things), or because in antiquity only free and noble men were accustomed to study them, while the populace and the sons of  men not free sought operative skill in things mechanical. In all this appears the great diligence of the ancients, who would leave nothing untried, but brought all things under definite rules and precepts. And mechanics is that science to which they declare the manufacture of  articles to belong. Cf. Stephen Parcell, Four Historical Definitions of Architecture (Montreal, 2012), pp. 5758: Chapter 3. Architecture as a Mechanical Art Because Eriugena did not explain the origin or meaning of his term “mechanical,” others who followed may have been puzzled by its apparent reference to mechanics. 4 This ambiguity led subsequent writers in the ninth century to speculate on its origin and make their own interpretations. One line of thought devised an etymology that associated the mechanical arts with adultery. This may have been prompted by the similar sounds of two words: mechanikos and moechos (moixo/j , Latin moechus) ‘adulterer’. 64 During the next three centuries other  writers struggled to make sense of this association between adultery and the mechanical arts. One explanation suggested that the mechanical arts emphasize secrecy and hiding “like a man who pollutes the marriage bed of another. From ‘ moechus’ we call ‘mechanical art’ an object which is clever and most delicate and which, in its making or operation, is beyond detection so that beholders find their power of vision stolen from them when they cannot  penetrate the ingenuity of the thing.” 65 3 N.B. I discuss the meaning of mechanê in an Appendix to my paper Aristotle on What Is Inside and Outside a Work of the Poetic Art (Papers In Poetics 4). 4 Why should anyone be puzzled by such a reference? 10 This interpretation may have been reinforced by an additional, metaphorical meaning of  moechos as ‘unfaithfulness to God,’ 66 referring to the “corrupt” earthly realm and the dissociation of the mechanical arts from the liberal arts leading to Christian wisdom. In the twelfth century, Hugh [57-58] of St. Victor introduced several other variations to explain why the mechanical arts are “adulterate”: because they pursue merely human works; because they are not nature but only imitative of nature; because they are concerned with the works of human labour; and because their concern is with the artificer’s product, which borrows its form from nature.67 [N.B. Footnotes not available online, but cf. the excerpt given above.] (b) Robert Grosseteste on the liberal arts. Cf. Robert Grosseteste, De Artibus Liberalibus (early 13th c.): 1 In operibus humanis triplici de causa ingerit se error et imperfectio: quia mens obtenebratur per ignorantiam et quia eius affectus citra debitum sistit, vel ultra progreditur   per immoderantiam et quia virtutes motivae corporis instrumenta debilia sunt et imperfecta  per carnis corruptelam. – In quo autem opere incipit error et imperfectio, necessarium est regimen et adjutorium, quibus purgetur error et suppleatur defectus. In humanis vero operibus erroris purgationes et ad perfectionem deductiones sunt artes septenae, quae solae inter partes philosophiae ideo censentur artis nomine, quia earum est tantum effectus operationes humanas corrigendo ad perfectionem ducere. – Opera enim nostrae potestatis aut in mentis aspectu, aut in eiusdem affectu, aut in corporum motibus, aut eorumdem motuum affectibus omnia consistunt. Aspectus vero primo aspicit; secundo aspecta sive cognita verificat et cum verificata fuerint apud mentem seu aspectum convenientia seu nociva, inhiat affectus ad amplexandum covenientia, vel in se ipsum retrahit, ut fugiat nociva. Aspectum grammatica recte informat. Recte informatum quale sit logica sine errore dijudicat. Ut judicatum quale sit moderate fugiat affectus vel appetat, rhetorica persuadet. Officium namque grammaticae est recte intelligere et recte intellecta recte enuntiando apud alterum recte formare. Officium vero logicae est, quod recte formatum est in intellectu, secundum tripartitam rationem sui quale sit judicare et discu-2tare. Rhetorica vero, licet eius officium sit ex dialecticis et propriis locis argumenta probationis elicere, quod maxime intendit, est affectum movere. Estque in eius potestate, affectum animosque torpentes excitare, effrenos modificare, timidos anìmare, truces mitigare. – Haec est enim virga Mercurialis, cuius uno capite vigilantibus somnum relictis ingerit, somnolentis vigilantiam, haec Orphei cythara, cuius modulationem saxa sequuntur et arbores et eius audita dulcedine  pax est lupo cum agno, cani cum lepore, et catulo cum leone. – Mentis ergo aspectum et affectum hae tres virtutes rectificant et ad perfectionem perducunt. Cum autem attendimus non ad illud, quod efficitur per motus corporeos, sed in ipsis motibus moderationem, modifìcatrix est musica. Haec enim, ut asseruit Macrobius motuum  proportionibus reperitur concordantia. – Proportiones vero motuum secundum duplicem motus divisibilitatem considerantur. Est enim motus divisibilis divisibilitate temporis et secundum hanc divisibilitatem dicitur motus duplus ad alium, qui duplo mensuratur tempore, sicut etiam syllaba longa respectu brevis dupla est; et motus divisíbilis et proportionalis  proportionalitate et divisibilitate spatii: sicque motus dicitur duplus ad motum, qui in eodem tempore duplum pertransit spatium. 11 Quinque ergo sunt proportiones, quarum tres sunt minime multiplicium et duae maxime superparticularium: quia haec sunt inter maximas et minimas divisiones in motu secundum tarditatem, vel velocitatem, vel secundum utramque. Haec numquam praestant in motibus  perfectum moderamen. Hinc motus locutionum intelligo, quae licet a motu efficiatur, a natura motus non censetur sejungenda. Cum enim corpus violenter percutitur, partes  percussae et constrictae a situ naturali secedunt. Quas virtus naturalis ad situm naturalem inclinans fortiter metas debitas facit transscendere ipso impulsu naturali; iterum a situ naturali egrediuntur et de una inclinatione naturali situm transgredientes revertuntur  generaturque hoc modo tremor in minutissi-3mis partibus percussi corporis, donec tandem inclinatio naturalis non ultra situm debitum eas impellat. – In hoc autem tremore et motu locali partium motarum necesse est, cum quaelibet pars per situm sibi naturalem transeat, eius diametrum longitudinalem esse in termino suae diminutionis et diametri transversales erunt in termino suae majorationis. –- Cum autem transierunt situm naturalem, diameter  longitudinalis extenditur et transversales contrahuntur, donec perveniant ad terminum motus sui localis; eruntque tunc diametri transversales in termino suae diminutionis et longitudinales in termino suae majorationis. Deinde, cum redierit, erit extensio et contractio diametrorum via conversa. Hanc autem extensionem et contractionem ingredientem  profunditatem materiae et praecipue id, quod est aëreum subtile in corpore, sonativum esse intelligo. Cumque inter quoslibet motus contrarios sit quies media, necesse est, sonum quantumcumque parvum audibilem non esse continuum, sed interruptum et numerosum, licet hoc non percipiatur. Cum itaque eisdem proportionibus humanae vocis et gesticulationibus humani corporis modulatio temperetur, quibus soni et motus corporum reliquorum, speculationi musicae subjacet non solum harmonia humanae vocis et gesticulationis, sed etiam instrumentorum et eorum, quorum delectatio in motu sive in sono consistit et cum his harmonia coelestium sive noncoelestium. – Et cum a motibus coelestibus sit concordantia temporum et compositio et harmonia mundi inferioris et rerum omnium compositarum ex quatuor elementis necesseque sit harmoniam efficientium in effectis reperire et extendit se speculatio musicae, ut  proportiones temporum et elementorum mundi inferioris constitutionem cognoscat et etiam omnium elementorum compositionem. Et quia sono numeroso sive mixto sonanti correspondet numerus in progressione ad auditum, cumque sonus auri illabitur, exercet anima numerum in aëre generali in auribus aedificato, quo numero exercito numero sonanti occurrit et ipsum sentit numerum sonantem.  – Exindeque progrediens in memoriam, [desinens]que extra et in sensu totus simul et in memoria totus simul reponitur. Exinde in tota anima aptatur numerus quidam, quo aptato cum numero, qui extra jam desinit per ipsum numerum, qui jam totus 4 est in memoria, delectatur anima absque rationis judicio in numero sonantis, si sit consonus, aut offenditur, si sit dissonus. Qui numerus, cum sit praestans delectationem, aut contrarium, sensualis congrue nominatur. Tandem adhibet anima numeros judiciales, quibus de reliquis discernit. Cum inquam ita sit in numeris sonantibus, protendit se musica speculatio ut harmoniam cognoscat, non solum in numeris sonantibus seu corporalibus, sed etiam in progressoribus et occursoribus, recordabilibus, sensibilibus et judicialibus. Cum autem per motus nostros praeter ipsos motus aliquid intendamus, aut conjuncta dividimus, aut divisa conjungimus, aut ordinem, aut situm damus, aut figuras extrahimus. In his configurandis arithmeticam et geometriam constat esse rectificantes. – Quibusdam tamen rebus non damus absque errore, nisi praecognito mundi situ; et quaedam opera nostra non exstant usquam ordinata, nisi certis temporum spaciis fuerint mensurata. Propter hoc  praedictis tribus accessit astronomia, mundi situm et spacium temporum motibus astrorum docens dignoscere. 12 Cum igitur sint opera quaedam naturae tantum, quaedam nostra tantum, quaedam vero nostra et naturae, et hae solae philosophiae partes, quae dicta sunt tantum opera nostra et etiam opera naturae et nostra, in quantum quae nostra sunt rectificent et perficiant, et artis sit diffinitio seu dispositio, quod sit regula nostrae operationis, merito hae solae artis vocabulo nuncupantur. Hae septem naturalis et moralis sunt ministrae: nam grammatica et logica cum habeant sermonem rectum, habent probationem rectam: manifestum est, quod probationem veram ministrant. Moralis scientia etiam, quid appetendum, quid fugiendum est, edocet. – Rhetorica vero movet concupiscibilem ad appetendum, vel irascibilem ad fugiendum. Quapropter moralis scientia cum ornatu rhetorico vult doceri et sciri, ut proveniat morum informatio. Reliquae vero ornatum repudiant, in quibus quaeritur sola veritatis ordinario. Musicae ministerium in philosophia naturali non minus utile, quam ad medendum, cum omnis aegritudo et in ordinatione spirituum et in temperantia curatur et omnis etiam, qui per  or- 5 dinationem aut spirituum temperantiam curatur, musicis sanatur modulationibus et sonis, ut etiam credunt philosophi. Et dicunt etiam vulneribus et surdidati musicis modulationibus posse mederi: Cum enim anima sequatur corpus in suis passionibus et corpus sequatur animam in suis actionibus, corpore patiente ex numeris sonantibus extrahit anima in se numeros proportionatos secundum proportionem numerorum sonantium, movetque spiritus ipse easdem numerorum proportiones. – Sapiens igitur est, qui corporis humani signati novit debitam proportionem et quibus proportionibus fiunt elementorum et humidarum partium principalium spirituum et animae cum corpore concordiae et easdem  proportiones in numeris sonantibus effectas ut progressores et occursores animae illabantur  et ex incommensuratione omnia redeunt ad propriam commensurationem; qui novit etiam, qualiter spiritus dilatantur in gaudio, qualiter in tristitia contrahantur, qualiter circumferantur  in ira, qualiter in animosis super seipsis innudando [?] sese impellunt et excitant, qualiter in timidis sese fugiant, qualiter in mitibus sese quadam tranquillitate sedant et proportionatos sonos in musicis instrumentis, qui sciat educere, facile poterit, in quos voluerit affectus animi permutare. Astronomiae ministerio plus ceteris eget philosophia naturalis: nulla enim aut rara est operatio, quae naturae sit et nostra, utpote vegetabilium plantatio, mineralium transmutatio, aegritudinum curatio, quae possit ab astronomiae officio excusari. Non enim agit natura inferior, nisi cum eam movet et de potentia in actum dirigit virtus coelestis. –- Luna autem est, quae virtutes coelestes mundo conjungit inferiori. Quapropter cum in hora plantationis fuerit luna aucta lumine in quarta orientali seu medio coeli a fortunis [?] respecta, quarum virtutem applicet inferius, quia tunc in fortitudine operationis suae calorem vitalem in  plantam fortiter movebit, accelerabitque ac confortabit crementum eius et fructificationem. Si vero fuerit in eadem hora respectus Saturni, movebit in plantam frigus impediens vel destruens. Si vero fuerit respectus Martis, movebit calorem urentem impedientem vel coquentem eritque planta tardi crementi vel fructificationis modicae, vel penitus marcescit. 6 In praeparatione vero lapidis, quo metallorum fit transmutatio, non minus necessaria est horarum electio. Omnia enim metalla de intentione naturae aurum esse debuerunt: nec differunt ab auro, nisi sicut imperfectum a perfecto. – Cum enim virtus solis movet fumum sulfureum mundum commiscens illum cum argento vivo et decoquit ipsum decoctione temperata, fit aurum. – Cum vero calore solis complectitur frigiditas lunae, ita quod parva sit  praedictorum decoctio, nascitur argentum. – Sed si calori solis commisceatur frigiditas Saturni, quia ipse est terreus, movetur fumus sulphureus cum immunditia terrestri et commiscetur cum argento vivo (et) mundo et decoquitur decoctione parva, nascitur  13  plumbum. – Si autem calori solis commisceatur calor et humiditas Jovis, movetur fumus sulphureum ingressione sua et commiscetur cum argento vivo (et) mundo, sed propter  humidi tatem Jovis parva fit decoctio et oritur stagnum. – Cum autem calori solis admiscetur  calor superfluus et siccitas Martis, sulphur grossum cum argento vivo grosso, superflue excoquitur et ferrum estrahitur. – Calor autem Veneris cum calore solis proxime dicta decoquens plus decoctione temperata, minus tamen quam sit decoctio excussa per Martis lotionem excutit. – Virtus vero Mercurii cum aqua viscosa fumum sulphureum commiscens vivum efficit argentum. – Reliqua vero ab auro non differunt, nisi secundum immunditiam materiae ant complexionis inaequalitatem. Quapropter transmutare ista est immunditias abstergere et mundificatis substantiam apponere assimilatam soli in virtute et operatione, quae ipsa reducit ab inaequalitate. – Haec substantia non qualibetcumque hora praeparatur, sed cum fuerit sol in exaltatione librae ab aspectu malorum; quae tunc est in fortitudine et extrahit in materia huius(modi) substantia virtutem sibi assimilatam, quam non potest nisi in certis horis de potentia ad actum producere. In morbis iterum valet horarum electio, quia, si hac postposita morbus curatur, magis est fortunae, quam artis. Medicina enim est instrumentum vel coadjutrix naturae, ut morbum expellat: nec sanat medicina sed natura per medicinam adjuta. Quapropter oportet considerare, quibus horis natura, quae languet, a virtute coelesti movetur, ne medicus operetur cum errore; et in quibus horis a virtute coelesti natura movetur immo regitur, et 7 in quibus naturam movet debiliter et in quibus fortiter et secundum has diversitates motionis naturae a virtute coelesti eam regente observanda est in virtute et duratione et quantitate  praeparatio medicinae. § 14 3. On the contemporary understanding of the seven liberal arts. Cf. Otto Willmann, “The Seven Liberal Arts”, The Catholic Encyclopedia. Vol. 1 (New York, 1907): The expression artes liberales, chiefly used during the Middle Ages, does not mean arts as we understand the word at this present day, but those branches of knowledge which were taught in the schools of that time. They are called liberal (Lat. liber , free), because they serve the purpose of training the free man, in contrast with the artes illiberales, which are pursued for economic purposes; their aim is to prepare the student not for gaining a livelihood, but for the pursuit of science in the strict sense of the term, i.e. the combination of philosophy and theology known as scholasticism. They are seven in number and may be arranged in two groups, the first embracing grammar, rhetoric, and dialectic, in other words, the sciences of  language, of oratory, and of logic, better known as the artes sermocinales, or language studies; the second group comprises arithmetic, geometry, astronomy, and music, i.e. the mathematico-physical disciplines, known as the artes reales, or  physicae. The first group is considered to be the elementary group, whence these branches are also called artes triviales, or trivium, i.e. a well-beaten ground like the junction of three roads, or a cross-roads open to all. Contrasted with them we find the mathematical disciplines as artes quadriviales, or  quadrivium, or a road with four branches. The seven liberal arts are thus the members of a system of studies which embraces language branches as the lower, the mathematical  branches as the intermediate, and science properly so called as the uppermost and terminal grade. Cf. Marcus Berquist, On the Art and Science of Grammar . Grammar and the Seven Liberal Arts, Part II (Thomas Aquinas College Handout, 1994), p. 12. The seven liberal arts are divided into a group of three—the trivium, and a group of four—  the quadrivium. The latter are mathematical: geometry and astronomy, arithmetic and music. Although they are preparatory for the more honorable and more difficult parts of philosophy, they are not practical or instrumental, but theoretical. On the other hand, the arts of the trivium—grammar, rhetoric, and logic—are methods rather than theoretical sciences, and teach about the modes to be observed in speaking and reasoning about things, rather than about things themselves. Even logic, though it is theoretical in its subject and mode of   procedure, is not an end in itself, but is instrumental to the work of philosophy proper. Thus, as Boethius says, it may reasonably be considered the instrument of philosophy rather than  philosophy (Comm. in Porph. Isag., 74 A-D), and with reason Aristotle names his own treatise on logic Organon (i.e. “tool”). Thus, the relation of logic to the particular sciences is not the same as that of pure mathematics to applied mathematics. Geometry, for example, has its proper method, as does any science, but it is not itself  a method, while logic is essentially a method—the common method of all the sciences. And rhetoric and grammar  are likewise methods, and consider the modes and “intentions” of things, rather than the things themselves. Cf. Thomas Aquinas College Bulletin. Curriculum: The liberal arts are first in the order of learning. These are seven arts the objects of which are constructed within the intellect, not outside, as in the technical arts. The carpenter’s house, the sculptor’s statue, the health of the doctor’s patient, the republic fashioned by the statesman, all these exist apart from the mind; the objects of the liberal arts do not. The principles proper to these liberal arts are formally studied in tutorials. 