Hume vs. Aquinas on Transubstantiation

Benedict Ashley, O.P., in his book The Way toward Wisdom (p. 511 n. 53), cites Hume's claim, which he borrowed from Dr. Tillotson, that the transubstantiation, "since it denies the evidence of the senses on which all certitude rests," "leads to skepticism:"

I flatter myself, that I have discovered an argument of a like nature, which, if just, will, with the wise and learned, be an everlasting check to all kinds of superstitious delusion, and consequently, will be useful as long as the world endures.

[...]

Suppose, for instance, that the fact, which the testimony endeavours to establish, partakes of the extraordinary and the marvellous; in that case, the evidence, resulting from the testimony, admits of a diminution, greater or less, in proportion as the fact is more or less unusual. The reason why we place any credit in witnesses and historians, is not derived from any connexion, which we perceive a priori, between testimony and reality, but because we are accustomed to find a conformity between them. But when the fact attested is such a one as has seldom fallen under our observation, here is a contest of two opposite experiences; of which the one destroys the other, as far as its force goes, and the superior can only operate on the mind by the force, which remains.

—David Hume's Enquiry of Human Understanding, sec. 10 "On Miracles" part 1

Benedict Ashley, O.P., responds:

Yet we experience that very unusual events do in fact occur! Why must we, then, always doubt the testimony of others about such events? Sense experiences are signs to be intellectually interpreted always in their contexts. The proper accidents of bread and wine naturally signify these substances, but for the Catholic faith the context of the Eucharist established by God permits the appearance of bread and wine to signify without deception [Summa Theologiæ, IIIª q. 75 a. 5 arg. 2 et ad 2] Christ's body and blood. Although this is not strictly a "miracle" (since the change is not evident to our senses and hence is extremely improbable as regard natural reason), as Aquinas shows [Summa Theologiæ, IIIª q. 75 a. 5 arg. 3 et ad 3], it is not impossible; and if the Catholic faith is credible, as apologetic seeks to show, reason demands that it be believed on the testimony of the Church. Similarly, the context of the Bible as read in the tradition of the Church (which one would suppose Tillotson accepted) permits it to signify the mind of God, not merely the intent of its human authors. Hume's argument amount to declaring that he is determined to interpret his experiences a way that will not disturb his "common sense" habits; but life is full of uncomfortable events.

The above-mentioned St. Thomas Aquinas Summa Theologiæ quotes are:

Objection 2. Further, there ought not to be any deception in a sacrament of truth. But we judge of substance by accidents. It seems, then, that human judgment is deceived, if, while the accidents remain, the substance of the bread does not. Consequently this is unbecoming to this sacrament.

Objection 3. Further, although our faith is not subject to reason, still it is not contrary to reason, but above it, as was said in the beginning of this work (Summa Theologiæ, Iª q. 1 a. 6 ad 2 et a. 8). But our reason has its origin in the senses. Therefore our faith ought not to be contrary to the senses, as it is when sense judges that to be bread which faith believes to be the substance of Christ's body. Therefore it is not befitting this sacrament for the accidents of bread to remain subject to the senses, and for the substance of bread not to remain.

[...]

Reply to Objection 2 and 3. There is no deception in this sacrament; for the accidents which are discerned by the senses are truly present. But the intellect, whose proper object is substance as is said in De Anima iii, is preserved by faith from deception. And this serves as answer to the third argument; because faith is not contrary to the senses, but concerns things to which sense does not reach.

The Truth of Science for Justice and Peace

Monsignor Marcelo Sánchez Sorondo, who graduated from the Angelicum magna cum laude and is chancellor of both the Pontifical Academy of the Sciences and the Pontifical Academy of the Social Sciences, gave the keynote speech for Arizona State University (ASU)'s Consortium of Science, Policy, & Outcomes entitled "The Truth of Science for Justice and Peace" on May 18, 2010. It included many references to St. Thomas Aquinas. Here is an excerpt of the interview afterwards:

The transcript and full presentation slides:

And a commentary by the ASU philosopher Farzad Mahootian:

Other enlightening reactions to the Monsignor's speech include those of Heather Douglas, Associate Professor, Philosophy, University of Tennessee and Carl Mitcham, Professor, Liberal Arts and International Studies, Colorado School of Mines.

