St. Albertus Magnus's Commentary on Euclid's Elements

St. Albertus Magnus (1206-1280) wrote extensively on physics methodology, among other fields like theology and the experimental sciences, and is credited for discovering arsenic. He said: "The aim of natural science is not simply to accept the statements [narrata] of others, but to investigate the causes that are at work in nature" (De Miner., lib. II, tr. ii, i) and "Experimentum solum certificat in talibus" ("Experiment is the only safe guide in such investigations;" De Veg., VI, tr. ii, i). Against what today one would call "intelligent design," St. Albert says: "In studying nature we have not to inquire how God the Creator may, as He freely wills, use His creatures to work miracles and thereby show forth His power: we have rather to inquire what Nature with its immanent causes can naturally bring to pass" (De Coelo et Mundo, I, tr. iv, x).

     The Dominican Scholastic philosopher Albertus Magnus (1193?-1280) acquired the title Doctor Universalis from the breadth of his learning, which astonished his contemporaries. His fame earned him a place in the Divine Comedy, where his most famous student, Thomas Aquinas, introduces him to Dante:

Questi che m'è a destra più vicino
Frate e maëstro fummi, ed esso Alberto
È di Cologna, e io Thomas d'Aquino. (Paradiso, X, 97-99)

He who is nearest to me on the right
Was my colleague and teacher, namely, Albert
Of Cologne, and I am Thomas Aquinas.

The program of the scholastic philosophers was to use the deductive method of mathematics to demonstrate by reason the existence of Deity and to describe His attributes, to prove the immortality of the soul, to assert free will, and in general to establish thereby the truth of the Catholic religion. Their first axiom was, that this was possible. Even Russell, who considered theology nothing more than organized ignorance, could nevertheless respect the Medieval mastery of logic:

     The medieval outlook of educated men had a logical unity which has now been lost. We may take Thomas Aquinas as the authoritative exponent of the creed which science was compelled to attack. He maintained—and his view is still that of the Roman Catholic Church—that some of the fundamental truths of the Christian religion could be proved by the unaided reason, without the help of revelation. Among these was the existence of an omnipotent and benevolent Creator. From His omnipotence and benevolence followed that He would not leave His creatures without knowledge of His decrees, to the extent that might be necessary to obey His will. There must therefore be a Divine revelation, which, obviously, is contained in the Bible and the decisions of the Church. This point being established, the rest of what we need to know can be inferred from the Scriptures and the pronouncements of oecumenical Councils. The whole argument proceeds deductively from premisses formerly accepted by almost the whole population of Christian countries, and if the argument is, to the modern reader, at times faulty, its fallacies were not apparent to the majority of learned contemporaries.
     Now logical unity is at once a strength and a weakness. It is a strength because it insures that whoever accepts one stage of the argument must accept all later stages; it is a weakness because whoever rejects any of the later stages must also reject some, at least, of the earlier stages. The Church, in its conflict with science, exhibited both the strength and the weakness resulting from the logical coherence of its dogmas [Religion and Science, 12-13].

Within this program, it was the special enterprise of Albertus Magnus to interpret the works of Aristotle for his Medieval contemporaries, insofar as the writings of that philosopher could be known through the veil of Latin translations of Arabic translations of the Greek texts, which at that time covered the hearts of the learned. In so doing, he made a major contribution to culture, for Aristotle was interested in the natural world, and investigation into his activities tended to promote the rebirth of knowledge, which was accomplished in the period called the Renaissance. The labors of pople like Albertus Magnus were appreciated by Macaulay, who noticed them in one of the most famous chapters in literature:

     Whatever reproach may, at a later period, have been justly thrown on the indolence and lukury of religios orders, it was surely good that, in an age of ignorance and violence, there should be quiet cloisters and gardens, in which the arts of peace could be safely cultivated, in which gentle and contemplative natures could find an asylum, in which one brother could employ himself in transcribing the Aeneid of Virgil, and another in meditating the Analytics of Aristotle, in which he who had a genius for art might illuminate a martyrology or carve a crucifix, and in which he who had a turn for natural philosophy might make experiments on the properties of plants and minerals [The History of English from the Accession of James II, I, 9]

     Albertus Magnus is one of those personalities who are appreciated even by those whith a critical attitude towarsd the Catholic religion. For example, White, cofounder and first president of Cornell University, a declared enemy of dogmatic theology, had a sympathetic opinion of him:

First among these was Albert of Bollstädt, better known as Albert the Great, the most renowned scholar of his time. Fettered though he was by the methods sanctioned in the Church, dark as was all about him, he had conceived better methods and aims; his eye pierced the mists of scholasticism; he saw the light, and sought to draw the world toward it. He stands among the great pioneers of physical and natural science; he aided in giving foundations to botany and chemistry, he rose above his time, and struck a heavy blow on those who opposed the possibility of human life on the opposite sides of the earth; he noted the influence of mountains, seas, and forests upon races and products, so that Humboldt justly finds in his works the germs of physical geography as a comprehensive science [A History of the Warfare of Science with Theology in Christendom, I, 377].

The most recent biography of Albert, written on the occasion of the seven hundredth anniversary of his death, is by Weisheipl ["The Life and Works of St. Albert the Great". Albertus Magnus and the Sciences — Commemorative Essays].

