The Father William Most Collection
The Scriptural Basis of St. Augustine's Arithmology
The "mystical" interpretation by many Fathers of the Church of various numbers found in Holy Scripture generally receives today unsympathetic attention if any attention at all. Not only many non-Catholics, but many Catholics as well, often agree to quickly brush aside all such speculations as mere "Pythagoreanism in the air". Thus, for example, Knappitsch, in commenting on Augustine's treatment of tile number six in De Genesi ad litteram 4.2.2ss., says that today no exegete would dare propose such an interpretation, and that Augustine and other Fathers were powerfully under the influence of Pythagorean-Platonic teaching.1 Still another writer, Marrou, himself famed for his work on Augustine, adds that what Augustine and his masters (does he mean the earlier Fathers?) considered as many profound mysteries, appear to us as puerile work founded on simple associations of ideas.2
It would be easy to add more quotations to the same effect, but there is hardly any need of that; for, unfortunately, such statements are well known to be common. It is our purpose here to examine to what extent such strictures are justified.
Even the authors cited above do provide data from which we may begin to suspect that their statements quoted above are excessive. Thus Knappitsch, though he had told us3 that the favorite numbers for Pythagoreans were four, eight, and ten, later remarks that Augustine's use of the number eight (so favored by Pythagoreans) is incomparably less frequent than his use of seven, which did not enjoy special Pythagorean esteem.4 Similarly, Marrou admits that the patristic arithmology is not a mere borrowing from pagan sources, and notes some minor but interesting differences, such as the fact that Augustine neglects the Neoplatonic use (as found in Iamblichus) of the number five, and also that he goes beyond ten, while the Pythagoreans did not treat of numbers above ten.5
To be entirely fair in our interpretation, let us hasten to admit that, in general, Augustine did undergo very considerable influence from Neoplatonism, a fact too well known to require documentation. We may also admit that in his early work De Ordine (written at Cassiciacum, in the fall of 386 A. D., while preparing for Baptism) he does speak with enthusiastic praise of Pythagoras,6 But neither should we forget that as early as the time of composition of the Confessions (probably 397-401 A.D.) he spoke with disdain of the Cassiciacum works as "adhuc superbiae scholam ... anhelantibus".7 Later, in his Retractations (written in 426 A. D. ), he specifically disavows his praise of Pythagoras, adding that someone reading the De Ordine passage might think he believed there were no errors in Pythagoras, whereas there are really many errors, capital errors at that.8 We may even admit that at one time Augustine was a devotee of astrology, as he himself tells us in his Confessions.9 But this was merely part of his early errors. Even before his conversion he had so far rejected astrology as to try to persuade a friend to give it up also.10
On the other side of the picture, we find that mystical use of number symbolism was in vogue in the Old Testament itself, long before the Pythagoreans first appeared. It was also cultivated by most of the early Fathers of the Church, several of whom openly state that they are not merely imitating Pythagoras. Thus when St. Jerome wishes to support his interpretation of the number two in regard to the second day of creation, he calls on a long list of Fathers: Clement, Hippolytus, Origen, Dionysius, Eusebius, Didymus, Tertullian, Cyprian, Victorinus, Lactantius, Hilary. He adds that he could also quote Pythagoras and some other pagans, but hardly means to suggest that he and the many Fathers cited depend on such pagans.11 St. Ambrose, commenting on the number seven in relation to the seventh day of God's rest, adds that the number seven is good, but that he does not treat it as good in the manner of Pythagoras and other pagans, but in relation to the sevenfold gifts of the Holy Spirit as given by the prophet Isaias.12
However, the purpose of this paper is to treat not all the Fathers, but only St. Augustine, who is probably the chief exponent of number symbolism. We shall endeavor to see the deeper foundations of his interest in numbers.