15 Three of these arts—grammar, rhetoric, and logic (the trivium)—use words as their outward symbols. Sentences, speeches and syllogisms, spoken or written, signify these internal constructions. The four remaining liberal arts (the quadrivium)—arithmetic, geometry, astronomy, and music—use mathematical symbols as their outward signs. The trivium is com prehended by the Language and Logic Tutorials, while the quadrivium is comprehended by the Mathematics and Music Tutorials. These tutorials introduce the program. § 16 4. The liberal arts and liberal education: Readings from Thomas Aquinas College (Santa Paula, CA). Cf. A Proposal For The Fulfillment Of Catholic Liberal Education; sec. VII. Liberal Education, Its Parts and the Order among Them (Thomas Aquinas College Blue Book): Some puzzlement may be occasioned by the fact that we have nowhere spoken of the liberal arts. Are they what we have been discussing all along? To be sure, in modern times, liberal education is usually identified with the liberal arts, but traditionally they are distinguished. Liberal education names the whole procedure of the philosophic life, including the study of wisdom itself; liberal arts, on the other hand, properly names seven introductory disciplines which though intrinsically of lesser philosophic interest are “certain ways by which the lively soul enters into the secrets of philosophy.” (Hugh of St. Victor) These arts are twofold: some concern the proper method of discourse, such as grammar, rhetoric, and logic (the trivium), while others treat of quantity and the quantitative, such as geometry, arithmetic, astronomy, and music (the quadrivium). (The introductory studies of the stars and of music consider only the quantitative aspects of their subjects.) The former are clearly instrumental in purpose, being concerned exclusively (though in quite different ways) with common methods; the latter study kinds of order which though less profound are more intelligible to the beginner, and inescapably provoke wonder about the more difficult and important issues of philosophy proper. Thus, it is clear that the quadrivium (the mathematical disciplines) have already been included in our survey. The trivium must here be added. Taking logic as the principal part of the trivium, we are thus left with a threefold division of doctrine, into theoretical, practical, and logical. We are encouraged to rest in this division by recalling that it is the one given by St. Augustine as a likeness of the Blessed Trinity. (City of God , Bk. XI, ch. 25) Cf. Thomas Aquinas College Bulletin. The Place of the Liberal Arts in the Curriculum: In recent times, liberal education has usually been identified with the liberal arts, but traditionally they are distinguished.  Liberal education names the whole procedure of the philosophic life, including the study of wisdom itself; liberal arts, on the other hand, properly names seven introductory disciplines which, though intrinsically of lesser philosophic interest, are “certain ways by which the lively soul enters into the secrets of philosophy” (Hugh of St, Victor). Both the trivium and the quadrivium of the liberal arts are intrinsically ordered toward science and philosophy. As already mentioned, the trivium provides the universal instruments of all scientific demonstration. The quadrivium, too, moves in the same direction. Pure mathematics is an art, inasmuch as the subject matter is constructed in the imagination,  but it is also a science, insofar as the mental constructs are not arbitrary; rather, they are constructed according to the nature of quantity. For example, the equilateral triangle that is constructed in the first proposition of Euclid’s  Elements is discovered, not invented. The mathematical sciences are the clearest and most accessible, and thus supply the logician with the readiest paradigm of scientific demonstration. They prepare the disciple for more difficult sciences and furnish him with rigorous knowledge that may be used to express the order  found in non-mathematical objects, as in astronomy and music. Philosophy is broadly divided into speculative and practical or moral philosophy. In its speculative aspect, philosophy is interested in nature and its causes. Moral philosophy, on the other hand, is concerned with right reason as it applies to our active life, that is, as it regulates the life of the passions and appetites, which move us. Astronomy and music take up these broadly divided parts of philosophy in an extrinsic way. They recognize an order in the cosmos and in the movements of men’s feelings, and this order is expressed in the light 17 of mathematical principles. It remains for philosophy to account for these things in terms of  the intrinsic natural and moral principles. Cf. Thomas Aquinas College Bulletin. Liberal Education and the Humanities. Marcus R. Berquist (excerpts):  Anomalies in the Modern Curriculum …Thirdly, the traditional liberal arts, which were conceived as an introduction to liberal education, do not favor this way of dividing the curriculum. Logic, for example, which is a  part of the trivium, is presumably as important to the scientist as it is to the humanist, and  perhaps more so. Furthermore, the arts which comprise the quadrivium —geometry and astronomy, arithmetic and music—are all mathematical. (The astronomy and music which are liberal arts explain their subject-matters by mathematical principles exclusively, since such explanations are proportioned to beginners)….  Another View of Liberal Education These difficulties, among others, immediately arise when we accept the modern distinction  between the sciences and the humanities. They were not proposed in order to refute conclusively, but in order to prepare the way for an alternate view of the division and order of  liberal studies. This view, of course, is not a new one but goes back, in its essentials, to the  best of Greek learning. Our presentation of it will involve a deeper criticism of the modern curriculum and its consequences. To begin with, we define liberal education as the education of a free man, much as the moderns do, although our understanding of freedom is somewhat different from theirs. A free man is a man who lives for himself in this sense: He realizes within himself the end for  which he lives and is joined to it in his own person. He is contrasted with the slave, for the good which the latter realizes by his activity exists in other men or even in other things. Thus, a free man is one whose life has intrinsic meaning, and liberal education will be that which befits such a person and enables him to live in such a way. 5 Now some would immediately dismiss this distinction between the liberal and servile as something entirely relative to those societies—happily long gone—in which there were masters and slaves. But here we do not mean that sort of slavery, the condition of certain men in certain places at certain times. Rather we are thinking of a universal slavery which oppresses all men, for human nature, as Aristotle says, is in many ways in bondage. For we see that, despite the legal freedom of which we boast, the better part of our lives is taken up with actions which are only necessary; they are not desirable in themselves and are no part of happiness, but are needed for something else. And this something else is all too often no 5 Cf. also Marcus Berquist, “Where Philosophers Disagree”. Lectio (1994) (Originally delivered as a lecture at Thomas Aquinas College): I think liberal education is largely the same as philosophy, “philosophy” understood in its original sense as “the love of wisdom”. A man who loves wisdom desires knowledge for its own sake, he thinks that knowledge is, in and of itself, a perfection of his soul, something worth living for. That’s very much what liberal education is about. Liberal education is the education of a free man. A free man is, if not by immediate definition, by implication a man who concerns himself with things that are intrinsically worthwhile. He’s not just a servant, or an instrument of other men, but someone who lives a life which is in itself worth living. So liberal education is concerned with the kind of knowledge that a man ought to have, not because he wants to put it to some particular use, a kind of knowledge that he would do without if he could have the end of that use without the knowledge, but something worth having just for itself. He sees a kind of happiness, a kind of completeness to his life as a human being just in having that knowledge. 18 more than simply to continue to exist. Already a third of our lives is taken up with sleep, and if we also subtract the time spent in necessary work or in amusement (which is also necessary in a way), the remainder is precious little and seems hardly enough, in quantity or quality, to justify the trouble of living. Perhaps the most bitter part of this condition is the bondage of the intelligence, which in spite of being the best and most divine thing in man, spends nearly all its time and effort in caring for the body and has little or nothing for itself. For the proper good of the intelligence is truth and knowledge, but because of the necessities of this mortal life, it is compelled to  put aside its quest for wisdom in order to attend to the inferior parts of man. In consequence, life is not intrinsically worthwhile; we are always preparing to be happy, but we are never  happy.  Liberal Education Ordered to the Divine However, this present life does allow some leisure to some of us, and liberal education seeks to exploit this leisure so that we might achieve as much freedom as possible. Accordingly, it is directed to the kinds of knowledge that human understanding seeks for its own perfection. Thus it is not concerned primarily with practical knowledge—the knowledge of making and doing—for no such knowledge is desirable in itself. If we could have the practical results without the knowledge, we would not bother with the latter; for exam ple, if the sick could get well by themselves, no one would study medicine. We might say, then, that the free man does not desire learning in order to change the world, but sees in learning itself the kind of change that the world needs. While he cannot neglect the necessities of life, he finds his end and freedom in knowledge. And this knowledge is primarily theoretical—that is, it is sought, and is worthy of being sought, for its own sake. But what is this knowledge which is a free man’s happiness? Surely it cannot be a knowledge of man himself and of the various expressions of his humanity? Or does this depend upon another question: Is man the most excellent of all things that are? If he is, we shall have an answer, since the knowledge of man will them be the most excellent and worthwhile knowledge, and the poet’s statement will be true: The proper study of mankind is man. For what better use could he make of his life? On the other hand, if man is not the primary being, but the effect of superior causes and derives all the excellence he possesses from them, he will not achieve happiness through knowledge of himself, but rather through the knowledge of those causes. Liberal education, then, will not be humanistic—it will not be ordered to the human but to the divine. Even though it may humanize man through self-awareness, this will not be the measure of its success. This is Aristotle’s argument in the tenth book of the  Nicomachean Ethics: But such a life would be too high for man; for it is not insofar as he is man that he will live so, but insofar as something divine is present in him; and by so much as this is su perior to our composite nature is its activity superior to that which is the exercise of the other kind of virtue. If reason is divine, then, in comparison with man, the life according to it is divine in comparison with human life. But we must not follow those who advise us, being men, to think of human things, and, being mortal, of mortal things, but must, so far as we can, make ourselves immortal, and strain every nerve to live in accordance with the best thing in us; for even if it be small in bulk, much more does it in power and worth surpass everything. On these premises, humanistic studies will never be the core of liberal education.  An Orientation to Things Better than Man 19 The traditional liberal arts are a sign that liberal education was not originally humanistic,  but rather followed Aristotle’s doctrine. Within the quadrivium especially, we find this doctrine confirmed; for astronomy and music are principal in that division, since geometry is ordered to the former and arithmetic to the latter. Now it is reasonable to suggest that astronomy is a prefiguration of the theoretical sciences generally, where knowledge is the end, since the stars are not something we can do something about—we can only learn about them. And the stars certainly seem to be, and were originally thought to be, of a higher order than man, immortal, and even divine. Furthermore, theoretical studies are ultimately concerned with the order of the universe as a whole, and it is from star-gazing and astronomy that we first begin to apprehend and wonder about that order. And the image of the astro-nomer, the man who does not see things at his feet because he is looking up, forcefully suggests that liberal education concerns things higher than man. This is perhaps the reason why mechanics, as interesting as it is, is not one of the liberal arts. For in mechanics, geometry is applied to certain problems which are sublunar and on our own level, so to speak. Thus, it does not express the fundamental orientation of the human mind, which is toward things better than man. Now whether the stars are really as the ancients supposed is not important for this argument; what is important is that they made astronomy rather than mechanics a liberal art. The science of music, on the other hand, would seem to prefigure the practical or moral sciences, which concern the ordering of man’s soul. For inasmuch as music imitates the  passions of the soul, the discovery that arithmetic principles many be applied to musical tones suggests that a parallel order exists within the passions themselves. One is thereby led to suppose that the inclinations and affections can be ordered by reason and that it is possible to understand how they ought to be ordered. However, the fact that the science of music is completely theoretical in mode also suggests that the basis of man’s moral life is given by nature, rather than instituted by man himself. This runs against the first principle of humanism, that man is the measure of all things, as well as against its corollary, that beauty is only in the eye of the beholder. (Hence the intimate connection that we observe between moral relativism and the denial that there is a natural musical harmony is understandable. The one view is very much akin to the other.) If, therefore, man is not the measure of all things, liberal education does not consist primarily of humanistic studies, and philosophy in particular is not rightly classed among the humanities. Rather, as Aristotle argues and the traditional liberal arts suggest, it is concerned  principally with things better than man. Now, in conclusion, we are going to take this argument one step further and attack something we conceded beforehand. We said that if man is the highest being of all, then education will primarily be concerned with man. Even as a hypothetical statement, this is not quite true. For even if man