Heather Douglas's article quotes this by St. Bernard of Clairvoux, which the Monsignor quoted in his speech:

“There are people who only wish to know for the sake of knowing: this is base curiosity. Others wish to know in order that they themselves may be known: this is shameful vanity, and such people cannot escape the mockery of the satirical poet who said about their likes: ‘For you, knowing is nothing unless someone else knows that you know.’ Then there are those who acquire knowledge in order to re-sell it, and for example to make money or gain honours from it: their motive is distasteful. But some wish to know in order to edify: this is charity. Others in order to be edified: this is wisdom. Only those who belong to these last two categories do not misuse knowledge, since they only seek to understand in order to do good.” (Quoted on pp. 5-6, from St. Bernardus, Sermo XXXVI in Cantica, PL, CLXXXIII, 968.)

Japan Earthquake ≈ Tsar Bomba's Energy

According to the United States Geological Survey (USGS)'s energy and broadband solution of the recent earthquake near the coast of Honshu, Japan, it has radiated an estimated 3.0×10¹⁷ Joules of energy. Fat Man, the atomic bomb dropped on Nagasaki during World War II, was 88 TJ (88 terajoules = 8.8×10¹³ Joules). So this earthquake was about 2,000 times more energetic. The largest nuclear bomb ever detonated was the Tsar Bomba, detonated on October 30, 1961, in Russia. It released 210 petajoules = 2.1×10¹⁷ Joules of energy, roughly 70% what this Japan earthquake released.

Does one need any more proof for original sin?

Despite the vision and farseeing wisdom of our wartime heads of state, the physicists have felt the peculiarly intimate responsibility for suggesting, for supporting, and in the end, in large measure, for achieving the realization of atomic weapons. Nor can we forget that these weapons as they were in fact used dramatized so mercilessly the inhumanity and evil of modern war. In some sort of crude sense which no vulgarity, no humor, no overstatement can quite extinguish, the physicists have known sin; and this is a knowledge which they cannot lose.

—J. Robert Oppenheimer, Physics in the Contemporary World (1948) pg. 66

OnlineSchools.org presents Japan One Year Later

St. Thomas Aquinas

St. Thomas Aquinas

Historical Method in Physics

The following email exchange with a professor in the State of Israel who studies physics education makes me really wonder if there is something flawed with the way physics is taught today (cf. "Why No 'New Einstein'?"). Out of all disciplines with PhDs, graduate students are obtaining fewer and fewer PhDs in physics than in any other field and more and more in psychology. There must be a reason for this. I wrote:

Dr. Galili,

I was glad to see that you do research following the admonition of Pierre Duhem in your "HISTORY OF PHYSICS AS A TOOL FOR TEACHING:"

The legitimate, sure and fruitful method of preparing a student to receive a physical hypothesis is the historical method. To retrace the transformations through which the empirical matter accrued while the theoretical form was first sketched; to describe the long collaboration by means of which common sense and deductive logic analyzed this matter and modeled that form until one was exactly adapted to the other: that is the best way, surely even the only way, to give to those studying physics a correct and clear view of the very complex and living organization of this science.

(And apparently Mach's "textbooks in mechanics and optics that adopted this approach remain to be valuable and interesting teaching resources.")

Your studies seem to focus on physics in secondary education. Has the historical method been applied in undergraduate and graduate physics programs? Do you do research on this?

I am a graduate physics student, and graduate-level physics seems mostly taught to a certain type of learner, i.e., to one who "learns by doing," who learns solely by solving written problems. I am from the United States, and this seems to be the predominant method most of the physics departments employ in training their students. Are there graduate programs—besides those HPS departments—that do things differently, who maybe even implement the historical method?