It is a truth acknowledged by all sound philosophers, that the truths of mathematics are of a high order of abstraction. In his dialogue De Libero Arbitrio, Augustine goes through his famous ascending process by which he shows the existence of God. Starting from the lower orders of reality, he endeavors to lead the searcher step by step, rising ever higher, above the things of the body, above the mind and soul itself, to God. In the course of this process he notes that there are some things that are necessarily true. We recognize their truth, he says, not from sense experience, but in a higher way, for they do not merely happen to be true, but are necessarily and eternally true. Among these truths are the truths of numbers:13
E. Nullo modo id putaverim: non enim si sensu corporis percepti numeros, idcirco etiam rationem partitionis numerorum vel copulationis sensu corporis percipere potui ... septem autem et tria decem sunt; et non solum nunc, sed etiam semper; neque ullo modo aliquando septem et tria non fuerunt decem, aut aliquando septem et tria non erunt decem.
A few paragraphs farther on the same work, Augustine tells us that these truths are above our minds-they dwell unchangeable in truth itself:14
A knowledge of this science of numbers is useful, he thinks, for the man who grasps it will be able more easily to understand the most profound truths of philosophy and theology.15
Sacred Scripture contains many numbers. The thoughtful man cannot escape being aroused to wonder why it is that Moses and Elias, and Our Lord Himself fasted forty days. Ignorance of the principles of numbers will mean that a man will fail to understand many things in the Scriptures:16
This knowledge of numbers can help explain apparent discrepancies in numbers given in Scripture. For example, the Hebrew and the Septuagint differ in the number given in Jonas 3:4. The one says the prophet threatens the destruction of Ninive in 40 days, the other in 3 days. But, Augustine shows at some length, these numbers are really symbolic. Hence the difference is only apparent. The same method might be properly applied to many other instances of this sort.17
Augustine admits that he himself may not always succeed in finding the correct mystical interpretation of a given number. Others may do better than he:18
But the attitude found in some today of ridiculing all attempts at this type of interpretation would be quite incomprehensible to Augustine; for, he says, no one would be so foolish and inept as to say there is no reason for these numbers in Scripture-he claims the backing of the authority of the teaching of the Church as handed down by the Fathers, the example of the Scriptures, and the science of mathematics. No one in his right mind will attack scientific reason, no Christian will attack Scripture, no peaceful man will fail to sentire cum Ecclesia:19
As the above quotation indicates, Augustine himself claims that his ideas on the symbolism of numbers are rooted in Scripture itself, as well as in tradition and sound philosophy. In more than one passage he shows us on which scriptural statements he will ground his claims. For, he says, it is not without reason that God is praised thus in the Book of Wisdom (11:21): "... but thou hast ordered all things in measure and number and weight."20 This is only the beginning-there are other passages, and more elaborate development of the theory to be found in other works of Augustine. We have already seen that in his ascending process of leading a soul to recognize the existence of God (see note 14 above), Augustine speaks of some truths as eternal and necessary, and above our very minds. After Evodius has given him the truths of number as an example of this type of truth, Augustine adds that he is pleased that Evodius has chosen that particular example: for, he says, it is not without reason that in Holy Scripture we find wisdom and number associated as they are in Ecclesiastes 7:26:21
After some intervening discussion, Evodius comments that Augustine has noted the association of number and wisdom in Scripture, and asks if the two are really the same thing. For, he adds, he knows many men who are skilled in numbers, but few who are skilled in wisdom. Augustine replies that he too marvels on this matter. He does not understand why men consider number commonplace, though they highly prize wisdom. Now, he says, since Wisdom 8:1 tells us that wisdom "reacheth from end to end mightily, and ordereth all things sweetly", perhaps the truth is that the power by which wisdom reaches everywhere is number, while that which orders all things sweetly is wisdom in the strict sense, for both functions belong to one and the same wisdom: "cum sit utrumque unius eiusdemque sapientiae".22 Perhaps the reason why few prize number is that even bodies have number, while only rational souls have wisdom. The situation might be compared to that of a fire; for a fire has both light and heat. These two are, as it were, of the same substance (consubstantialis). Things near to the fire receive both light and heat: things farther removed receive light only, and not heat also. Similarly, while wisdom reaches to all things, only rational souls are capable of sharing in it in the full sense of the word: they receive both light and heat. But irrational beings are incapable of wisdom: their participation is in number alone:23
If we cannot determine whether number is in or from wisdom, or even the reverse, yet it is beyond all doubt that both number and wisdom give truth, immutable truth.