is the most excellent of beings, he is still something which comes to be and passes away. Therefore, there must be explanatory causes and principles of man, for we ask the question “Why?” first and foremost in the case of beings which come to be and pass away. And, in point of fact, there is no philosopher, even among those who hold that man is the supreme being, who does not think that man needs to be explained and who does not look for principles in terms of which to make an explanation. Now, if these principles are to explain the human, they must be other than human. But also, by our present hypothesis, they would have to be subhuman. Therefore, the human would have to be explained in terms of the subhuman and the rational in terms of the subrational, and, furthermore, they would have to be fully explained in such terms. Now what this means is that man could not be, in final analysis, anything essentially better than the nonhuman and nonrational. This consequence may be gathered from the testimony of the  philosophers themselves. For not one of those who attempt to explain human nature in terms of the subhuman has not finally said that man is essentially no different from the rest of  things. For example, the atomists, both ancient and modern, hold that higher beings are sim ply combinations of various simple particles, and not essentially different from or better than 20 those particles or the other things made out of them. We see this also in the evolutionary  philosophers. Darwin, for example, holds that the difference between one species and another is at bottom the same sort of difference as that between one variety and another. So the difference between man and horse is in principle the same as the difference between one horse and another. Teilhard de Chardin is a more recent example of this point of view. And, given the premises, this is the only reasonable point of view, for to assume otherwise would  be to assume that an effect is more than all its causes put together. The final outcome of humanism, then, is that we are led to regard the difference between man and the animals (as we ordinarily conceive it) as an illusion. Thus, all the reasons given for the preeminence of humane studies are finally destroyed by the logic of humanism itself. The upshot is that each man orders his education by his own particular taste or by what is currently fashionable, for he can no longer find any reasons for preference in the natures of  the objects he studies. The wonder which characterizes the philosopher has been replaced by curiosity. It would be a mistake, of course, to attribute the mindless disorder of modern education to a bad division of the curriculum. However, those who are attempting to restore some order  usually fail to realize how much a defective understanding of such matters stands in their  way. The alternative to such “muddling-through” is a wholehearted return to older traditions of liberal education, particularly as regards the natures of the various disciplines, the order of  their importance, and the order in which they are to be learned. Cf. John W. Neumayr, “Death of the Mind: The Anti-Intellectualism of ‘Cultural Diversity’ in Education”, in Measure, no. 120, January/February 1994. pp. 1-9 (excerpt). PREFACE “Liberal education” also has more than one sense. Perhaps the dominant sense in colleges today is equivalent to the meaning of the “humanities”. The “humanities” have stood for a  body of studies that is not so much concerned with reality as with intellectual interpretations, achievements and assumed interests of mankind. These studies purport to take into account not only the object to be known, but also the subject who knows and reacts to it. Social studies and appreciation courses fall within its limits, while mathematics and science 2 do not  —for the latter appear to leave the knowing object out of the picture. Although this notion of  the “humanities” is very ancient, it came into prominence especially in the Renaissance. The classical notion of “liberal education”, on the other hand, the notion associated with Plato and Aristotle and the Medieval Schoolmen, is purely concerned with things or objects themselves. Human opinion or invention are only of concern to the extent that they lead to an understanding of reality. Rather than to make individual man and his thought the object of  study, liberal education in this classical sense develops the tools of learning, called the liberal arts, and seeks a grounding in philosophy and in the variety of disciplines that form the foundation of all wisdom. Mathematics and science are as much a part of this tradition as are ethics and poetics. “Liberal education” in the second sense is the focus of this paper. 2 Although quantum theory of physics involves observers as triggers of the act of observation, such observers are still a part of the objective theoretical framework and have no reactive influence on the process at hand. Cf. also Liberal Education and Cultural Diversity. Thomas Aquinas College, pp. 1, 4-5, 8:6 6 Note that this paper, the source of the foregoing article, arose in response to the work of a Commission of  the Western Association of Schools and Colleges (WASC), a regional accrediting agency. 21 By “liberal education” is meant a certain body of learning consisting of the trivium, quadrivium, and several philosophical studies that are proportioned to the “generally educated man”. (p. 1) II. DIVERSE “UNIVERSALISMS” There is even a third sense of “universal” and, consequently, of “universalism”, that deserves to be mentioned. In this third sense, the one-to-many is not of a whole to its many  parts, nor of one nature found in many subjects, but of one cause that extends itself to many effects, such as the sun which heats all the objects beneath it. If we look carefully at Standard 4.B.2 mentioned above, we can see that the Commission implicitly notes this sense and uses it. We recall that the Standard states that the “outcomes” to be ensured by undergraduate studies include: (a) competence in written and oral communication, (b) quantitative skills, and (c) the habit of critical analysis of data and argument. The Standard then states that to these “basic abilities and habits of mind, an appreciation of cultural diversity” should  be added. Notice that the first three “outcomes” are characterized as “basic abilities” in relation to this last “outcome”, which is “an appreciation of cultural diversity”. In designating the skills of communication, calculation, and analysis as “basic abilities”, the Standard recognizes the group as the necessary means to further study. As “abilities”, they are tools to  be used in the more advanced studies such as those of “cultural diversity”, and as “basic” they are seen to be so fundamental that no advanced study can take place without them. They are, in fact, like reason itself, the universal means of the whole spectrum of learning. Thus, the group of “basic abilities” stands to all the other arts and sciences as one-to-many. (p. 4) III. FALSE DICHOTOMY At the opening of his treatise On the Parts of Animals , Aristotle speaks for the whole of  liberal education when he observes: Every systematic science, the humblest and the noblest alike, seems to admit of two distinct kinds of proficiency; one of which may be properly called scientific knowledge of the subject, while the other is a kind of educational acquaintance with it. For an educated man should be able to form a fair off-hand judgement as to the goodness or badness of the method used by a professor in his exposition. To be educated is in fact to be able to do this; and even the man of universal education we deem to be such in virtue of his having this ability. It will, however, of course, be understood that we only ascribe universal education to one who in his own individual person is thus critical in all or nearly all branches of knowledge, and not to one who has a like ability merely in some special subject. We see in Aristotle’s account of the liberally educated person, that his concern is not with specialized knowledge, but with the breadth of disciplines that makes it possible for him to advance into any further field of knowledge. It emerges from Aristotle’s description of the generally educated man that the whole of his liberal education stands as the “basic abilities”  brought to perfection and thus as the tools par excellence for all further inquiry. The inherent limit and purpose of his liberal education is to prepare him for any and all investigations. The habit of mind he possesses stands to the rest of knowledge as the one means to the many  possible ends. In a phrase, liberal education is the  passe-partout , the master key that opens all the doors of wisdom. In this sense, liberal education is the universal that extends itself  into all inquiry, including “cultural diversity”. It is distinct from diversity but hardly exclusive of it. (pp. 4-5) VI. THE CLASSICAL COLLEGE TODAY 22 The curriculum of the college where I teach falls wholly within the classical model of li beral education. Not only are its parts, the trivium, quadrivium, and various philosophic studies, at the center of that tradition, but the curriculum also draws exclusively for its texts on the original sources of that tradition, the “Great Books”. The College even follows the  pedagogy of Socrates as closely as possible. Teaching is done by way of discussions instead of through lectures, with small groups of students in tutorials and seminars. (p. 8) Cf. Rev. Thomas A. McGovern, S.J., “Liberal Education and Freedom”: Liberal Education and Freedom By Rev. Thomas A. McGovern, S.J. Tutor, Thomas Aquinas College, 1972–1985 Thomas Aquinas College defines itself in terms of liberal education and is concerned exclusively with such education. That phrase itself may suggest different notions to different  people, but there is one traditional meaning thereof that the College intends to signify, and to which it adheres when it identifies itself as dedicated to liberal education. According to this understanding, the term liberal in the context is derived from the Latin adjective liber meaning free. Used substantively, liberi signifies free men or the sons of free men. Clearly, then, education denominated liberal will be so named because of some connection seen and implied between such education and human freedom. What is here implied  by the adjective is, however, not education denominated liberal because it flows from a spirit that is free in the sense of uncommitted, unbound to principle, approving everything and excluding nothing; rather, it refers to its end, or purpose. The kind of education here envisioned is called liberal because it is ordered to freedom as to its goal; it is called liberal, in other words, because its intended effect is the genuinely free person. Human Freedom: To Be Achieved through Knowledge In this, our day, we tend to regard freedom as our natural birthright; we see ourselves as born free and this liberty of ours as a heritage to be jealously guarded against restrictions stemming from without — from political systems, for instance, or social structures. But clearly others, in the past, have seen human freedom in quite another light, not as a natural endowment, but as a great good to be achieved for the individual by his own efforts, and this, at least in part, through his education. Our Savior Himself appears to have regarded human freedom in this light, as a good to be achieved and to be achieved through knowledge of the truth. Speaking on one occasion in the Temple precincts to those “Jews who believed in Him,” he informed them: “If you remain in the truth, you will be truly my disciples, and the truth will make you free” (John 8:32). Christ’s words clearly ran counter to their cherished belief that descent from Abraham was their guarantee of freedom. “We are children of Abraham and have never been slaves to any man.” But Our Savior’s words imply that, if a person is to be truly free, more is necessary than birth into a nation called free: freedom is to be acquired, and its acquisition involves some knowledge of the truth He taught. Relation of the Truth to Freedom As instances of such, we recall the beatitudes that begin the Sermon on the Mount, and that sermon in its totality. The world hears these precepts and sees them as inhibiting, restrictive, anything but liberating. Yet they are all part of the truth “that will make you free.” 23 The relation of such truth to freedom begins to emerge when we consider what is actually implied in the notion of a free person. The free man must be understood in opposition to the slave. The latter is other-directed. The free person, then, is the one who is self-directed; he directs his own activities, the course of his own life, and it is precisely this self-direction that calls for some knowledge of the truth. No man can direct himself in the dark. But it is Christ who is “the light of the world.” But he who knows the teaching of the Word Incarnate knows that his God-given goal in life is membership in the Kingdom of God. He knows the kind of  living that is conducive to that end — life in accord with Christian virtue. He knows that freedom implies control over his own lower nature since it is this, rather than any exterior   power, that is the enslaving tyrant. He knows, in sum, that the free man, the happy man, the good man, are all one and the same. In this light he can direct his own steps; he is not the slave of the blind who would lead the blind. The Kind of Knowledge That Perfects Man Such knowledge as this would, then, clearly be part of the education of the free man, and a course of liberal studies must include the moral teachings of the Church through which Christ speaks, and the ethics and politics which are the natural counterpart of the same. Christ’s liberating doctrine teaches that man’s true end and happiness consist in the beatific vision – face-to-face knowledge of the infinite God. This truth contains implicitly another, namely that the kind of knowledge which does, of itself, perfect man, contributing to human goodness and happiness, is knowledge not of those things that he himself produces and which are, accordingly, less than he is, but of things greater than he. But, again, the free person, in opposition to the slave, whose activities are for the good of  another, is his own man; he devotes himself to what is really for his own good. Supernatural theology, therefore, which studies God and divine things, and metaphysics, which is both its counterpart on the natural plane and necessary for it, will be essential parts of the education of the free man. Nature, too, in the sense of particular principles of motion inherent in created things, the products of the Divine Wisdom that designed them, and beyond the  power of man to produce, will engage his attention. There is an order, too, inherent in things as quantified which is also an effect of the Divine Wisdom inherent therein; hence mathematics and geometry, which consider that kind of order, and which, further, are necessary if  nature is to be adequately understood, are parts of the education of the free man. Liberal Education: Basic to the Good Life The seven liberal arts and sciences are “certain ways by which the lively soul enters into the secrets of philosophy” (Hugh of St. Victor). As preparatory, then, to the properly philosophical and theological enterprise, these, too, play their role as parts of the entire program of liberal education. The above is, in skeleton form, the program for the education called liberal at Thomas Aquinas College and the rationale thereof. Its natural effect, of course, is not good accountants, or  good carpenters, or good musicians, but good men. Such education tends to be regarded as impractical, but the fact is that a people cannot long neglect the type of questions it raises and answers except at that people’s own peril, for such matters are basic to the good life. More than a decade of experience has confirmed the College in its conviction that such education is indeed beneficial in a deeply human way. Were this land of ours committed to education along these lines, its face would be remarkably changed — in the direction of justice and the other virtues, of general happiness, and, finally, in the direction of true human freedom. 24 § See also: Thomas Aquinas College, Founding & Governing Document 25 5. Additional readings by certain authors in the Great Books tradition. Cf. Mortimer Adler on the liberal arts and liberal education. WHAT IS LIBERAL EDUCATION?  