     Albertus Magnus conceived and carried out the plan of commenting on all human knowledge by beginning with the natural sciences, proceeding to mathematics, and finishing in philosophy and theology. Thus, in his writings in the natural sciences, he refers to mathematics as the object of future activity:

     Primo complebimus, Deo adiuvante, scientiam naturalem, et deinde loquemur de mathematicis omnibus, et intentionem finiemus in scientia divina (Physica, Book I, Treatise 1, Chapter i).
     With God's help, we shall first complete natural science, and then we shall talk about all of mathematics, and we shall finish our program in divine science.

     Longum esset demonstrare, sed in geometria hoc docebitur et in astronomia, Domino concedente (Op. cit., I, 2, i).
     It would be long to prove, but, God willing, this will be taught in geometry and astronomy.

     Haec autem omnia supponenda sunt, probanda autem in libris de visu in Perspectivis, quae scientia compleri non potest, nisi primum consideremus ea quae pertinent ad geometriam (De Sensu et Sensato, Treatise 1, Chapter 14).
     All these things, however, must be supposed for now; they are to be proven, though, in the books on sight in Perspective, which science cannot be completed unless we shall first consider those things that pertain to geometry.

In his compositions on philosophy and theology, however, Albert refers to his work on geometry as at hing of the past, for he accepted the idea of Plato, that one could not competently study philosophy without having first mastered mathematics.

     Naturalibus et doctrinalibus iam, quantum licuit, scientiis elucidatis, iam ad veram philosophiae sapientiam accedamus (Metaphysica, Book I, Treatise I, Chapter i).
     Now that the natural and mathematical sciences have been elucidated as much as was possible, let us proceed to the true wisdom of philosophy.

     Hoc autem iam a nobis in geometricis est demonstratum (Ibid., I, 2, x).
     For this [sc. that the diameter and side of a square are incommensurable] has already been proven by us in the geometrical [works].

     Sicut in XV and XVI tertii geometriae nostrae demonstratum est (Ibid., III, 2, iii).
     Just as has been proven in the fifteenth and sixteenth [propositions] of the third [book] of our Geometry [sc. namely, that a tangent line to a circle intersects it at only one point].

     Sicut nos in I nostrae geometriae ostendimus (Ibid., V, 3, i).
     As we showed in the first [book] of our Geometry [sc., that two straight lines do not enclose a surface].

—Albertus Magnus on Euclid's Elements of Geometry, pgs. xi-xv

Here is St. Albertus Magnus's commentary on Euclid's famous proof of the Pythagorean Theorem, Proposition 46 here:

The science before science

Galileo Truly Recanted.

Was Galileo really a martyr of modern science, the theories and explanations of which are in a constant state of flux, or did he ultimately seek an absolute, unchanging, objective Truth and recant of holding a changeable scientific theory to be objectively true? Galileo wrote to Francesco Rinuccini, Arcetri, 29 March 1641, the year before his death:

The falsity of the Copernican system needs not be called into doubt, and especially by us Catholics, having the irrefragable authority of Sacred Scripture, interpreted by the supreme masters in Theology, whose concordant consensus renders us certain of the stability of the Earth placed in the center, and of the mobility of the Sun around it. The conjectures then for which Copernicus and his other followers have professed the contrary, are all lifted with that most solid argument of the Omnipotence of God, Who can do in diverse—rather, in infinite ways—that to our opinion and observation seem done in one particular way; we should not want to shorten the hand of God and tenaciously sustain that in which we can be deceived.

—Le opere di Galileo Galilei, vol. 7 edited by Vincenzio Viviani [my translation]

Galileo, were he alive in the 19th and 20th centuries, respectively, would agree with these statements:

[...] if writers on physics travel outside the boundaries of their own branch, and carry their erroneous teaching into the domain of philosophy, let them be handed over to philosophers for refutation.

—Pope Leo XIII's Providentissimus Deus

Human science gains greatly from revelation, for the latter opens out new horizons and makes known sooner other truths of the natural order, and because it opens the true road to investigation and keeps it safe from errors of application and of method. Thus does the lighthouse show many things they otherwise would not see, while it points out the rocks on which the vessel would suffer shipwreck.

—Pope St. Pius X's Iucunda Sane

Consecration of the Chapel: Our Lady of Guadalupe Seminary

Assumpta est Sedes Sapientiæ in cælum; gaudet exercitus Angelorum.

Interface between Theology and the Other Sciences

Related to this is again the question of why intellectual knowledge must come through the senses (Nothing is in the intellect that is not first in the senses: Nihil est in intellectu quod non prius in sensu.). The faithful hold by faith that:

For the invisible things of him, from the creation of the world, are clearly seen, being understood by the things that are made; his eternal power also, and divinity.

—Romans 1:20

As well as these:

If anyone shall have said that the one true God, our Creator and our Lord, cannot be known with certitude by those things which have been made, by the natural light of human reason: let him be anathema

—Denzinger 1806

The same Holy Mother Church holds and teaches that God, the beginning and end of all things, can be known with certitude by the natural light of human reason from created things; "for the invisible things of him, from the creation of the world, are clearly seen, being understood by the things that are made" [Rom 1:20]; nevertheless, it has pleased His wisdom and goodness to reveal Himself and the eternal decrees of His will to the human race in another and supernatural way, as the Apostle says: "God, who at sundry times and in divers manners, spoke in times past to the fathers by the prophets, last of all, in these days hath spoken to us by His Son" [Heb. 1:1].