Here we see a hesitant tendency to almost identify number and wisdom. They are consubstantialis ... nec separari ab invicem possum. Gilson,24 in commenting on this passage, remarks that here we have an ontological illumination (note the expression lumine numerorum) of all things comparable to the intellectual illumination of the mind by divine light, and to the illumination of the will by grace. These three are on similar metaphysical bases: man is viewed as radically insufficient for himself in the three orders. This insufficiency is made up by wisdom and number (ontological), by divine light (intellectual) and by grace (moral).
Augustine's thought carries him still further: he had already noted from Wisdom 11:21 that God has arranged all things in measure and number and weight. He asks if these three were anywhere before creation, and replies that they were in God. Not that God is these in the material sense. But in another sense: insofar as measure imposes a measure on all things, and number imposes species on all, and weight brings all to stable rest-in this sense God Himself is all three of these, for He bounds all things, He forms all things, He orders all things. Hence when Scripture says that He disposed all in measure and number and weight, it means that He disposed all things in Himself. Few can rise above all that can be measured to the Measure without measure; few can rise above all that can be numbered and reach the Number without number: few can rise above all that can be weighed to the Weight without weight:25
This leads us into a further development. We note that in the above passage Augustine states that number gives species to every being, and forms it. In the De Libero Arbitrio we find a passage which is related in thought. In it wisdom is represented as impressing its mark on all things, and we are told that everything pleasurable to look on is numerosus:26 (the subject is sapientia)
It appears then that it is number which gives beauty to things, and not only that. It is not merely superficial beauty that is under consideration. Augustine speaks of the formae of each thing. In other words, pulchrum appears to be a transcendental, which is interchangeable with being itself. For, he continues the passage cited above:27
Therefore things are beautiful insofar as they are. And their beauty has the same source as their numeri, namely, sapientia, which, as we have seen above, is practically if not entirely consubstantialis with numerus.
In what way does numerus provide the pulchrum, and do it in such a way that a being is in so far as it is numerosum? Apparently it does this by way of order. For order is also a measure of being, and it is parallel to species, which, as we have seen, is an effect of numerus:28
Now things which tend to order tend to be. Attainment of order is the same as attainment of participation in being. The reason for this is the fact that order puts things into a harmonious arrangement and fitting place. In so doing, it makes them imitate the unity of God, who is supremely One, who is supremely Being:29
Beauty, too, is related to this unity. The more balanced the parts of a body are, the more it imitates unity. This is the measure of its participation in Being:30
Cum autem omne quod esse dicimus, in quantum manet dicamus, et in quantum unum est, omnia porro pulchritudinis forma unitas sit...