by Mortimer Adler  Let us first be clear about the meaning of the liberal arts and liberal education. The liberal arts are traditionally intended to develop the faculties of the human mind, those powers of  intelligence and imagination without which no intellectual work can be accomplished. Liberal education is not tied to certain academic subjects, such as philosophy, history, literature, music, art, and other so-called “humanities.” In the liberal-arts tradition, scientific disciplines, such as mathematics and physics, are considered equally liberal, that is, equally able to develop the powers of the mind. The liberal-arts tradition goes back to the medieval curriculum. It consisted to two parts. The first part, the trivium, comprised grammar, rhetoric, and logic. It taught the arts of  reading and writing, of listening and speaking, and of sound thinking. The other part, the quadivium, consisted of arithmetic, geometry, astronomy, and music (not audible music, but music conceived as a mathematical science). It taught the arts of observation, calculation, and measurement, how to apprehend the quantitative aspect of things. Nowadays, of course, we would add many more sciences, natural and social. This is just what has been done in the various modern attempts to renew liberal education. Liberal education, including all the traditional arts as well as the newer sciences, is essential for the development of top-flight scientists. Without it, we can train only technicians, who cannot understand the basic principles behind the motions they perform. We can hardly expect such skilled automatons to make new discoveries of any importance. A crash  program of merely technical training would probably end in a crashup for basic science. The connection of liberal education with scientific creativity is not mere speculation. It is a matter of historical fact that the great German scientists of the nineteenth century had a solid  background in the liberal arts. They all went through a liberal education which embraced Greek, Latin, logic, philosophy, and history, in addition to mathematics, physics, and other  sciences. Actually, this has been the educational preparation of European scientists down to the present time. Einstein, Bohr, Fermi, and other great modern scientists were developed not by technical schooling, but by liberal education. Despite all of the ranting and hullabaloo since Sputnik I was propelled into the skies, this has been broadly true of Russian scientists, too. If you will just note the birth dates of the men who have done the basic work in Soviet science, it will be apparent to you that they could not have received their training under any new system of education. As for the present educational setup in the Soviet Union, which many alarmists are demanding that we emulate, it seems to contain something besides technical training and concentration on the natural sciences and mathematics. The aim of liberal education, however, is not to produce scientists. It seeks to develop free human beings who know how to use their minds and are able to think for themselves. Its  primary aim is not the development of professional competence, although a liberal education is indispensable for any intellectual profession. It produces citizens who can exercise their   political liberty responsibly. It develops cultivated persons who can use their leisure fruitfully. It is an education for all free men, whether they intend to be scientists or not. Our educational problem is how to produce free men, not hordes of uncultivated, trained technicians. Only the best liberal schooling can accomplish this. It must include all the humanities as well as mathematics and the sciences. It must exclude all merely vocational and technical training. 26 WISDOM AS THE GOAL OF LIBERAL LEARNING  by Mortimer Adler  In our common speech we call a man wise either because he shows good judgment in the  practical affairs of life, or because he has deep insight into the ultimate principles and causes of things. The term “wisdom” has both moral and intellectual significance for us today, as it has had throughout our tradition. The ancient Greeks conceive of two kinds of wisdom – practical wisdom, or “prudence,” and speculative or philosophical wisdom. They consider a man practically wise if he judges situations correctly and chooses the means best suited to secure his objectives. Aristotle, however, insists that the objectives must be morally good. In his view, practical wisdom is linked with moral virtue. The Greeks consider a man philosophically wise if he understands the first principles or  causes of things. Wisdom in this sense is the highest form of knowledge. It is the culmination of man’s pursuit of truth. It gives him the peace that accompanies perfect fulfillment. Plotinus states that wisdom brings perfect repose, for it is the knowledge for  which our mind has sought. And Samuel Johnson notes the “the philosophically wise man” has no needs, for he is complete. Our religious tradition places a high value on wisdom. The Greeks consider it a divine attribute. Socrates says that God alone is wise and the man can love or seek wisdom but he cannot possess it. The Book of Proverbs extols wisdom as an eternal principle that sustains and guides the physical order and human life. The Bible also praises as wisdom the prudent and righteous conduct of everyday affairs, and the astute and just decrees of rulers. Here again wisdom is both a kind of knowledge and an aspect of moral character. But here God is the teacher, and wisdom is attained by listening to his teaching – not by intellectual inquiry alone. “The fear of the Lord is the beginning of wisdom,” says the Bible. In this context, “fear” means hearkening to God’s word. Aquinas explains that this is a filial, not a servile, fear—a true respect for the divine law, not dread of punishment. It rests on faith in God’s revelation of His will to man. And it ends in wisdom, the perfection of the intellect that accompanies  perfect love. For Spinoza, wisdom is a form of love, “the intellectual love of God.” How do we attain wisdom? Wisdom is the ultimate aim of learning. Such learning is a long  process, which involves a lifetime of thoughtful inquiry and wide experience. Book learning and good schooling help, but they are not enough to form this supreme virtue of mind and character. Yet experience and age alone are not the sole passports to wisdom. Some men remain foolish all their life long. Indeed, few men sustain the effort and have the devotion that are required to become wise. These few men teach the rest of us what wisdom is and what it means to be wise. Cf. Otto Bird, The Liberal Arts: Their History and Philosophy. Lecture 2: The Tradition of  the Liberal Arts (International Catholic University): In this second lecture I will discuss with you the history and philosophy of the liberal arts. In the first lecture we considered the nature of learning and came to see how the liberal arts are especially and preeminently the arts of learning. In this lecture we are going to look at some of the history of those arts and consider the long tradition that they have.  Now the oldest and longest tradition of the liberal arts begins in Greek antiquity and continues through the Middle Ages. For the most part that history still remains to be told. Some of its range and high points are only beginning to be explored – notably, for example,  by Gaussian in his account of  The Transmission of Classical Culture ; by McKeown in his Study of Rhetoric and Dialectic ; by Bochenski in his  History of Formal Logic; and most 27 recently by Noam Chomsky in his account of seventeenth-century linguistics. Their work  has made it clear that the story of the liberal arts is much more complicated than was once thought. As soon as we attempt to recount that history or even start it we run into a peculiar difficulty. It is as though we were to try telling the story of a group of characters who had lived through many centuries but who frequently changed their names and even their personalities – or at least assumed such disguises that it becomes extremely difficult to identify them. In such a situation, the best way of attempting to learn their identity lies in starting with the appearance they have kept for the longest period. For the liberal arts this is the period of the Middle Ages, say from the time the great Church Fathers down to the 16th century. Even within this period there are many changes, many differences about the arts, their  nature, their number, their function but in reading Augustine, Alcuin, John of Salisbury, Hugh of St. Victor, Roger Bacon, we find that there is a common tradition of the liberal arts which is taken for granted. As this tradition comes to assume a more or less fixed form, seven arts are distinguished as liberal and organized into two groups, the Trivium and the Quadrivium. Trivium, the threefold way; Quadrivium, the fourfold way. This indicates that the arts are means, not ends in themselves. They are ways to something else. The Trivium consists of grammar, logic, rhetoric. The Quadrivium, the fourfold way, consists of  arithmetic, geometry, music, and astronomy. But we will see that this music has a special meaning. It’s not the music, the instrumental or psalm music, that we’re used to. It’s a mathematical study. In this lecture we are going to look at some of the history, and in the next two lectures we will look at these arts of the Trivium. And then in the following two lectures we will look at the mathematical arts of the Quadrivium. The identity of these arts, their nature and content, depends much on the company they keep. With the exception of “music”, however, they  prove on first acquaintance to be much as we would expect them to be today. Grammar  consists in the understanding and skill in the use of verbal signs to accomplish the purposes of speaking, listening and writing. Rhetoric is the art of speaking and writing effectively. Logic is the art of reasoning and disputing. Arithmetic and geometry appear as they still do in our first meeting with them as the arts of number and of magnitude. “Music” however, is scarcely recognizable, which is why we had better keep its name in quotation marks. It is  predominantly mathematical and consists for the most part in the study of proportions of  numbers and their properties. Astronomy is likewise predominantly mathematical and is associated with the stars through the study of the geometrical motions that they exemplify. I’ve made assumptions about the liberal arts which would not always be accepted even during the Middle ages. However, although there may be disagreement about the individual arts and even their number, the division of the liberal arts into these two groups is undisputed. The basis of the distinction lies in the difference between linguistic and mathematical arts. The Trivium it might be said consists of the merely verbal arts. Even when it is held that their truth depends on the nature of things and not on human institution, it will still be admitted that this truth is manifested and exhibited in a linguistic structure, and such a structure, as we have seen from the first lecture, is conventional in character, agreed upon by a social group of people. The Quadrivium on the other hand is felt to be somehow more natural and less conventional than the Trivium and its truths to be rooted in the nature of things. This difference between the two groups is described in what is the first recorded use of the name Trivium. It occurs fittingly enough in a series of notes that some eighth or ninth century scholar made of the  Ars Poetica of Horace. The distinction between linguistic and mathematical arts is of course 28 much earlier, as we will see, and as supposed by Plato, for example, in his discussion of the arts in his dialogue, The Republic. The note to the poem of Horace is offered as an explanation of Horace’s declared intention to teach the function and duty of writing, and what trains and forms the poet. Those are Horace’s words. According to this commentator the difference between training and forming corresponds to the difference between the Trivium and the Quadrivium. The poet is trained in language and all the arts necessary for their use, but he is formed by information about human actions which belongs generally to the realm of ethics and natural things, the latter of  which is the concern of the Quadrivium. Hence training precedes forming: that puts the Trivium before the mathematical arts of the Quadrivium. The commentator goes on to say that one can come to the knowledge of the Quadrivium only through the Trivium. There is still some recognition of this fact. The greatest effort in recent times is to develop an artificial language for mathematics and for logic. But it’s been found that you can’t begin to construct such an artificial language unless you have a natural language of which to speak in the first place. That’s the point this eighth or ninth century commentator was making when he said that the Trivium is needed as a training before you could go on to the formative arts of the mathematics of the scientists. The difference between these two groups of arts is so great that different names should be used for them. Thus Cassiodorous writing in the sixth century holds that we should call the mathematical studies disciplines rather than arts, since discipline is concerned with those things that cannot be otherwise than they are, whereas an art is a faculty of dealing with contingent things which can be otherwise. This supposes, for example, that astronomy, say, deals with the actions of the planets which are as they are to such an extent that we can forecast their future appearance – forecast eclipses of the sun and moon for instance, centuries in advance. Certainly at first sight the difference would seem to be a radical one. The relations in a simple addition, a simple sum, such as 7 plus 5 equals 12, seem to be a different kind of  thing from the words just used to name the addition. The same thing can be said in many different languages: that 7 plus 5 is 12 – so that the words naming it may change whereas the numbers themselves and the relation they have in this addition remain the same. Some, which we shall see later, would deny such a distinction and concede mathematics as only another kind of language. Yet common experience would seem to accept this difference readily enough. Finding a number in things, to see the number of petals in a flower, seems more natural than the name we give to the fact, the name we give to the flower, the name we give to the petals. It’s a property of the flower rather than an imposition of man’s linguistic ability. The number belongs to the nature of the case in a way that the name for the number  does not. The name for the number can be given in different languages in the case of the same flower that has the same number of petals. At any rate this difference taken as such was used to divide the Liberal Arts into two groups. The difference may generate attention and develop into an outright fight. It might even be considered the classical locus of the  present strife between the humanities and the sciences. This distinction within the arts whereby the Trivium can serve as a means to the Quadrivium images the greater distinction  between the arts as means and the end they serve. Aristippus, a Greek sophist, who lived from about 435 to 350 B.C., is reported to have likened the arts in relation to philosophy as handmaids to Penelope. Penelope, you remember, was the wife of Odysseus who waited at home twenty years while Odysseus was returning from the wars. Now if a program of arts was already established by this time, it would support the contention of some historians that the liberal arts owe their inception to 29 the work of the Sophists. Nor is this unlikely, since the Sophists in offering to teach wisdom could be expected to formulate a program of studies leading to it. However, as we know from Plato’s battle with the Sophists over the nature of wisdom, the love of wisdom which is  philosophy may arouse conflicting views. Before an issue of such scope it may be asked whether the liberal arts remain unaffected. If it is their function to prepare for knowledge and  philosophy, then there are differences about the best knowledge, the best philosophy. On this issue, whether the arts are affected or not, there is a strong reply in the negative. It is given by Cicero, who figures largely in any story of the liberal arts both because of his own contributions to them in his study of eloquence and because of his incisive influence on the Fathers of the Church most responsible for the arts program in the Middle Ages. Now Cicero, the great orator, writer and politician, seeks an explanation of the bad times into which eloquence, learning and statesmanship had fallen in his day. He attributes that fall to the corruption of philosophy and as evidence provides a short history of philosophy. For him as for many others the golden age of philosophy lies in the past. He is writing in the first century B.C. There was a time, he tells us, when wisdom meant the union of thought and word. In philosophy, which is the love of wisdom, was a unity in knowledge and action of the best things, a union in both knowledge and action. His examples of such wisdom are men who even in Cicero’s day were already ancient, such legendary figures as Lycurgus and Solon, founders of Sparta and Athens, two of the sages of antiquity. Nearer to Cicero’s own day Pericles, the great fifth-century Greek leader, is cited. If Cicero could choose from our  time, a man such as Churchill would certainly also qualify for a union of action and knowledge. Of course we would not call Churchill a philosopher. But this only proves Cicero’s point, which is that he once would have been a philosopher, and that he should be a  philosopher, and if he is not now or wasn’t Cicero’s time