—Denzinger 1785

Most relevant is this:

All knowledge of God, even natural knowledge, even in the pagan philosophers, cannot come except from God; and without grace knowledge produces nothing but presumption, vanity, and opposition to God Himself, instead of the affections of adoration, gratitude, and love.

—Denzinger 1391

How does the study of God's creatures, by doing physics in the broad sense of studying the natural world, lead to knowledge of Him? St. Thomas elucidates this:

Chapter 1

THE CONNECTION BETWEEN THE FOLLOWING CONSIDERATIONS AND THE PRECEDING ONES

“I meditated upon Your works: I meditated upon the works of Your hands” (Ps. 142-5).

[1] Of no thing whatever can a perfect knowledge be obtained unless its operation is known, because the measure and quality of a thing’s power is judged from the manner and type of its operation, and its power, in turn, manifests its nature; for a thing’s natural aptitude for operation follows upon its actual possession of a certain kind of nature.

[2] There are, however, two sorts of operation, as Aristotle teaches in Metaphysics IX [8]: one that remains in the agent and is a perfection of it, as the act of sensing, understanding, and willing; another that passes over into an external thing, and is a perfection of the thing made as a result of that operation, the acts of heating, cutting and building, for example.

[3] Now, both kinds of operation belong to God: the former, in that He understands, wills, rejoices, and loves; the latter, in that He brings things into being, preserves them, and governs them. But, since the former operation is a perfection of the operator, the latter a perfection of the thing made, and since the agent is naturally prior to the thing made and is the cause of it, it follows that the first of these types of operation is the ground of the second, and naturally precedes it, as a cause precedes its effect. Clear evidence of this fact, indeed, is found in human affairs; for in the thought and will of the craftsman lie the principle and plan of the work of building.

[4] Therefore, as a simple perfection of the operator, the first type of operation claims for itself the name of operation, or, again, of action; the second, as being a perfection of the thing made, is called making so that the things which a craftsman produces by action of this kind are said to be his handiwork.

[5] Of the first type of operation in God we have already spoken in the preceding Book of this work, where we treated of the divine knowledge and will. Hence, for a complete study of the divine truth, the second operation, whereby things are made and governed by God, remains to be dealt with.

[6], In fact, this order we can gather from the words quoted above. For the Psalmist first speaks of meditation upon the first type of operation, when he says: “I have meditated on all your operations”; thus, operation is here referred to the divine act of understanding and will. Then he refers to meditation on God’s works: “and I meditated on the works of Your hands”; so that by “the works of Your hands” we understand heaven and earth, and all that is brought into being by God, as the handiwork produced by a craftsman.

Chapter 2

THAT THE CONSIDERATION OF CREATURES IS USEFUL FOR INSTRUCTION OF FAITH

[1] This sort of meditation on the divine works is indeed necessary for instruction of faith in God.

[2] First, because meditation on His works enables us in game measure to admire and reflect upon His wisdom. For things made by art are representative of the art itself, being made in likeness to the art. Now, God brought things into being by His wisdom; wherefore the Psalm (103:24) declares: “You made all things in wisdom.” Hence, from reflection upon God’s works we are able to infer His wisdom, since, by a certain communication of His likeness, it is spread abroad in the things He has made. For it is written: “He poured her out,” namely, wisdom, “upon all His works” (Eccli. 1:10). Therefore, the Psalmist, after saying: “Your knowledge is become wonderful to me: it is high, and I cannot reach it,” and after referring to the aid of the divine illumination, when he says: “Night shall be my light,” etc., confesses that he was aided in knowing the divine wisdom by reflection upon God’s works, saying: “Wonderful are Your works, and my soul knows right well” (Ps. 138:6, 11, 14).

[3] Secondly, this consideration [of God’s works] leads to admiration of God’s sublime power, and consequently inspires in men’s hearts reverence for God. For the power of the worker is necessarily understood to transcend the things made. And so it is said: “If they,” namely, the philosophers, “admired their power and effects,” namely of the heavens, stars, and elements of the world, “let them understand that He that made them is mightier than they” (Wis. 13:4). Also it is written: “The invisible things of God are clearly seen, being understood by the things that are made: His eternal power also and divinity” (Rom. 1:20). Now, the fear and reverence of God result from this admiration. Hence, it is said: “Great is Your name in might. Who shall not fear You, O King of Nations?” (Jer. l0:6-7).

[4] Thirdly, this consideration incites the souls of men to the love of God’s goodness. For whatever goodness and perfection is distributed to the various creatures, in partial or particular measure, is united together in Him universally, as in the source of all goodness, as we proved in Book I. If, therefore, the goodness, beauty, and delightfulness of creatures are so alluring to the minds of men, the fountainhead of God’s own goodness, compared with the rivulets of goodness found in creatures, will draw the enkindled minds of men wholly to Itself. Hence it is said in the Psalm (91:5): “You have given me, O Lord, a delight in Your doings, and in the works of Your hands I shall rejoice.” And elsewhere it is written concerning the children of men: “They shall be inebriated with the plenty of Your house,” that is, of all creatures, “and You shall make them drink of the torrent of Your pleasure: for with You is the fountain of life” (Ps. 35:9-10). And, against certain men, it is said: “By these good things that are seen,” namely, creatures, which are good by a kind of participation, “they could not understand Him that is” (Wis. 13:1), namely, truly good; indeed, is goodness itself, as was shown in Book I.