The absolute character of the Unity of God is brought out especially well in the following passage from the De Trinitate. God is viewed as identical with His perfections:31
Indeed, for Augustine, the very word "universe" implies beauty, for he sees in it the root of unus. He speaks of "pulchritudo universitatis ... quae profecto ab uno cognominata est."32
Now that we have seen at what depth the concept of number lies in Augustine's metaphysics, we may examine a difficult passage. Augustine being deeply impressed with the notion of God's rest on the seventh day of creation, and feeling that any creative activity beyond the original creation might negate that rest, made use of the theory of rationes seminales, some notion of which had already appeared in Greek philosophy. Though there is still controversy over the exact nature and action of the rationes seminales, it is at least clear that Augustine adapts them to the concept of Providence, and considers them as powers whose action produces new individuals of the old species which were once set up on the six days of creation. In this way he avoids supposing any further creative activity of God today. Now in a passage in his De Genesi ad Litteram, he speaks of the rationes seminales as having in them efficacissismi numeri:33
To understand this statement it is necessary to sketch a bit of background. To Augustine's mind there are three levels of reality: 1) Things that are mutable in space and times (bodies); 2) Things that are mutable in time but not in place (souls); 3) That which is immutable in place and time (God alone).34 Corresponding to these three levels of reality we find three sorts of ratio. In God Himself we find the rationes aeternae. In the middle we find ratio humana. In irrational matter we find rationes seminales. It is in the latter that we find efficacissismi numeri. In the course of time, new individuals appear by the unfolding of these efficacissimi numeri:85
Obviously then, these efficacissimi numeri are to be understood as part of the workings of that providential sapientia which penetrates all things lumine numerorum, thereby giving them beauty, form, and being itself. They are efficacissimi, for, in accord with the original disposition of Providence which thereby created all future individuals in semine, they do, under the evocation of extrinsic causes (even the process of agriculture mentioned above) produce new individuals of the old species. But Augustine does not forget that the creative power is still that of God Himself, who by this means still works. For neither he who plants, nor he who waters is anything, "sed qui incrementum dat Deus. Ipse namque operatione qua nunc usque operatur, facit ut numeros suos explicent semina...."36
To sum up, then, what we have seen: Augustine rightly sees that the truths of mathematics are not merely above the senses, but even above our minds, for they are eternal. Creative Wisdom, which is Being Itself, gives to all created beings a participation in itself. To rational beings is given wisdom in the full sense of the word. To irrational beings is given number, which is probably to be considered as consubstantial with wisdom, or at least as having the same source. In any event, this is the ontological illumination of every being, comparable to the illumination of minds by the divine light and of wills by grace. By it every being insofar as it has being, also has beauty, form, and order. Through these, though it has parts, a body imitates the Unity that is God, who is Being Itself. This same power of God, though resting on the seventh day, yet produces new individuals of each species, unfolding the inchoative creation of the six days through the operative numbers of the rationes seminales.
These are the deeper philosophical and theological foundations of Augustine's respect for the truths of number. The numbers he finds in Scripture, though lying more on the surface of things, are still part of this whole picture. They are the effects of the Divine Wisdom which reaches into all things. He knows this from Scripture, from the example of the Fathers and the sensus Ecclesiae, and from sound reasoning. Though he may not always find the reasons of fittingness (and let us not forget that fittingness is a part of order, and a thing is insofar as it has order) which Providence had in mind in placing each number in Scripture, yet he is sure they are there. He himself has seen the hand of Providence working very openly in his own life (as seen in the Confessions) and