this only shows that something has happened to philosophy. What has happened, according to Cicero, is a divorce between tongue and heart, words and thought – between speaking well and acting rightly. Specialization began to develop as men turned away from public affairs to devote themselves, Cicero says, more than was necessary to poetry, geometry, music, even worse to dialectic. They became specialists, you see. But worst of all men turned their backs from duties of state and attacked and condemned the  power of speech and civil affairs, and snatched to themselves for their own pursuits the noble name of philosopher thereby destroying the name which until then had been common to judging wisely and speaking eloquently, Cicero’s words. The culprit according to Cicero – though this is hard for us to believe, we’ve learned a very different history of philosophy – the one person most to blame for the divorce of knowledge and action of words and knowledge was Socrates. From him Cicero traces the entire development of philosophy and science as pursuits of the mind, divorced from political eloquence and political action. Scientific specialization and neglect of politics go hand in hand for Cicero, and in condemning both Cicero sounds like some contemporary politicians and educators. But he condemns them in the name of philosophy as well as of politics. Condemning the separation of these two, of thought and action. Cicero obviously has one definite purpose for the arts and indeed for all knowledge: that of  serving the political wisdom of the statesmen. It is equally clear that one of the liberal arts  becomes predominant over the others as serving to order the rest to their end and enabling them to achieve it. Cicero himself represents that art at its highest. It’s the art of rhetoric or  eloquence. Cicero may claim that the arts must be ordered to philosophy as their end, yet it is his conception of philosophy that determines the kind of order he obtains. He even admits explicitly that he is interested not in the philosophy that is truest but in that which best 30 accords with the function of the orator and statesman. Needless to say this is not the only  possible conception of philosophy. Another view of philosophy and knowledge, one for example that aims at truth about reality rather than political action, would tell a very different story about the development of the arts. The objects of Cicero’s criticism have a strong case to be made on their side. Yet Cicero’s history still provides a type for any history of the liberal arts. It shows first that the liberal arts can be conceived as a means to an end. Any change in the end will be reflected in the structure of the arts as means. Any change in the means may affect the achievement of  the end. Such changes give rise to different constructions of the arts individually and as a whole group. Such changes give rise to different constructions of the arts according to the  preconceptions of the their nature and function. Among the arts themselves this may appear  in the prominence given to one over another and the establishment of different hierarchies of  the arts, just as Cicero puts rhetoric at the top of all the arts. In this way the history of the liberal arts becomes the narrative of the changes which the arts undergo in themselves and in their relation to one another – to each other and to their end as means. Viewed as a battle, as it sometimes is, it is the story of the shifts of the various arts to favored positions in the hierarchy as they are ordered to different ends or as they are used in different ways for the same end. The change wrought by a shift in their end is apparent in the Medieval tradition of the arts. By this time they had long existed under the Christian dispensation. Their incorporation into it is already fully achieved, at least theoretically, in the work of Saint Augustine. In being integrated –to the Christian it is a means to wisdom – they  became ordered to a radically different end from any they had before. For with Saint Paul wisdom is identified with Christ himself. The arts as ordered to such a wisdom were consequently subordinated to the truth of faith, since Christ is known as God and hence His wisdom came only through faith. The repository of faith is primarily the revelation of God as contained in the Sacred Scriptures, and the tradition of the Church. In such a view of  wisdom, the work of the liberal arts becomes one of interpreting the Sacred text and its tradition with the end of knowing and loving God and carrying out his will in the world. Throughout the Middle Ages theology reigns supreme as the end of which the liberal arts are ordered as means. We have what might be called, after the title of the work by Saint Bonaventure, the reduction of the arts to theology. Yet it would be a mistake to suppose from this that they cease to have a history. Although the end may remain fixed at least in theory to serve theology in the faith, the arts are still at work in differing and changing ways to achieve that end. Their relation to each other does not always remain the same. In fact, a struggle ensues which comes to be described explicitly as a battle, the battle of the arts. Some of the more apparent shifts within the liberal arts appear very early. Thus according as the task of the arts is conceived as predominantly that of interpreting the Sacred Text and making it known, then grammar and rhetoric assume the leading position and the other arts are subordinated to their use. This is fully illustrated in Saint Augustine’s work on Christian Doctrine, which may be viewed as a reorganization of the Ciceronian program to achieve the Christian teacher rather than the secular statesman. However the truths of faith may also be taken as an object of rational analysis, and of the dialectical movement to bring about the assent of the mind to God. This tendency also finds expression in the work of Saint Augustine and especially in such an early work as the  De Ordine, On Order . After him, although the same general end is pursued, there is a tendency to follow one of these directions exclusively. Thus in the Carolingian Renaissance Alcuin in the eighth century follows the way of grammar and approximates the classical program of  Cicero that is ordered now to Christian wisdom. Whereas Origen also in the ninth century in 31 Gaul follows the way of dialectic, and stressing the mathematical arts of the Quadrivium as a means of assent tends to approximate a philosophical program such as that of Plato. Although mathematics is the least developed of the arts during the Middle Ages, there are cases where the Quadrivium seems to be given predominance. Thierry of Chartres in the twelfth century claims that all rational explanation depends upon number. There is in the thirteenth century a French poem on the battle of the arts. The fight between the Trivium and the Quadrivium and between the arts within the Trivium  particularly became most violent, changing most, in the twelfth and thirteenth centuries in Europe because the twelfth and thirteenth centuries saw the reentry into Europe of the entire corpus of the works of Aristotle. All of Greek science was available for the first time in centuries to the West. This rediscovery of Greek science and philosophy extending to every aspect of human natural realms exhibited a fully constituted natural wisdom. At a time it appeared to some that this natural wisdom could only be a rival to the Christian wisdom that had been reigning supreme for centuries. To others it appeared as something that could and should be incorporated within the faith in theology. At any rate there was all the appearance of a tension and a strife between science and religion. From another point of view however, the strife is another aspect of the battle of the liberal arts, and it is described as such in a French poem of the thirteenth century entitled The Battle of the Seven Arts. Although all seven arts are engaged, the battle is primarily between logic and grammar, each with its own army. It is significant, however, that logic has all the seven arts on its side, while ranks of logic include a perverse grammar described by the poet as lined up against Druid antiquity. This is sufficient to show that logic has already carried the day, at least in the schools. The rationally organized new science of Aristotle appears now under the aegis of logic. And grammar, instead of studying the language of the poets, had  become a philosophical inquiry into the nature of language in the modes it signified. It’s something like the recent developments in linguistics and the rediscovery of the idea of the universal grammar. Logic had won the students and gained such a vogue that every boy has gone through her  course before he has reached his fifteenth year. That means the students at the universities were taking the logic and opposing the study of grammar with the study of poetry and literature. Opposed to logic is the true grammar, the poet says, in whose ranks are the old Latin grammarians and the poets from Homer and Virgil down to twelfth century poets such as Alain de Lille and Bernard Silvestre. Theology, or divinity – my lady of the high sciences, she is called – is pictured as not taking  part in the battle since she has no care about the dispute. Yet she is described: theology is described as foolishly holding disputations in the schools, abandoning the old tradition and trumpeting philosophy. Already we foresee the triumph of scholasticism and its greatest monument, the Summa Theologiae, in which we see the whole of theology with scientific and logical organization. Logic and her cohorts with Plato, Aristotle, Socrates carry everything before them, yet the poet whose sympathies are entirely with the defeated, with the ranks of grammar and her poets, is not without hope. He prophesied that not thirty years would pass away before a new race will arise and return again to grammar as it was when he was born. He was not such a bad prophet, that poet, since the generation he awaited was to be, not thirty but some seventy years later, when in the class of the modest grammarian in Southern France a small nine-year-old boy named Petrarch would hear for the first time the music of  Cicero. So if grammar was defeated, its day was not to die but only to retire, to gather up her  32 forces to do battle again and this time to triumph under the Ciceronianism and Augustinianism of Petrarch and the Renaissance. The Renaissance of the fifteenth and sixteenth centuries is certainly much too complicated to  be summed up in a few sentences, and yet there is much to be said for the poet’s prophesy. There was to be a triumph of grammar. At least the feud is a part of the history of the liberal arts. On its literary side in the Renaissance we find an intense cultivation of the classical languages and a truly tremendous work of editing and commenting on text, the text of  antiquity, classical antiquity. All of which belong primarily to the work of grammar. Great learning is accumulated and expended for the most part on the elucidation of the text. Although Cicero is hailed as its master and theorist, it is quite un-Ciceronian in its  predominantly literary and scholarly character – since for all his literary terms and delight in verbal beauty Cicero never forgets the problem of state, the work of the statesman. The literary humanists of the Renaissance were not statesmen. The poet also foresaw in his  Battle of the Seven Arts that the side he represented in the arts was profoundly and violently opposed to logic. The scholastic achievement, one of the greatest in the whole history of logic, is dismissed as useless, and logic becomes a matter of  no importance and no concern to grammar and her cohorts. Bochenski in telling the history of formal logic finds that the Renaissance is a dark age for logic, and some of its greatest lights knew less logic than boys at the age of fifteen did in the Middle Ages. However this  predominantly literary side of the Renaissance which is anti-logical is also anti-scientific. There is also a scientific side in the Renaissance, and viewed from this aspect it gives a new  prominence to the arts of the Quadrivium since modern science arises in the Renaissance. And with the rise of modern science we also see that the Quadrivium, the mathematical arts of the Quadrivium, appear again and come, in fact, to prominence. The triumph of the mathematical arts appears most manifestly in the conquest of science, in the industrialization of the world that has happened since the seventeenth century. It might even be claimed that the atom bomb is the latest achievement of the Quadrivium. It seems strange to speak of  science and the atom bomb as works of liberal art. It’s not at all unusual to oppose the sciences to the liberal arts, and educators often talk of the need of making the sciences more liberal. If the liberal arts are present they must be well disguised – and so they are. As we come into the times called modern the arts frequently go unrecognized. This is particularly true of science with its strongly technological side. Technology is engineering, primarily a mechanical not a liberal art, and yet the technology is possible only because of the knowledge by which it is blessed, and this is especially in mathematics, in physics. And these are works of liberal art. We look back to the founders of modern science we find that they constantly considered science a work of liberal art. Perhaps they did so because they were more conscious than we are of the tradition of the liberal arts. In a justly famous  passage of Saggiatore that wise man Galileo writes: Science has written in that great book which is always open before our eyes, I mean the universe, that it cannot be understood if one does not understand the language and know the characters in which it is written. It is written in the language of mathematics, its characters are triangles, circles and other geometrical figures. Remember that at the time of Galileo geometry was the supreme mathematical science. You’ll see more about that later on. Without knowledge of these, these mathematical arts, we cannot understand the speech of  nature and can but wander vainly through an obscure labyrinth. 33 In this passage Galileo is giving expression to what was common doctrine among Renaissance scientists and artists too. We need only recall Leonardo da Vinci, Piero della Francesca, and Albrecht Durer. The passage could still be used as a description of  contemporary science, although few scientists would think of doing so. Yet the comparison it employs possesses the advantage of making clear the function of liberal art in science, since to compare science to reading a book expounds it in the more familiar terms of the linguistic arts. Galileo is saying in effect, nature has a story to tell and once we know the story we have a scientific understanding of nature. But we cannot read or even hear the story until we know the language in which it is written. In other words we need a symbolic discipline which will provide us with the facility to grasp and interpret the signs and symbols with which the story is told. As a symbolic discipline used for the purpose of knowledge it is a liberal art that is needed. Distinction between the book, or rather its story, and the language in which it is written corresponds to the difference between science and liberal art – or still more generally, to the difference between the end and the means for achieving it which are the liberal arts. Galileo identifies the language in nature with mathematics, with geometry. Modern physics would substitute the calculus and differential equations and higher geometries for the old geometry, and this substitution affords an indication of a shift among the arts of the Quadrivium in which geometry has yielded its place of supremacy to another. The more immediate interest, however, is the question of the relation between mathematics and the natural world. We have already looked at the earlier contention that this is much more intimate relation than that between the Trivium and nature. Galileo again affirms that the symbolic means for knowing the natural world are a different kind from those of our ordinary discourse. He continues at the tradition in affirming that there is a basic distinction between the arts of the Trivium and those of the Quadrivium. To appreciate his analogy we would say that man in his intellectual endeavor has two different kinds of books to read: the book written by men and by women and the book written by nature. Both books tell primarily of things other than themselves. They talk about men, the world, and God. Mathematical arts in the first creative advance of their modern development receive little or no help from the ancient arts of language, the Trivium. There are many reasons for this. In part it was a continuation of the ancient view of the utter diversity  between the Trivium and the Quadrivium. In part also the ancient linguistic and logical doctrine did not appear relevant. Much of it was not generally known and what passed for it was so degraded that a man like Descartes, a very great philosopher and scientist, could dismiss the past logic and linguistic arts as useless for the purpose of the sciences. At any rate the new developments in mathematics and science that began in the sixteenth century seemed to take place pretty much on their own without any influence from the old arts of the Trivium. The result was a split and a divorce between two kinds of arts which at least in theory had always been joined. So much then for the history. What can it tell us about the nature of the liberal arts themselves? In the first place, that they are arts, certain kinds of arts. Hence we need to consider the nature of art and its kinds if we are to be able to place at all accurately the nature of the liberal arts. Now, for the understanding of art and its kinds the basic and essential distinctions are given by Aristotle. The first of these occurs in the six books of his Nicomachean Ethics where he is concerned to identify and distinguish the intellectual virtues, as he called them. He means by virtues the dispositions or habits by which the mind is developed to carry out well its various functions. The virtue of a faculty or a power is relevant to the work or function that that power   performs. 