[5] Fourthly, this consideration endows men with a certain likeness to God’s perfection. For it was shown in Book I that, by knowing Himself, God beholds all other things in Himself. Since, then, the Christian faith teaches man principally about God, and makes him know creatures by the light of divine revelation, there arises in man a certain likeness of God’s wisdom. So it is said: “But we all beholding the glory of the Lord with open face, are transformed into the same image” (2 Cor. 3:18).

[6] It is therefore evident that the consideration of creatures has its part to play in building the Christian faith. And for this reason it is said: “I will remember the works of the Lord, and I will declare the things I have seen: by the words of the Lord are His works” (Sirach 42:15).

Chapter 3

THAT KNOWLEDGE OF THE NATURE OF CREATURES SERVES TO DESTROY ERRORS CONCERNING GOD

[1] The consideration of creatures is further necessary, not only for the building up of truth, but also for the destruction of errors. For errors about creatures sometimes lead one astray from the truth of faith, so far as the errors are inconsistent with true knowledge of God. Now, this happens in many ways.

[2] First, because through ignorance of the nature of creatures men are sometimes so far perverted as to set up as. the first cause and as God that which can only receive its being from something else; for they think that nothing exists beyond the realm of visible creatures. Such were those who identified God with this, that, and the other kind of body; and of these it is said: “Who have imagined either the fire, or the wind, or the swift air, or the circle of the stars, or the great water, or the sun and moon to be the gods” (Wis. 13: 2).

[3] Secondly, because they attribute to certain creatures that which belongs only to God. This also results from error concerning creatures. For what is incompatible with a thing’s nature is not ascribed to it except through ignorance of its nature—as if man were said to have three feet. Now, what belongs solely to God is incompatible with the nature of a created thing, just as that which is exclusively man’s is incompatible with another thing’s nature. Thus, it is from ignorance of the creature’s nature that the aforesaid error arises. And against this error it is said: “They gave the incommunicable name to stones and wood” (Wis. 14:21). Into this error fell those who attribute the creation of things, or knowledge of the future, or the working of miracles to causes other than God.

[4] Thirdly, because through ignorance of the creature’s nature something is subtracted from God’s power in its working upon creatures. This is evidenced in the case of those who set up two principles of reality; in those who assert that things proceed from God, not by the divine will, but by natural necessity; and again, in those who withdraw either all or some things from the divine providence, or who deny that it can work outside the ordinary course of things. For all these notions are derogatory to God’s power. Against such persons it is said: “Who looked upon the Almighty as if He could do nothing” (Job 22:17), and: “You show Your power, when men will not believe You to be absolute in power” (Wis. .12: 17).

[5] Fourthly, through ignorance of the nature of things, and, consequently, of his own place in the order of the universe, this rational creature, man, who by faith is led to God as his last end, believes that he is subject to other creatures to which he is in fact superior. Such is evidently the case with those who subject human wills to the stars, and against these it is said: “Be not afraid of the signs of heaven, which the heathens fear” (Jer. 10:2); and this is likewise true of those who think that angels are the creators of souls, that human souls are mortal, and, generally, of persons who hold any similar views derogatory to the dignity of man.

[6] It is, therefore, evident that the opinion is false of those who asserted that it made no difference to the truth of the faith what anyone holds about creatures, so long as one thinks rightly about God, as Augustine tells us in his book On the Origin of the Soul [De anima et ejus origine, IV, 4]. For error concerning creatures, by subjecting them to causes other than God, spills over into false opinion about God, and takes men’s minds away from Him, to whom faith seeks to lead them.

[7] For this reason Scripture threatens punishment to those who eff about creatures, as to unbelievers, in the words of the Psalm (27:5): “Because they have not understood the works of the Lord and the operations of His hands, You shall destroy them, and shall not build them up”; and: “These things they thought and were deceived,” and further on: “They did not esteem the honor of holy Souls” (Wis. 7:2122).

Chapter 4

THAT THE PHILOSOPHER AND THE THEOLOGIAN CONSIDER CREATURES IN DIFFERENT WAYS

[1] Now, from what has been said it is evident that the teaching of the Christian faith deals with creatures so far as they reflect a certain likeness of God, and so far as error concerning them leads to error about God. And so they are viewed in a different light by that doctrine and by human philosophy. For human philosophy considers them as they are, so that the different parts of philosophy are found to correspond to the different genera of things. The Christian faith, however, does not consider them as such; thus, it regards fire not as fire, but as representing the sublimity of God, and as being directed to Him in any way at all. For as it is said: “Full of the glory of the Lord is His work. Did the Lord not make the saints declare all His wonderful works?” (Sirach 42: 16-17)

[2] For this reason, also, the philosopher and the believer consider different matters about creatures. The philosopher considers such things as belong to them by nature-the upward tendency of fire, for example; the believer, only such things as belong to them according as they are related to God—the fact, for instance, that they are created by God, are subject to Him, and so on.

[3] Hence, imperfection is not to be imputed to the teaching of the faith if it omits many properties of things, such as the figure of the heaven and the quality of its motion. For neither does the natural philosopher consider the same characters of a line as the geometrician, but only those that accrue to it as terminus of a natural body.