also in the world as a whole (as set down in the City of God). It is no wonder that he can see the hand of God even in number symbolism. It is true, these instances are, even in his mind, not the greatest examples of the infinite care of God. But they are part of the whole picture. They contribute to stimulating his admiration of God. Now any psychologist knows that admiration is one of the steps to love. It is perhaps partly because men have lost some of their ability to admire the works of God, admiring instead the sacred cow of natural science, that "the charity of many shall grow cold"?37 If so, Augustine has much to offer us. And even though, as he himself admits, he does not always succeed in finding the really fitting reasons, yet his meditation on number may make some small contribution to our love of the all-pervading care of Providence, and to our understanding of Scripture.38
|1||A. Knappitsch, "St. Augustins Zahlensymbolik", in Jahresbericht des Fürstbischöflichen Gymnasiums (Graz, 1905), p. 13: "Auf diese Art der Erklärung dürfte sich heutzutage wohl kein Exeget mehr einlassen. Wir finden aber ein Verständnis dafür, wenn wir, wie schon erwähnt, bedenken, dasz die Väter zu ihrer Zeit von der pythagoräisch-platonischen Zahlensymbolik mächtig beeinfluszt waren." Similar comments are to be found elsewhere in the same work, cf. pp. 3 and 4.|
|2||H. Marrou, Saint Augustin et la Fin de la Culture Antique (Paris, 1949), pp. 451-52: "Au fond cette science dans laquelle saint Augustin comme ses maîtres en pythagorisme tenaient à apercevoir tant de profonds et ravissants mystères nous apparaît comme issue d'une technique assez puérile fondée sur de simples associations d'idées."|
|3||Op cit., p. 3.|
|4||Ibid., p. 21.|
|5||Op. cit., p. 451, esp. note 3.|
|6||De Ordine 2.20.53-54: PL 32.1020.|
|7||Confessions 9.4.7: PL 32.766.|
|8||Retractations 1.3.3: PL 32.589.|
|9||Confessions 4.3.4-6: PL 32.694-96.|
|10||Ibid., 7.6.8-10: PL 32.737-39.|
|11||Epist. 48.19-20: PL 22.508-09: cf. esp.: "Scilicet nunc enumerandum mihi est, qui Ecclesiasticorum de impari numero disputarint, Clemens, Hippolytus, Origenes, Dionysius, Eusebius, Didymus, nostrorumque Tertullianus, Cyprianus, Victorinus, Lactantius, Hilarius: quorum Cyprianus de septenario, id est, impari numero disserens, quae et quanta dixerit ad Fortunatum, fiber illius testimonio est. An forsitan Pythagoram et Architam Tarentinum, et Publium Scipionem in sexto de Republica, de impari numero proferam disputantes? Et si hos audire noluerint obtrectatores mei. Grammaticorum scholas eis faciam conclamare 'Numero Deus impare gaudet'". (Verg. Ecl. 8.)|
|12||Epist. 44.3: PL 16.1185: "Sex itaque diebus mundum creavit, septimo die requievit ab operibus suis. Bonus septimus numerus, quem non Pythagorico et caeterorum philosophorum more tractamus, sed secundum formam et divisiones gratiae spiritalis; septem enim virtutes principales sancti Spiritus propheta Isaias complexus est."|
|13||De Libero Arbitrio 2.8.21: PL 32.1251-52.|
|14||Ibid., 2.11.31: PL 32.1258.|
|15||De Ordine 2.16.44: PL 32.1015: "... facilius autem cognoscet ista, qui numeros simplices atque intelligibiles comprehenderit."|
|16||De Doctrina Christiana 2.16.25: PL 34.48. Cf. also ibid., 3.35.51: PL 34.86.|
|17||De Civitate Dei 18.44: PL 41.605. It is worth noting that a similar suggestion was recently made by Fr. Arbez. Writing in the American Ecclesiastical Review, Sept. 1950, pp. 208-09, he suggests that the symbolic approach might help to explain the numbers in the genealogies of Genesis. Fr. Arbez adds the further observation that perhaps the large numbers found in the Babylonian king lists may be related.|
|18||De Trinitate, 4.6.10: PL 42.895. Cf. also Sermo 51.24.35: PL 38.354.|
|19||De Trinitate 4.6.10: PL 42.895.|
|20||De Civitate Dei 11.30: PL 41.344: "Unde ratio numeri contemnenda non est, quae in multis sanctarum Scripturarum locis, quam magni aestimanda sit, elucet diligenter intuentibus. Nec frustra in laudibus Dei dictum est, Omnia in mensura et numero et pondere disposuisti.|
|21||De Libero Arbitrio 2.8.24: PL 32.1253.|
|22||Ibid., 2.11.30-32: PL 32.1257-58.|