34 Aristotle accordingly distinguishes three activities of intellect each of which performs a different function, and these three activities, each performing a different function, are knowing, doing, and making. Knowing as distinct from the other two is concerned with that which is not either arguing or making. It is known for the sake of knowing. The qualities or  habits that enable this activity to be good and excellent are the speculative virtues of  understanding or insight. There are three of them. Understanding or insight (Aristotle’s Greek is nous), speculative or philosophical wisdom ( sophia), and scientific knowledge (episteme, from which our word epistemology comes). Although knowledge is epistemean Aristotle says it is not to be equated with our empirical science. Episteme for Aristotle as science is more relative to our concern than the other two virtues here, and he defines it as an apodictic, that is the ability to demonstrate a conclusion from prior or better known principles, principles which Aristotle would claim must be certain and necessary. So you see what he is calling science, episteme, is essentially rational demonstration. Doing,  praxis in the Greek, making,  poietris,7 from which our word  poetry comes, both differ from speculative or theoretical knowing in that they both aim at something more than the knowing itself. Making is concerned with a thing to be made. Doing is concerned with the action to be done.  Praxis, doing, is the realm of moral and  political action of human behavior, which may be good or evil. Its specific virtue is prudence which is defined as a practical habit with true reason concerning the goods and evils of  human beings.  Now  poietris, making, from which our word  poetry comes, is the activity of making something, or producing or performing it. It aims at something more than either the knowing or the action that is involved with it. Its specific virtue is art, techne, Aristotle’s Greek from which our word technology is derived.  Poietris is defined as a productive habit.  Productive here is a translation of  poietikos. It’s a making habit, a productive habit with true reason, and about it Aristotle notes, all art is concerned with coming into being, that is with contriving and considering how something may come into being which is capable of either being or not  being and whose origin is in the maker not in the thing made. For art is concerned neither  with things that are or come into being by necessity nor with things that do so in accordance with nature, since these have their origin in themselves. Before considering more closely this definition of art, a productive habit with true reason, we have to note and emphasize how broad this notion of art is, and yet also how distinct. First, art is a disposition or quality of the mind. The excellence of the intellectual activity of  making. It is distinct and different from science and prudence, which are the virtues of  knowing and doing respectively, in that apart from the exercise of the art the work would not exist at all. Its end in the work it aims to produce is external to the activity in the art –  whether it is a hearth or whether it is a house, a hat, a pot, a chair, a lyric, a symphony, a tragic drama, a dance, an automobile, an airplane, a satellite, a computer, whatever it is, as long as it is a man-made object existing external to the maker. Turning back then to our definition, a productive habit with true reason, the note that it is  productive, poietikos, restricts it to making in the makeable. That it is a habit indicates that it is a disposition or quality of mind by which one has developed an ability that others may not have. Thus a carpenter possesses an ability so perfected that he can saw, plane, nail, put wood together in a way or a better way than one who lacks the skill, that being the art that he has. Why then does Aristotle add true reason, a productive habit with true reason? This qualification indicates two things. First that an art involves knowledge as reason. Second that it is one that might fail of its purpose. So an artisan who lacks the skill may fail to saw a straight cut, or plane a fine surface, just as a beginner may cook a soufflé that falls and tastes 7 This should be corrected to poiesis. 35  bad. The possession of the skill can be seen in the goodness or badness of the product. Hence the adage that art does not fail: the failure lies in the maker who fails to possess it. The art itself can’t fail, Aristotle says. Perhaps a clearer although equally literal translation of the definition is that art is having the right know-how of things makeable. To include the reference to knowledge and the true or right serves to emphasize that art is an intellectual activity however much it may call also for muscular adaptations and training such as those needed for playing a musical instrument or sawing a board. The difference  between the work that is made and the knowing that contributes to its making also emphasizes an important point. The work made, whether a kitchen pot or an automobile, a dramatic or musical production, is in each case a concrete, material, individual thing regardless of how many times it may be reproduced. However the knowing involved in art is not individual or singular but universal. The house builder’s art is capable of producing not  just one house but many, many houses. The thing made, the artwork, may be singular and contingent and in some cases destined to endure for only a short while as does a dance. But the knowledge in the art as skill contains rules and methods capable of being applied again and again to many diverse, singular works. To narrow in upon the notion of liberal art we need still a further distinction. Aristotle also  provides it in his  Politics, in the eighth book where he discusses education. There he notes that one must distinguish between two different sorts of arts according as they are liberal or  illiberal. He makes this distinction according to kinds of activity that befit a freeman or a slave. But this sociological basis for the way he expresses it should not be allowed to conceal its ontological basis. Aristotle’s language may betray the contingencies of the society in which he lived and wrote. But there is an ontological basis to the distinction that power  transcends the sociological contingency of its expression. Aristotle makes this distinction largely in negative terms by pointing out what is illiberal. Such is identified as any occupation, art or science which makes the body, soul, or mind of  the free man less fit for the practice or exercise of virtue. But for Aristotle the highest activities of virtue for the free man are consistent with filling the duties of civic life or the  pursuit of philosophical wisdom. Both of these require the freedom of leisure, and the unhampered exercise of the intellect or mind in deliberation and speculation. Hence the great obstacle is any activity or occupation that dulls the mind and prevents its full and free operation. And of these the heaviest lies in the concerns of the body tying them down to the needs of the singular here and now. Hence Aristotle’s demand is much like the old religious sanction that forbade menial work on the Sabbath. In both instances the need is for freedom of the mind. Cf. Leo Strauss, “What Is Liberal Education” (1959): What Is Liberal Education? By Leo Strauss Robert Maynard Hutchins Distinguished Service Professor Department of Political Science The University of Chicago An Address Delivered at the Tenth Annual Graduation Exercises of the 36 Basic Program of Liberal Education for Adults June 6, 1959 Leo Strauss was born in Germany in 1899. Since coming to the United States in 1938 he has  been professor of political science and philosophy at the New School for Social Research and professor of political science at the University of Chicago. In 1954-55 he was visiting  professor of philosophy and political science at the Hebrew University of Jerusalem. Among the books Professor Strauss has written are The Political Philosophy of Hobbes ,  Natural   Right and History, and Thoughts on Machiavelli . You have acquired a liberal education. I congratulate you on your achievement. If I were entitled to do so, I would praise you for your achievement. But I would be untrue to the obligation which I have undertaken if I did not supplement my congratulations with a warning. The liberal education which you have acquired will avert the danger that the warning will be understood as a counsel of despair. Liberal education is education in culture or toward culture. The finished product of a liberal education is a cultured human being. “Culture” ( cultura) means primarily agriculture: the cultivation of the soil and its products, taking care of the soil, improving the soil in accordance with its nature. “Culture” means derivatively and today chiefly the cultivation of  the mind, the taking care and improving of the native faculties of the mind in accordance with the nature of the mind. Just as the soil needs cultivators of the soil, the mind needs teachers. But teachers are not as easy to come by as farmers. The teachers themselves are  pupils and must be pupils. But there cannot be an infinite regress: ultimately there must be teachers who are not in turn pupils. Those teachers who are not in turn pupils are the great minds or, in order to avoid any ambiguity in a matter of such importance, the greatest minds. Such men are extremely rare. We are not likely to meet any of them in any classroom. We are not likely to meet any of them anywhere. It is a piece of good luck if there is a single one alive in one’s time. For all practical purposes, pupils, of whatever degree of proficiency, have access to the teachers who are not in turn pupils, to the greatest minds, only through the great books. Liberal education will then consist in studying with the proper care the great  books which the greatest minds have left behind – a study in which the more experienced  pupils assist the less experienced pupils, including the beginners. This is not an easy task, as would appear if we were to consider the formula which I have  just mentioned. That formula requires a long commentary. Many lives have been spent and may still be spent in writing such commentaries. For instance, what is meant by the remark  that the great books should be studied “with the proper care”? At present I mention only one difficulty which is obvious to everyone among you: the greatest minds do not all tell us the same things regarding the most important themes; the community of the greatest minds is rent by discord and even by various kinds of discord. Whatever further consequences this may entail, it certainly entails the consequence that liberal education cannot be simply indoctrination. I mention yet another difficulty. “Liberal education is education in culture.” In what culture? Our answer is: culture in the sense of the Western tradition. Yet Western culture is only one among many cultures. By limiting ourselves to Western culture, do we not condemn liberal education to a kind of parochialism, and is not parochialism incompatible with the liberalism, the generosity, the open-mindedness, of liberal education? Our notion of liberal education does not seem to fit an age which is aware of the fact that there is not the culture of the human mind but a variety of cultures. Obviously, “culture” if  susceptible of being used in the plural is not quite the same thing as “culture” which is a  singulare tantum, which can be used only in the singular. “Culture” is now no longer, as 37  people say, an absolute but has become relative. It is not easy to say what culture susceptible of being used in the plural means. As a consequence of this obscurity people have suggested, explicitly or implicitly, that “culture” is any pattern of conduct common to any human group. Hence we do not hesitate to speak of the culture of suburbia or of the cultures of   juvenile gangs both non-delinquent and delinquent. In other words, every human being outside of lunatic asylums is a cultured human being, for he participates in a culture. At the frontiers of research there arises the question as to whether there are not cultures also of  inmates of lunatic asylums. If we contrast the present day usage of “culture” with the original meaning, it is as if someone would say that the cultivation of a garden may consist of the garden being littered with empty tin cans and whiskey bottles and used papers of  various descriptions thrown around the garden at random. Having arrived at this point, we realize that we have lost our way somehow. Let us then make a fresh start by raising the question: what can liberal education mean here and now? Liberal education is literate education of a certain kind: some sort of education in letters or  through letters. There is no need to make a case for literacy; every voter knows that modern democracy stands or falls by literacy. In order to understand this need we must reflect on modern democracy. What is modern democracy? It was once said that democracy is the regime that stands or falls by virtue: a democracy is a regime in which all or most adults are men of virtue, and since virtue seems to require wisdom, a regime in which all or most adults are virtuous and wise, or the society in which all or most adults have developed their reason to a high degree, or the rational society. Democracy in a word is meant to be an aristocracy which has broadened into a universal aristocracy. Prior to the emergence of modern democracy some doubts were felt whether democracy thus understood is possible. As one of  the two greatest minds among the theorists of democracy put it, “If there were a people consisting of gods, it would rule itself democratically. A government of such perfection is not suitable for human beings.” This still and small voice has by now become a high powered loudspeaker. There exists a whole science – the science which I among thousands  profess to teach, political science – which so to speak has no other theme than the contrast  between the original conception of democracy, or what one may call the ideal of democracy, and democracy as it is. According to an extreme view which is the predominant view in the  profession, the ideal of democracy was a sheer delusion and the only thing which matters is the behavior of democracies and the behavior of men in democracies. Modem democracy, so far from being universal aristocracy, would be mass rule were it not for the fact that the mass cannot rule but is ruled by elites, i.e., groupings of men who for whatever reason are on top or have a fair chance to arrive at the top; one of the most important virtues required for the smooth working of democracy, as far as the mass is concerned, is said to be electoral apathy, i.e., lack of public spirit; not indeed the salt of the earth but the salt of modern democracy are those citizens who read nothing except the sports page and the comic section. Democracy is then not indeed mass rule but mass culture. A mass culture is a culture which can be appropriated by the meanest capacities without any intellectual and moral effort whatsoever  and at a very low monetary price. But even a mass culture and precisely a mass culture requires a constant supply of what are called new ideas, which are the products of what are called creative minds: even singing commercials lose their appeal if they are not varied from time to time. But democracy, even if it is only regarded as the hard shell which protects the soft mass culture, requires in the long run qualities of an entirely different kind: qualities of  dedication, of concentration, of breadth and of depth. Thus we understand most easily what liberal education means here and now. Liberal education is the counter-poison to mass culture, to the corroding effects of mass culture, to its inherent tendency to produce nothing  but “specialists without spirit or vision and voluptuaries without heart.” Liberal education is the ladder by which we try to ascend from mass democracy to democracy as originally meant. Liberal education