[4] But any things concerning creatures that are considered in common by the philosopher and the believer are conveyed through different principles in each case. For the philosopher takes his argument from the proper causes of things; the believer, from the first cause—for such reasons as that a thing has been handed down in this manner by God, or that this conduces to God’s glory, or that God’s power is infinite. Hence, also, [the doctrine of the faith] ought to be called the highest wisdom, since it treats of the highest Cause; as we read in Deuteronomy (4:6): “For this is your wisdom and understanding in the sight of nations.” And, therefore, human philosophy serves her as the first wisdom. Accordingly, divine wisdom sometimes argues from principles of human philosophy. For among philosophers, too, the first philosophy utilizes the teachings of all the sciences in order to realize its objectives.

[5] Hence again, the two kinds of teaching do not follow the same order. For in the teaching of philosophy, which considers creatures in themselves and leads us from them to the knowledge of God, the first consideration is about creatures; the last, of God. But in the teaching of faith, which considers creatures only in their relation to God, the consideration of God comes first, that of creatures afterwards. And thus the doctrine of faith is more perfect, as being more like the knowledge possessed by God, who, in knowing Himself, immediately knows other things.

[6] And so, following this order, after what has been said in Book I about God in Himself, it remains for us to treat of the things which derive from Him.

—Contra Gentiles, lib. 2 cap. 1-4

Faith Seeks Understanding

Galileo's Giant: Nicole Oresme

Nicole Oresme (c. 1320 - 1382) argued, a couple hundred years before Galileo, that a rotating earth is a simpler explanation than that of Ptolemy. He invented the coordinate system long before Descartes (1596-1650). He also investigated fractional powers and determined that the distance a freely falling body travels (x) is proportional to the square of the time (t) it has been traveling, viz., x = ½ g t², where g is the acceleration due to gravity. He used a slightly different notation, however, beginning in his first page of Algorismus proportionum:

—Cajori's A History of Mathematical Notation, Vol. 1 pgs. 91-93

From the excellent introductory physics textbook Physics for Realists (available here) by the M.I.T. and Princeton physicist Dr. Anthony Rizzi, founder of the Institute for Advanced Physics:

Nicole Oresme (o'rem) was born c. 1320 AD in Normandy, France, and died in 1382. He was, among other things, a mathematician, a physicist and a priest (made bishop of liseaux, France, in 1377). His major mathematical work is "Tractatus de Difformitatum." Among his accomplishments are the use of rectangular coordinates and graphing of the intensity of a quality then called latitudo (say, temperature of a rod), against a length then called longitudo (e.g., distance along the same rod), on such a rectangular coordinate system. He also discovered that speed versus time graphs can be constructed. Further, he investigated, in his own notation, fractional powers, saying 4^3/2 = 8.

In dynamics, he shows, following Jean Buridan [...], that the movement of the Earth is consistent with immediate experience, though it does not seem so at first. And, he points out that the movement of the Earth, not the geocentric hyothesis, is, indeed, the simpler one. These arguments we be employed by his successors, including Copernicus and Galileo.

He also made an argument for an international dateline. His argument fundamentally rests on noticing that only the relative motion of the earth and sun defines a conventional day (i.e., based on the rising and setting of the sun for a given observer). The principle can be understood by noting that if one moved fast enough to say "under" the sun, one would never experience a single conventional day. The roundness of the earth, which is also needed in the argument, was commonly assumed in the Middle Ages.

He proved, using graphical methods, the mean speed theorem [...] which Galileo imported into his work without reference. He determined the distance = ½ acceleration time² law for uniformly accelerated motion that was later applied by Fr. Dominic De Soto (1494-1560 [...]) to free falling objects.

—PFR pg. 48

—"Nicole Oresme" in the MacTutor History of Mathematics archive: A page from Oresme's Tractatus de latitudinibus formarum (1505 reprint)

Could not have Oresme, being a theologian, progressed science and mathematics more had he not seemingly wasted his time becoming a Master of Theology at the University of Paris? The answer is no. Fr. Benedict Ashley, O.P.—a key contributer and reviewer of Physics for Realists—explains that philosophy, which includes mathematics and science, is a handmaiden of theology:

—Benedict Ashley, O.P.

True philosophy, the perennial philosophy of St. Thomas Aquinas, supports true theology, both of which demand a pursuit of truth. Mentioning the horrible state of the philosophy that Pope Pius XII condemned in Humani Generis, "Nouvelle Théologie" (New Theology)—which is opposed to true, scientific theology and definitely merits the stereotypes of theology being an irrational, unscientific discipline, proceeding haphazardly from from shaky first-principles and jumping to non sequitur conclusions, ignoring that parvus error in principio magnus est in fine ("a small error in principle is a big error in conclusion"), and ultimately upholding the relativism of truth, that it is based on the changing state of man—the great 20th century Thomistic philosopher Fr. Reginald Garrigou-Lagrange, O.P., wrote that

no new definition of truth is offered in the new definition of theology: “Theology is no more than a spirituality or religious experience which found its intellectual expression.” And so follow assertions such as: “If theology can help us to understand spirituality, spirituality will, in the best of cases, cause our theological categories to burst, and we shall be obliged to formulate different types of theology…For each great spirituality corresponded to a great theology.” Does this mean that two theologies can be true, even if their main theses are contradictory and opposite? The answer will be no if one keeps to the traditional definition of truth. The answer will be yes if one adopts the new definition of truth, conceived not in relation to being and to immutable laws, but relative to different religious experiences. These definitions seek only to reconcile us to modernism.