|23||Ibid. It is interesting to note that a similar comparison of a fire is to be found in Plato, Timaeus 39 B. Plato says that in making the universe, in order to provide a ready measure of relative speeds of the heavenly bodies in the eight orbits, God made a light, the sun, "that it might shine, as much as possible, through all the heaven, and that all living things for whom it was proper should share in number, learning it from the revolutions of the Same and the Similar". We are certain that Augustine had read the Timaeus in Cicero's translation (cf. De Civitate Dei 13.16.1 :PL 41388). We also know of Augustine's high respect for Plato, and his willingness to use Plato and other pagans whenever they had the truth: "... apud Platonicos me interim quod sacris nostris non repugnet reperturum esse confido".—Contra Academicos 3.20.43: PL 32.957. It may be that this statement of Plato's helped to suggest to Augustine the simile here given. But there are important differences. Plato does not speak of two things, wisdom and number, but of number only. Further, Plato speaks of the sun, not of a fire, and does not mention the distinction of the range of light and heat. Plato is speaking literally, while Augustine is only making a comparison. Cf. also note 24 below.|
|24||E. Gilson, Introduction à l'Étude de Saint Augustin (Paris, 1943), p. 167. There is also here a similarity to Plato's thought. For Plato, according to the interpretation of Aristotle (Metaphysics 1.6:987 b), stated that things exist by their participation in number: cf. F. Copleston, A History of Philosophy (Westminster, Md., 1946), I, 193ff. The precise sense of Plato's thought on this subject is still not clear today. It is, therefore, difficult to assess Augustine's indebtedness to him for suggesting this notion. Whatever the truth may be, Augustine surely did baptize the concept. He makes it part of the Christian concept of the natural concursus of God which sustains all creatures, and he explicitly states that he bases his ideas directly on certain Old Testament sapiential texts, especially Wisdom 8:1, as we have seen. Therefore, if he is influenced by Plato, the Platonic influence is only partial, and is well Christianized. And there are important differences even in the comparison under consideration here, as was shown in note 23 above. Further, in the passage from Timaeus 39 B mentioned above, Plato might easily be understood to say that not all living creatures participate in number (in fact, the passage can more easily be taken of mere learning number than of ontological participation). He says, that the sun is to shine throughout the heaven so that as Jowett translates, "... that the animals, as many as nature intended, might participate in number, learning arithmetic from the revolution of the same and the like" (the restriction: as many as nature intended, is to be noted). Similarly Bury (in L.C.L.) renders: "... that all the living creatures entitled thereto might participate in number, learning it from the revolution of the Same and Similar." But it is not necessary to argue over the interpretation of the passage in Plato himself, since, as we have seen (in note 23), Augustine knew Plato's Timaeus through the medium of Cicero's translation (it is not impossible that he also consulted the Greek text). Now fortunately, we still have Cicero's translation of the passage in question:|
We note the restrictive clause is preserved in the translation: quibus ius esset doceri. But as to the important notion of paricipation in number, which might have suggested the thought to Augustine, we find it for practical purposes omitted. The emphasis is merely on learning: ut ... numerorum naturam vimque cognoscerent. Hence the probability of Augustine being under the influence of this passage in Plato, the passage which in itself most closely resembles his thought (though there are great differences, as noted above in n. 23), is not very great.
|25||De Genesi ad Litteram 4.3.7-9: PL 34.299.|
|26||De Libero Arbitrio 2.16.41: PL 32.1263.|
|27||Ibid., 2.16.42: PL 32.1263.|
|28||De Natura Boni 3: PL 42.553.|
|29||De Moribus Manichaeorum 2.6.8: PL 32.1348.|
|30||De Genesi ad Litteram Liber Imperfectus 16.59: PL 34.243 and Epist. 18.2: PL 33.85.|
|31||De Trinitate 6.10.11: PL 42.931.|
|32||De Ordine 1.2.3 :PL 32.979.|
|33||De Genesi ad Litteram 5.7.20:PL 34.328.|
|34||Vernon J. Bourke, Augustine's Quest of Wisdom (Milwaukee, 1945), pp. 225-27.|
|35||De Trinitate 3.9.16: PL 42.878.|
|36||De Civitate Dei 22.24.2: PL 41.789.|
|38||Not all writers today do ridicule Augustine's speculations. Some competent writers today have found excursions into this field quite profitable. To mention but a few, we might note that in this quarterly in recent years we have had two articles by Fr. Skehan (vol. X (1948) 398 and vol. IX (1947) 190-98). Cf. also the article by Arbez listed above in note 17.|