is the necessary endeavor to found an aristocracy within 38 democratic mass society. Liberal education reminds those members of a mass democracy who have ears to hear, of human greatness. Someone might say that this notion of liberal education is merely political, that it dogmatically assumes the goodness of modem democracy. Can we not turn our backs on modem society? Can we not return to nature, to the life of preliterate tribes? Are we not crushed, nauseated, degraded by the mass of printed material, the graveyards of so many  beautiful and majestic forests? It is not sufficient to say that this is mere romanticism, that we today cannot return to nature: may not coming generations, after a man-wrought cataclysm, be compelled to live in illiterate tribes? Will our thoughts concerning thermonuclear wars not be affected by such prospects? Certain it is that the horrors of mass culture (which include guided tours to integer nature) render intelligible the longing for a return to nature. An illiterate society at its best is a society ruled by age-old ancestral custom which it traces to original founders, gods or sons of gods or pupils of gods; since there are no letters in such a society, the late heirs cannot be in direct contact with the original founders; they cannot know whether the fathers or grandfathers have not deviated from what the original founders meant, or have not defaced the divine message by merely human additions or subtractions; hence an illiterate society cannot consistently act on its principle that the  best is the oldest. Only letters which have come down from the founders can make it  possible for the founders to speak directly to the latest heirs. It is then self-contradictory to wish to return to illiteracy. We are compelled to live with books. But life is too short to live with any but the greatest books. In this respect as well as in some others, we do well to take as our model that one among the greatest minds who because of his common sense is the mediator between us and the greatest minds. Socrates never wrote a book but be read books. Let me quote a statement of Socrates which says almost everything that has to be said on our  subject, with the noble simplicity and quiet greatness of the ancients. “Just as others are  pleased by a good horse or dog or bird, I myself am pleased to an even higher degree by good friends. . . . And the treasures of the wise men of old which they left behind by writing them in books, I unfold and go through them together with my friends, and if we see something good, we pick it out and regard it as a great gain if we thus become useful to one another.” The man who reports this utterance, adds the remark: “When I heard this, it seemed to me both that Socrates was blessed and that be was leading those listening to him toward perfect gentlemanship.” This report is defective since it does not tell us anything as to what Socrates did regarding those passages in the books of the wise men of old of which he did not know whether they were good. From another report we learn that Euripides once gave Socrates the writing of Heraclitus and then asked him for his opinion about that writing. Socrates said: “What I have understood is great and noble; I believe this is also true of what I have not understood; but one surely needs for understanding that writing some special sort of a diver.” Education to perfect gentlemanship, to human excellence, liberal education consists in reminding oneself of human excellence, of human greatness. In what way, by what means does liberal education remind us of human greatness? We cannot think highly enough of  what liberal education is meant to be. We have beard Plato’s suggestion that education in the highest sense is philosophy. Philosophy is quest for wisdom or quest for knowledge regarding the most important, the highest, or the most comprehensive things; such knowledge, he suggested, is virtue and is happiness. But wisdom is inaccessible to man and hence virtue and happiness will always be imperfect. In spite of this, the philosopher, who, as such, is not simply wise, is declared to be the only true king; be is declared to possess all the excellences of which man’s mind is capable, to the highest degree. From this we must draw the conclusion that we cannot be philosophers – that we cannot acquire the highest form of education. We must not be deceived by the fact that we meet many people who say that they are philosophers. For those people employ a loose expression which is perhaps 39 necessitated by administrative convenience. Often they mean merely that they are members of philosophy departments. And it is as absurd to expect members of philosophy departments to be philosophers as it is to expect members of art departments to be artists. We cannot be philosophers but we can love philosophy; we can try to philosophize. This  philosophizing consists at any rate primarily and in a way chiefly in listening to the conversation between the great philosophers or, more generally and more cautiously,  between the greatest minds, and therefore in studying the great books. The greatest minds to whom we ought to listen are by no means exclusively the greatest minds of the West. It is merely an unfortunate necessity which prevents us from listening to the greatest minds of  India and of China: we do not understand their languages, and we cannot learn all languages. To repeat, liberal education consists in listening to the conversation among the greatest minds. But here we are confronted with the overwhelming difficulty that this conversation does not take place without our help – that in fact we must bring about that conversation. The greatest minds utter monologues. We must transform their monologues into a dialogue, their “side by side” into a “together.” The greatest minds utter monologues even when they write dialogues. When we look at the Platonic dialogues, we observe that there is never a dialogue among minds of the highest order: all Platonic dialogues are dialogues between a superior man and men inferior to him. Plato apparently felt that one could not write a dialogue between two men of the highest order. We must then do something which the greatest minds were unable to do. Let us face this difficulty – a difficulty so great that it seems to condemn liberal education as an absurdity. Since the greatest minds contradict one another regarding the most important matters, they compel us to judge of their monologues; we cannot take on trust what any one of them says. On the other hand we cannot but notice that we are not competent to be judges. This state of things is concealed from us by a number  of facile delusions. We somehow believe that our point of view is superior, higher than those of the greatest minds – either because our point of view is that of our time, and our time,  being later than the time of the greatest minds, can be presumed to be superior to their times; or else because we believe that each of the greatest minds was right from his point of view  but not, as be claims, simply right: we know that there cannot be the simply true substantive view but only a simply true formal view; that formal view consists in the insight that every comprehensive view is relative to a specific perspective, or that all comprehensive views are mutually exclusive and none can be simply true. The facile delusions which conceal from us our true situation all amount to this, that we are, or can be, wiser than the wisest men of the  past. We are thus induced to play the part not of attentive and docile listeners but of  impresarios or lion-tamers. Yet we must face our awesome situation, created by the necessity that we try to be more than attentive and docile listeners, namely, judges, and yet we are not competent to be judges. As it seems to me, the cause of this situation is that we have lost all simply authoritative traditions in which we could trust, the nomos which gave us authoritative guidance, because our immediate teachers and teachers’ teachers believed in the possibility of a simply rational society. Each of us here is compelled to find his bearings  by his own powers however defective they may be. We have no comfort other than that inherent in this activity. Philosophy, we have learned, must be on its guard against the wish to be edifying – philosophy can only be intrinsically edifying. We cannot exert our understanding without from time to time understanding something of importance; and this act of understanding may be accompanied by the awareness of our understanding, by the understanding of understanding, by noesis noeseos, and this is so high, so pure, so noble an experience that Aristotle could ascribe it to his God. This experience is entirely independent of whether what we understand primarily is pleasing or displeasing, fair or ugly. It leads us to r ealize that all evils are in a sense necessary if there is to be understanding. It enables us to accept all evils which befall us and which may well  break our hearts in the spirit of good citizens of the city of God. By becoming aware of the dignity of the mind, we realize the true ground of the dignity of man and therewith the 40 goodness of the world, whether we understand it as created or as uncreated, which is the home of man because it is the home of the human mind. Liberal education, which consists in the constant intercourse with the greatest minds, is a training in the highest form of modesty, not to say of humility. It is at the same time a training in boldness: it demands from us the complete break with the noise, the rush, the thoughtlessness, the cheapness of the Vanity Fair of the intellectuals as well as of their  enemies. It demands from us the boldness implied in the resolve to regard the accepted views as mere opinions, or to regard the average opinions as extreme opinions which are at least as likely to be wrong as the most strange or the least popular opinions. Liberal education is liberation from vulgarity. The Greeks had a beautiful word for “vulgarity”; they called it apeirokalia, lack of experience in things beautiful. Liberal education supplies us with experience in things beautiful. § See also: Liberal Arts and Liberal Education by Christopher Flannery 41 6. The place of grammar in the liberal arts. Cf. Marcus Berquist, On the Art and Science of Grammar . Introduction. Part I, p. 1: Liberal education begins with the seven liberal arts, which are an introduction to the life of  study and a preparation for the more difficult sciences, which are the principal concerns of  such a life. Grammar is the first among these arts, not in excellence or in intrinsic importance, but in the order of learning, insofar as it is presupposed to all the other liberal arts and sciences, is involved in the learning and exercise of them, and is necessary for their well being. It has its reward, not in itself, but in what it contributes to the others. Like logic, the  principal part of the trivium, it is not so much an intrinsic part of philosophy as its instrument. Cf. Michael A. Augros, Philosophical and Theological Scrapbook. Summer, 1994. Logic, n. 9: n. 9. Is Logic Speculative? I asked Mr. Marcus Berquist (in June of 1994) how there can be a speculative science of  grammar if it is of things less intelligible than the subject of logic, which is considered to be  primarily a tool. He answered that logic, too, is speculative, and more so than grammar,  precisely because there is so much necessity in its subject matter. It is called practical  because of its end; it is a knowledge sought primarily for its utility. But if a knowledge is useful, it is not necessarily not worth knowing for its own sake; it is not necessarily knowledge of contingent singulars. Also, he said, there is some necessity in the subject matter of  grammar, and it is to the extent that there is such that there is a speculative science there. For  instance, what is signified must be signified in some way (in some mode of signifying). Although the familiar modes of signifying, such as the genders and numbers and cases etc. are not any one of them absolutely necessary, it is necessary that anything signifying have more in it than just sound and agreement about what the sound is to signify. Likewise, although no one accident is necessary in a substance, it must have some accidents. § 42 7. The place of logic in the liberal arts. Cf. Duane H. Berquist, “The Proemium to Logic” (The Society for Aristotelian Studies):8 THE PLACE OF LOGIC IN THE DIVISION OF PHILOSOPHY Philosophy is sometimes divided into two parts and sometimes into three. If we divide it into two, it is divided into its two chief parts, which are theoretical or looking philosophy and  practical philosophy. Hence, when Lady Wisdom appears to Boethius in the Consolation of   Philosophy, she has on her dress the Greek letters naming these two parts. These differ by their end. The end of looking philosophy, as its name indicates, is to see or understand. And the end of practical philosophy, as its name also indicates, is to do well. This is like the use we make of our eyes, sometimes just to see something beautiful, and at other times, to do something like walking or driving. But sometimes philosophy is divided into three parts where we add to the two chief parts, a third part which is the tool  of philosophy. Logic is a tool for acquiring philosophy rather than a chief or principal part of philosophy. But if we divide philosophy into only two parts (looking and practical), logic would be more reduced to looking philosophy, as Thomas explains in this text: Thomas Aquinas, In Boetii de Trinitate , Lectio II, Q. I, Art. 1, Ad 2: scientiae speculativae, ut patet in principio  Metaphysicorum , sunt de illis quorum cognitio quaeritur propter seipsa. Res autem de quibus est logica, non quaeruntur ad cognoscendum propter seipsas, sed ut adminiculum quoddam ad alias scientias. Et ideo logica non continetur sub philosophia speculativa quasi principalis pars, sed sicut quoddam reductum ad eam, prout ministrat speculationi sua instrumenta, scilicet syllogismos et definitiones et alia huiusmodi, quibus in speculativis scientiis indigemus. Unde secundum Boetium in Comment. super Porphyrium (L. 1, cap. 3) non tam est scientia quam scientiae instrumentum. [adminiculum: I a prop, a support, the pole on which the vine is trained I Transf. aid help] Thomas Aquinas, In Boetii de Trinitate , Lect. II, q. 1, a. 1, ad 2: Looking sciences, as is clear in the beginning of the  Metaphysics, are about things the knowledge of which is sought for its own sake. The things however which logic is about, are not sought to be known for themselves, but as a help to the other sciences. And therefore logic is not contained under looking philosophy as a principal part, but as something reduced to it; insofar as it provides looking with its tools, namely syllogisms and definitions and others of this kind which we need in the looking sciences. Whence according to Boethius in his Commentary on Porphyry, it is not so much a science as the tool of  science. Sometimes logic is placed among the liberal arts and in this consideration we can also see its connection more with looking philosophy than practical philosophy. The distinction of the seven liberal arts into the quadrivium and the trivium goes back to Pythagoras (who divided the four mathematical sciences of the quadrivium) and Plato (who was distinguishing the trivium). The distinction of the seven and their place in education was formalized in the Middle Ages (hence, their Latin names). In the following text, Thomas explains why they are called liberal arts and their place and that of logic in particular at the beginning of philosophy. 