It should be remembered that on December 1, 1924, the Holy Office condemned 12 propositions taken from the philosophy of action, among which was number 5, or the new definition of truth: “Truth is not found in any particular act of the intellect wherein conformity with the object would be had, as the Scholastics say, but rather truth is always in a state of becoming, and consists in a progressive alignment of the understanding with life, indeed a certain perpetual process, by which the intellect strives to develop and explain that which experience presents or action requires: by which principle, moreover, as in all progression, nothing is ever determined or fixed.” The last of these condemned propositions is: “Even after Faith has been received, man ought not to rest in the dogmas of religion, and hold fast to them fixedly and immovably, but always solicitous to remain moving ahead toward a deeper truth and even evolving into new notions, and even correcting that which he believes.”

Many, who did not heed these warnings, have now reverted to these errors.

—“Where is the New Theology Leading Us?” by Fr. Reginald Garrigou-Lagrange, O.P.

Oresme did not fall into these errors. He studied true theology because he did true science.

Fr. Coyne & Dawkins

Nota bene: The Church does not necessarily endorse all Fr. Coyne's opinions, and he is not necessarily speaking infallibly.

A related speech's transcript.

Vatican Astronomer on "Intelligent Design Theory"

Fr. Coyne's presentation and question-and-answer session at the American Association for the Advancement of Science (AAAS)'s "Dialogue on Science, Ethics, and Religion" lecture. Can modern science truly do without God, as he says? Are true philosophy and theology necessary for modern science to be true science, i.e., to search for absolute truth?

Part 1 and Part 2

Nota bene: The Church does not necessarily endorse all Fr. Coyne's opinions, and he is not necessarily speaking infallibly.

Current Methodologies of Physics & Astronomy

Regarding the correct division and method of the sciences, this lecture, given at the American Astronomical Society (AAS)'s January 2008 meeting in Austin, Texas, highlights the current state of the methodologies in two branches of physical science (specif. scientia media), astronomy and physics.

[Duhem] seems to regard [the non-falsifiability theses, which "is that 'if the predicted phenomenon is not produced, not only is the questioned proposition put into doubt, but also the whole theoretical scaffolding used by the physicist' (Duhem 185),"] as an obvious corollary of another thesis, which could be called the non-separability thesis, that the physicist can never submit an isolated hypothesis to experimental test: “To seek to separate each of the hypotheses of theoretical physics from the other assumptions upon which this science rests, in order to subject it in isolation to the control of observation, is to pursue a chimera” (Duhem 199-200).

—Roger Ariew, "Pierre Duhem"

Modern scientists do indeed consider issues pertaining to this, else their science's arguments risk being circular.

Creation Mingled with Works of Nature? No.

My responses are red and Dr. Tkacz's are green.

Hello Prof. Tkacz,

Thank you for the excellent article "Thomas Aquinas vs. The Intelligent Designers." [...] I understand the flaws of ID [Intelligent Design] as it is presently conceived by people like Behe, but I am confused when you wrote about the hippo:

Consider another example: a large quadrapedic mammal, such as a hippopotamus, gives live birth to its young. Why? Well, we could answer this by saying that “God does it.” Yet, this could only mean that God created hippopotamuses—indeed the mammalian order, the whole animal kingdom, and all of nature—such that these animals have the morphology, genetic make-up, etc. that are the causes of their giving live birth. [So God is a deist's God who only sets up the natural conditions and leaves them alone?] It cannot be that God “reaches into” the normal operations of hippopotamuses to cause them to give live birth. [Why not? Is He not involved at all past some level?] Were one to think that “God does it” must mean that God intervenes in nature in this way, one would be guilty of the Cosmogonical Fallacy. [Or I just wouldn't be a deist?]

Isn't this an issue of proximate versus remote causes? A proximate cause (what biology would study) of a hippo giving birth is the female hippo, and a remote cause (what theology would study) is God, so both the Thomists and ID folk are right; to me it just seems to be an issue of epistemology. What exactly are you trying to know: how the hippo's existence is due ultimately to God or how it's due to its hippo nature—its "hipponess"?

From St. Thomas's Summa Contra Gentiles:

Accordingly if we be asked the wherefore of a particular natural effect, we can assign the reason to some proximate cause: provided, however, that we refer all things to the divine will as their first cause. Thus if it be asked: Why was the wood heated at the presence of fire? we reply: Because to heat is fire's natural action: and this, because heat is its proper accident: and this results from its proper form: and so on until we come to the divine will. Hence if we reply to the question Why was the wood made hot? by saying: Because God so willed: we shall answer rightly, if we intend to trace the question back to its first cause, but incorrectly if we intend to exclude all other causes.

—Summa Contra Gentiles, lib. 3 cap. 97 n. 17

His response:

Thank you for your message. I understand your question about my “hippo” example. I certainly do not intend to claim that St. Thomas is a deist. He most certainly is not—indeed, he would consider deism heretical because it denies God’s omnipresence and immanence to creation. The point of my example is that God’s creation is not a substitute for natural causes. Any natural thing or process has natural causes of the kinds that we discover in our scientific research. At the same time, any natural thing or process requires God’s immediate act of creation to keep it in existence. Both are true at once. This is St. Thomas’ view. So, the hippopotamus is created by God in the sense that it is immediately caused to exist and is kept in existence by God. What God causes here, however, is the animal as caused by its natural causes. So, divine creation is not a substitute for natural causes, nor is it like a natural cause. It is a unique kind of cause in a class of its own.