8 (http://www.aristotelian.org/lyceum/logic/proemium_to_logic.php [3/19/04]) 43 Thomas Aquinas, In Boetii de Trinitate , Lect. II, q. 1, a. 1, ad 3: Ad tertium dicendum quod septem liberales artes non sufficienter dividunt philosophiam theoricam, sed ideo, ut dicit Hugo de Sancto Victore in III sui Didascalicon, praetermissis quibusdam aliis septem connumerantur, quia his primum erudiebantur, qui philosophiam discere volebant, et ideo distinguuntur in trivium et quadrivium, eo quod his quasi qui busdam viis vivax animus ad secreta philosophiae introeat. Et hoc etiam consonat verbis Philosophi qui dicit in II Metaphysicae quod modus scientiae debet quaeri ante scientias; et Commentator ibidem dicit quod logicam, quae docet modum omnium scientiarum, debet quis addiscere ante omnes alias scientias, ad quam pertinet trivium. Dicit etiam in VI Ethicorum quod mathematica potest sciri a pueris, non autem physica, quae experimentum requirit. Et sic datur intelligi quod post logicam consequenter debet mathematica addisci, ad quam pertinet quadrivium; et ita his quasi quibusdam viis praeparatur animus ad alias philosophicas disciplinas. Vel ideo hae inter ceteras scientias artes dicuntur, quia non solum habent cognitionem, sed opus aliquod, quod est immediate ipsius rationis, ut constructionem syllogismi vel orationem formare, numerare, mensurare, melodias formare et cursus siderum computare. Aliae vero scientiae vel non habent opus, sed cognitionem tantum, sicut scientia divina et naturalis; unde nomen artis habere non possunt, cum ars dicatur ratio factiva, ut dicitur in VI Metaphysicae. Vel habent opus corporale, sicut medicina, alchimia et aliae huiusmodi. Unde non possunt dici artes liberales, quia sunt hominis huiusmodi actus ex parte illa, qua non est liber, scilicet ex parte corporis. Thomas Aquinas, In Boetii de Trinitate , Lect. II, q. 1, a. 1, ad 3: To the third it should be said that the seven liberal arts do not sufficiently divide looking  philosophy, but rather, as Hugo of St. Victor says in the third book of his  Didascalicon, seven are numbered (setting aside some others) because those who wish to learn philosophy are first instructed in these, and therefore they are distinguished into the trivium and the quadrivium, in that through these as by certain roads the lively soul enters into the secrets of philosophy. And this also fits with the words of the Philosopher who says in the second book of the  Metaphysics that the mode of science ought to be sought before the sciences; and the Commentator there says that one ought to learn logic that teaches the common mode of all the sciences and to which pertains the trivium, before all the other sciences. And he [Aristotle] says also in the sixth book of the  Ethics that mathematics is able to known by boys. But not natural science which requires experience. And thus is given to be understood that after logic one ought to learn mathematics to which  pertains the quadrivium; and thus by these as by certain roads the soul is prepared for the other philosophic disciplines. Or rather, these among the other sciences, are called arts, because they not only have knowledge, but some work that is immediately of reason itself, as the construction of a syllogism or to form a speech, to number, to measure, to form melodies, and to compute the course of the stars. But other sciences either do not have a work but knowledge only, as divine and natural science (whence they cannot have the name of art since art is called making reason, as is said in the  N. Ethics , VI.) or they have a bodily work, as medicine, chemistry and others of this kind. Whence they cannot be called liberal arts, because acts of this kind belong to man by that part in which he is not free, namely the bodily part. Duane H. Berquist § 44 8. The place of mathematics in the liberal arts. Cf. James Chastek, Just Thomism (Blog). Posted Sept. 14, 2005: Mathematics as the First Speculative Science. Mathematics is the body of knowledge which gives us the greatest certainty, and so it is the model for us of what all sciences should be. If we view all Mathematics as a tool, we can do no other than view science as a tool; if we view math as nothing other than the manipulation of its subject matter, we will view all science as manipulation of the subject matter; if we view all math as art, we view all science as an art. Our view of science cannot be higher than our view of math, for mathematics simply is the body of knowledge about which we have the greatest certainty, and we know we are most certain of it. The loss of liberal mathematics in modern times was a devastation. There is no measure for  the things we lost. In a very real sense, we lose all science when we lose mathematics: what remains and calls itself science is really an art that treats nature as pure matter to be informed  by the scientist. The only joy or intrinsic worth to such a “science” is the banal fascination of  a game or hobby. Mathematics, when taught as a speculative science and liberal art, provides us an irreplaceable grasp of what it means to know something for its own sake, and through this we can know the joy of contemplation- which is the true life of science- the highest and most noble life a man can live, in this life or any other. Again, mathematics is the indispensable first grasp we have of science, and there is some sense in every man that science ought to be the rule and measure of human life. We use the word “science” to describe the most precise, objective, penetrating, and sure kind of  knowledge. But too often this natural respect for science gets contracted and distorted so as to apply only to physical sciences based on disprovable hypotheses and verified by experiment. This leads to the conclusion- commonly heard and experienced by all- that man, when he is most certain about something (having science) in fact has only probability. The modern mind, having lost the paradigm of mathematics, divides all learning into the sciences and the humanities. The common element in both of these is their uncertainty and groundlessness. A student goes to a science class and learns that nothing can count as a science unless it is disprovable; then he goes to a humanities course and be told that the whole goal of humanities is to “enter into the great conversation” or “learn the various ways that people have struggled with the great questions”. Gone is any sense of paideia, of that sense awareness in man that knowledge is the sort of thing that should be sought for its own sake; and that the goal of an educated man was to tell the difference between the things he was certain of, and not certain of. One of the best signs of the educated man is that he knows what needs to be proven, and what doesn’t need to be proven. But without mathematics, we can’t even be expected to know what proof means.  ——–  Published in: Default Category on September 14, 2005 at 6:38 pm Comments (0) § 45 9. The place of music in the liberal arts. Cf. Marcus Berquist, Good Music and Bad . Excerpt from a lecture given at St. Thomas Aquinas College, Ojai, California, Oct. 1991: There are three places in the course of study where music is considered. The first in the order of learning, is the liberal art of music, a part of the quadrivium, which examines music in the light of certain mathematical principles which it exhibits. Here, we first see in the order of learning that music is characterized by a reasonable order. We see in music a kind of unity and harmony between the passions and reason. This kind of order is a good thing to see at the beginning because it is proportioned to us. This is the easiest sort of order for us to see and appreciate. Even the young, without a great deal of experience, can apprehend an order of this kind. The next place that music would come up in the course of study is in a way analogous to Aristotle’s consideration of tragedy in the  Poetics, as a mode of imitation. This would be a thorough or definitive consideration in terms of the proximate genus, which is imitation, and the specific differences, imitation of what? and by what means? We can contrast this with the kind of treatment you’d have in a liberal art where you are applying a doctrine which is abstract and general to a particular subject matter, a doctrine which you have not derived from that subject matter, and from a consideration of its peculiarities, but from a more general and abstract consideration. The numerical ratios and proportions you study in harmony are common to music and other things as well. The third consideration of music in the course of study is in ethics and political  philosophy. We find this, for example, in Book VI of Plato’s  Republic, in Book II of his  Laws, and in Book VIII of Aristotle’s  Politics. Here, music is considered in terms of  education. This is because, in the opinion of Aristotle and Plato and many others, music not only amuses and pleases, which is perhaps a sufficient reason for its being, it is a kind of  recreation and rest from life’s effortful activities, but it is also dispositive. It has an effect on the soul for good or for ill. Therefore it pertains to ethics and politics to consider it. It  pertains to education, which is concerned with the acquisition of virtue, which is of political and social as well as familial concern. We are all concerned that citizens be good men. § 46 10. The place of astronomy in the liberal arts. Cf. Mortimer J. Adler, The Great Ideas: A Syntopicon of Great Books of the Western World (Chicago, 1952), Vol. I{I}, Chapter 5, “Astronomy” (Introduction): THE GREAT BOOKS of astronomy most lucidly exhibit the essential pattern of that kind of  natural science which has, in modern times, come to be called “mathematical physics.” Though that phrase may be modern, the ancients recognized the special character of the sciences which apply mathematics to nature and which consult experience to choose among hypotheses arising from different mathematical formulations. Outlining a curriculum for liberal education, Plato, in The Republic, groups music and astronomy along with arithmetic and geometry as mathematical arts or sciences. In that context he treats them as pure mathematics. Astronomy is no more concerned with the visible heavens than music is with audible tones. Music is rather the arithmetic of harmonies, astronomy the geometry of motions. But in the Timaeus Plato turns mathematical formulas and calculations to use in telling what he calls “a likely story” concerning the formation and structure of the sensible world of becoming. Here, rather than in The Republic, we have, according to Whitehead, the initial conception of mathematical physics as well as deep insight into its nature and pattern. Aristotle criticizes the notion of astronomy as a purely mathematical science. Just as “the things of which optics and mathematical harmonies treat” cannot be divorced from the sensible, so the objects of astronomy are also the visible heavens. “Astronomical experience,” Aristotle writes, “supplies the principles of astronomical science.” Yet, though its subject matter is physical and its method is in part empirical, astronomy, like optics and harmonics, takes the form of mathematical demonstration; and it is for this reason that Aquinas later calls such disciplines “mixed and intermediate sciences.” Cf. ibid., Vol. II{II}, Chapter 67, “Physics” (Introduction): Aristotle’s teacher Plato was not a physicist in this sense. In his formulation of the liberal arts and sciences that was part of the early education of the guardians in The Republic, the four mathematical disciplines were enumerated as arithmetic, geometry, music, and astronomy. All four were strictly mathematical disciplines, not empirical sciences. However, in one dialogue, the Timaeus, Plato is concerned with what looks like a physical problem - the formation of the cosmos and its structure. Yet even here his process of thought relies heavily on mathematical concepts and configurations. He regards the elaborate theory that he develops as only a likely story, aimed at saving the appearances by explaining them in mathematical terms. Thus Plato is more nearly than Aristotle the precursor of mathematical  physics – of Ptolemy, Copernicus, and Kepler, of Galileo, Newton, and Huygens. § 47 11. The division of liberal art into its principal parts. The trivium: The quadrivium: grammar, logic, rhetoric arithmetic, geometry, music, astronomy 12. The works of the trivium. to form a construction9 belongs to grammar, a syllogism, to logic, a speech, to rhetoric. 13. The works of the quadrivium. to number belongs to arithmetic, to measure, to geometry, to form melodies, to music, to reckon the course of the stars, to astronomy. 14. The work belonging to the liberal art of music. According to the text of St. Thomas Aquinas from his commentary on the Trinity of  Boethius, the work belonging to the liberal art of music is melodias formare, ‘the forming of melodies’. But this forming must not be confused with the characteristic activity of  mousike techne aute, the art of music itself. Whereas the former is the act of ars liberalis musicae (which is a virtue of the speculative intellect), the latter proceeds from that virtue of the practical intellect which enables its possessor to compose a symphony or a song. The work of the liberal art of music is to apply formal number to sounds as matter in order to understand such things as intervals, the consonances they make, and the scales com-posed of them. Accordingly, one must understand “forming melodies” to pertain to this. But the work of mousike techne is to produce an imitation naturally delightful to man by moving the passions in accordance with reason. Hence, for the liberal artist in music to do his work, he must acquire by study a knowledge of the application of arithmetical princi-ples to musical sound, as well as the demonstrations that follow from them (which, as al-ready noted, are habits of the speculative intellect), but the composer of music requires a natural gift for composition (euphues or ingenium), apart from which he can do nothing. 15. Supplementary remarks on the meaning of melodias formare. In the previous section we pointed out that ‘forming melodies’ cannot be taken to mean “composing melodies” in the sense in which that activity belongs to the composer of  music. Given its unfamiliarity, further remarks are in order here. To begin with, we must consider St. Thomas’ description of the work belonging to the art of grammar: formare constructionis. As we pointed out in a footnote, this is equivalent to saying “to construct a sentence”. By a proportion then, melodias formare, expressed in English, may mean something like “to construct the work expressed by melodia”. What, then, are the melodiae to be constructed? In commenting on the  De Anima, book II where Aristotle attributes melos to the voice (420b 9), St. Thomas understands this to mean melodia, the distinguishing in the voice of the high and low, and equates it with consonantia. ( In II De Anima, lect. 18, n. 3). 9 That is, to put together a sentence, inasmuch as the right construction of the sentence is the goal of the art of  grammar. 48 But St. Thomas uses this latter word as a synonym for harmonia. We must, then, look at the definitions of these terms. First, we must note that the term melos, equivalent to the Latin melodia, has two meanings for Greek writers on harmonic science: taken in one way, it means ton phthongon taxei ton oxeon kai bareon, the order of high and low sounds (Aristotle,  Problems XIX. 27, 919b 33, cf. XIX, 29, 920a 29) which we call ‘melody’; in another way, it signifies that which consists in logos, harmoniai, and rhythmos, speech, tunings or attunements, and rhythm (Plato, Republic III, 398d), which we call ‘song’ or ‘tune’.10 As for the harmoniai, in the Philebus (17d) Plato defines them as the systemata that result from dia stemata…tes phones oxutetos te peri kai barutetos, that is, the scales put together from intervals between high and low ‘voices’, or sounds in the sense of ‘notes’. Harmonia also means a consonance in sounds ( In I De Anima, lect. 9, n. 4), but consonance is the ratio or   proportion in numbers according to the high and low ( In II Post. Anal ., lect. 1, n. 8). (In the  De Anima commentary St. Thomas understands this to mean the composite of sounds that results from an instrument whose parts, such as strings, or flutes, or the like, have been well-ordered.) In the light of the foregoing definitions, we can understand melodias in St. Thomas’ text in either of two ways. First, the word can be taken in the first of the two meanings of  melos given above, since the student of harmonic science must be able to construct an ordered sequence of intervals according to the various systems of tuning in order to understand what they are.11 Second, it can be understood as equivalent to consonantia, inasmuch as here, again, it belongs to the student of harmonics to construct the intervals in which consonances consist in order, e.g. to determine whether they can be evenly divided, or to  build a scale, or to divide the monochord (such work requiring him to apprehend their  ratios in numbers and to perform on them such operations as compounding and separating) and the like. In sum, then, melodias  formare means either to construct an ordered sequence of  high and low sounds, thereby constituting ‘melody’, or to construct the consonant intervals  presupposed to this, together with the other arithmetical operations this involves. On the work of the liberal art of music, cf. also the following observations from St. Thomas Aquinas: “Music considers sounds, not insofar as they are sounds, but insofar as they are proportionable according to numbers.”12 ( In Boetii De Trin. III, q. 5, art. 3, ad 6) “So number simply, which is the subject genus of arithmetic, and number of sounds, which is the subject genus of music, are not one genus simply.” ( In I Post. An., lect. 15, n. 5) “For music applies formal number (which the arithmetician considers) to matter—that is, to sounds.” ( In I Post. An., lect. 25, n. 2) 10 A later writer on music, Aristides Quintilianus (perhaps from the fourth century AD), calls this melos teleia, complete or perfect melody, which he distinguishes from the “intertwining ( ploke) of the high and low”, which he says is the sense of melos proper to harmonics ( De Musica I, 12). 11 For the ancients, these systems consisted in the several harmoniai, like the Dorian, Phrygian, and Lydian, according to which they tuned their instruments; for the moderns, they are the modes like the major and minor scales belonging to the tuning called equal temperament found in present day pianos. 12 In other words, harmonic science considers sounds insofar as one sound has to another the ratio a number  has to a number. 49