As you know, deism is the view that creation is some primordial cause. Thomas rejects this view. He holds that creation is not an event that took place at some primordial time. [But some creation could; it's not necessary, though, right? No. This is the point St. Thomas is making: it is impossible that God creates the way human beings and other natural things create. God’s act of creation does not take place in time and it must be immediately present to the thing being created. Thus, it cannot be that God created way back when. God creates here and now at every here and now of the universe, whether that here and now is, from our temporal point of view, a present here and now or a future here and now or a past here and now. Remember: According to St. Thomas, creation is not an event, but a relationship of absolute dependence of creature on creator. I think you misunderstood me; I was implying that creatio ex nihilo is possible at a certain moment in time for some creatures, such as the soul of a newly conceived human, or is that false? I think you would say it just appears that way form our temporally-bound viewpoint? I see. You are right and St. Thomas would agree, but he would point out that the creation of the individual human soul must be true in a way that does not commit the Cosmological Fallacy (the confusion of natural cause with God’s divine agency). Because God is absolutely immanent to all of nature, then he is omnipresent with his power to the conception of the individual human being making it be. Basically, this is no different from God’s being present to any other new natural event. But there is a sense in which the creation of the individual human soul is different from God’s general immanence: the human soul is the image of God in a more perfect way than is any other natural thing or process. God’s creation of the individual rational human soul, then, is God sharing his own divine essence in a particular manner that is different from his creation of other natural things. We often tend to think of this in an event manner, but this is, as you say, just part of our “temporally-bound viewpoint.”] Rather, creation is the radical dependence of everything on God for its existence. So, creation is not an event at all, but a relationship of absolute dependence. As in the text you cite from SCG, St. Thomas often uses the term “first cause” to refer to God’s act of creation. He does not here mean “first” in the sense of first in time, but in the sense of absolutely fundamental. God’s actions do not occur in time, they are eternal or to put it another way from our point of view, God is always making us be, he is always creating us. Were God to crease being our creator, we would pass out of existence. So, there is no deism here.

The problem with ID theorists such as Dr. Behe is that he confuses divine causation with natural causation. [As I understand it, he thinks that biology, e.g., can understand the supernatural's effect on the natural order? I get the feeling that he considers life to be a miracle of the first degree:

The highest degree in miracles comprises those works wherein something is done by God, that nature can never do: for instance, that two bodies occupy the same place, that the sun recede or stand still, that the sea be divided and make way to passers by. Among these there is a certain order: for the greater the work done by God, and the further it is removed from the capability of nature, the greater the miracle: thus it is a greater miracle that the sun recede, than that the waters be divided.

—Summa Contra Gentiles, lib. 3 cap. 101

How does science know when it's dealing with the natural or supernatural if miracles do indeed happen? Miracles is something I have never seen discussed in the ID debate. Maybe they have been, and I'm just unaware. According to St. Thomas, a miracle is not just a wonderful event, but a revelation of God—it is one of the ways in which God tells us about himself. Miracles must meet three criteria: [1] they must be unusual events out of the regular order of nature (this rules out Behe’s notion that “irreducible complexity” is a miracle), [2] they must draw attention of human beings and evoke wonder in them, and [3] they must have theological significance (that is, they must reveal to us something that is part of the deposit of faith). So, the raising of Lazarus is a miracle because [1] it is out of the regular order of nature (this is not the usual way in which nature creates life), [2] it evokes wonder in human witnesses, and [3] it is a type of the resurrection of Christ.] He treats God’s agency as a sort of super-powerful natural cause. [Yes, definitely] From the Thomistic perspective this is incorrect, for it implies that God requires a material potentiality in order to create, as do natural causes. God’s agency is not just a more powerful sort of cause, but it is totally unlike natural causes. God does not actualize a potentiality when he creates, but he simple is the reason why things are. How can this be? Well, we would have to be God to understand how something can be caused to be without the actualization of a potentiality, but then we are not God. God is the transcendent creator and his very transcendence means that we cannot comprehend how he does what he does. But we can distinguish God’s action from the actions of created things and, therefore, know that God is the transcendent creator. This is important, because if we are not careful, we can be slip into error in our thinking about who God is. The natural universe is intelligible and scientific research is the means by which we know it. God made it that way. But the fact that we can explain natural things in terms of natural causes does not rule out their being created by God. In fact, the only way to explain why there are natural things and their natural causes at all is to understand that they radically depend on God for their existence.

M. Tkacz

Dr. Michael W. Tkacz
Associate Professor of Philosophy
Gonzaga University

I think every ID advocate correctly understands that God and only God creates ex nihilo ("out of nothing"), but they do not understand that God does not override nature. Thus, every ID advocate should read this article in St. Thomas Aquinas's Summa Theologica: "Whether creation [i.e., creatio ex nihilo] is mingled with works of nature and art?" While ID advocates would say "Yes," St. Thomas says "No." He says that "in the works of nature creation does not enter, but is presupposed to the work of nature." This is fully consistent with God simply letting things be. He does not say, e.g., "I create light!" but "Let there be light." (Genesis 1:3). Nor does He say "I bring forth the living creature!" but "Let the earth bring forth the living creature." (Genesis 1:24).

Philosophically Speaking

Assenting to Things Above Natural Reason

Intellectual assent to things that are above human reason is not contrary to human reason nor to science.

Chapter 6: THAT IT IS NOT A MARK OF LEVITY TO ASSENT TO THE THINGS THAT ARE OF FAITH, ALTHOUGH THEY ARE ABOVE REASON

Now those who believe this truth, of which reason affords a proof, believe not lightly, as though following foolish fables (2 Pet. i. 16). For divine Wisdom Himself, Who knows all things most fully, deigned to reveal to man the secrets of God's wisdom: and by suitable arguments proves His presence, and the truth of His doctrine and inspiration, by performing works surpassing the capability of the whole of nature, namely, the wondrous healing of the sick, the raising of the dead to life, a marvellous control over the heavenly bodies, and what excites yet more wonder, the inspiration of human minds, so that unlettered and simple persons are filled with the Holy Ghost, and in one instant are endowed with the most sublime wisdom and eloquence. And after considering these arguments, convinced by the strength of the proof, and not by the force of arms, nor by the promise of delights, but—and this is the greatest marvel of all—amidst the tyranny of persecutions, a countless crowd of not only simple but also of the wisest men, embraced the Christian faith, which inculcates things surpassing all human understanding, curbs the pleasures of the flesh, and teaches contempt of all worldly things. That the minds of mortal beings should assent to such things, is both the greatest of miracles, and the evident work of divine inspiration, seeing that they despise visible things and desire only those that are invisible. And that this happened not suddenly nor by chance, but by the disposition of God, is shown by the fact that God foretold that He would do so by the manifold oracles of the prophets, whose books we hold in veneration as bearing witness to our faith. This particular kind of proof is alluded to in the words of Heb. ii. 3, 4: Which, namely the salvation of mankind, having begun to be declared by the Lord, was confirmed with us by them that heard Him, God also bearing witness by signs and wonders, and divers. . . distributions of the Holy Ghost.

Now such a wondrous conversion of the world to the Christian faith is a most indubitable proof that such signs did take place, so that there is no need to repeat them, seeing that there is evidence of them in their result. For it would be the most wondrous sign of all if without any wondrous signs the world were persuaded by simple and lowly men to believe things so arduous, to accomplish things so difficult, and to hope for things so sublime. Although God ceases not even in our time to work miracles through His saints in confirmation of the faith.

On the other hand those who introduced the errors of the sects proceeded in contrary fashion, as instanced by Mohammed, who enticed peoples with the promise of carnal pleasures, to the desire of which the concupiscence of the flesh instigates. He also delivered commandments in keeping with his promises, by giving the reins to carnal pleasure, wherein it is easy for carnal men to obey: and the lessons of truth which he inculcated were only such as can be easily known to any man of average wisdom by his natural powers: yea rather the truths which he taught were mingled by him with many fables and most false doctrines. Nor did he add any signs of supernatural agency, which alone are a fitting witness to divine inspiration, since a visible work that can be from God alone, proves the teacher of truth to be invisibly inspired: but he asserted that he was sent in the power of arms, a sign that is not lacking even to robbers and tyrants. Again, those who believed in him from the outset were not wise men practised in things divine and human, but beastlike men who dwelt in the wilds, utterly ignorant of all divine teaching; and it was by a multitude of such men and the force of arms that he compelled others to submit to his law.

Lastly, no divine oracles of prophets in a previous age bore witness to him; rather did he corrupt almost all the teaching of the Old and New Testaments by a narrative replete with fables, as one may see by a perusal of his law. Hence by a cunning device, he did not commit the reading of the Old and New Testament Books to his followers, lest he should thereby be convicted of falsehood. Thus it is evident that those who believe his words believe lightly.

—St. Thomas Aquinas's Summa Contra Gentiles, lib. 1 cap. 6

∃ Two Separate Laws?

Section a1.4 of the top-selling book of Islamic Sharia law says:

a1.4: The measure of good and bad [...] is the Sacred Law, not reason.

This is totalitarian, diabolic, and irrational, "For all the gods of the Gentiles are devils: but the Lord made the heavens." (Ps. 95:5). Catholic Christians believe that the natural law,

written in [even the Gentiles'] hearts,

—Romans 2:16

"is a participation in us of the eternal law," of the Divine law (Summa Theologica Iª-IIae q. 91 a. 4 arg. 1). A gloss on this verse says: "'written in their hearts,' as to the existence of a God [and that] their reason tells them that many sins are unlawful." Moral law is founded on reason and perfected by faith; grace builds on nature. Muslims apparently think that Allah and Sharia law is so far above human reason that it can even contradict it. It is no wonder Sharia law also condemns as

a7.2 Unlawful knowledge [...] (2) philosophy [...] (5) the science of the materialists [...] (6) and anything that is a means to create doubts (n: in eternal truths).

Of course truth to Muslims must means whatever Allah's messengers say, a sort of relativism of truth. It is within this context of faith and reason that Pope Benedict so skillfully gave his Regensburg lecture in 2006 which affirmed that the Trinity, Λόγος, is the God of reason.