Thank you

(The quote is from Duhem's Aim and Structure of Physical Theory pg. 268.) He responded:

Thank you for your message and interest to my work.
The subject you write about actually presents a sensitive discourse in physics teaching. Nothing is harder than to cause a conceptual change to physics educators,and researchers especially. Currently, the prevailing mode of teaching adopts profession oriented pragmatic approach which is very instrumentalist although widely uses the rhetoric of conceptual understanding. Within this understanding problem solving and modeling occupy the central role. I hold a different perspective oriented to physics education (different from physics as a profession). Such education aims at learning physics as a special culture people create in making sense of nature and natural phenomenon.
Not to cause people much negative emotions and resistance, I prefer to investigate secondary school students. However, I am convinced that my materials are applicable and perhaps even more effective for university students who deal with these the same subjects. They all need good conceptual bases in the physics they learn. Complex formalism does not replace understanding fundamentals. Such is, for example the issue of weight definition. Although included in middle school physics curriculum, it presents a great controversy in university physics textbooks of physics.
Best regards,
igal

Where did this "profession oriented pragmatic approach which is very instrumentalist although widely uses the rhetoric of conceptual understanding" originate? Perhaps the pragmatism originates from the progressive education movement of John Dewey (cf. these articles by Fr. Hardon, S.J., on Dewey: Part 1, 2, and 3)? Duhem's philosophy of science is considered instrumentalist, yet he would agree that "modeling," which he criticized the English physicists like Maxwell for advocating as physical explanations, should not "occupy the central role." And "the rhetoric of conceptual understanding?" Rhetoric? Would all physicists agree what they do is rhetoric? Feynman might have, because he said he won the Nobel prize for "sweeping [e.g., inconsistencies] under the rug." Perhaps all the psychology PhDs will finally get it across to physicists what it actually means to know and to understand, assuming an epistemology grounded on sound philosophy,

The Magi were astronomers. Really.

The three Magi really were astronomers. This is clever depiction of them from the Vatican Observatory's homepage:

River Forest & Æterni Patris

From Edward Feser's "The Thomistic Tradition (part 1)" (vide also part 2):

This approach emphasizes the Aristotelian foundations of Aquinas’s philosophy, and in particular the idea that the construction of a sound metaphysics must be preceded by a sound understanding of natural science, as interpreted in light of an Aristotelian philosophy of nature. Accordingly, it is keen to show that modern physical science can and should be given such an interpretation. Charles De Koninck (1906-1965), James A. Weisheipl (1923-1984), William A. Wallace, and Benedict Ashley are among its representatives. It is sometimes called “Laval Thomism” after the University of Laval in Quebec [which produced this brilliant thesis: Thomism and Mathematical Physics], where De Koninck was a professor. The alternative label “River Forest Thomism” derives from a suburb of Chicago, the location of the Albertus Magnus Lyceum for Natural Science, whose members are associated with this approach. It is also sometimes called “Aristotelian Thomism” (to highlight its contrast with Gilson’s brand of existential Thomism) though since Neo-Scholastic Thomism also emphasizes Aquinas’s continuity with Aristotle, this label seems a bit too proprietary. (There are writers, like the contemporary Thomist Ralph McInerny, who exhibit both Neo-Scholastic and Laval/River Forest influences, and the approaches are not necessarily incompatible.)

See also:

• River Forest Thomism
• Scholasticism in Empiriological Sciences
• The Modeling of Nature by William Wallace, O.P.
• The Way toward Wisdom or "The River Forest School and the Philosophy of Nature Today" by Benedict Ashley, O.P.
• The Writings of Charles de Koninck (Volume 1) by Charles de Koninck

E.g., Heisenberg recognized in his Physics and Philosophy that the probability wave concept in quantum mechanics "was a quantitative version of the concept of 'potentia' in Aristotelian philosophy" (p. 41) and that the "concept of the soul for instance in the philosophy of Thomas Aquinas was more natural and less forced than the Cartesian concept of 'res cogitans,' even if we are convinced that the laws of physics and chemistry are strictly valid in living organisms." (p. 80). Pope Leo XIII, who was trained in the natural sciences as well as in theology, wrote in 1879 that the study of the natural sciences is epistemologically prior to that of theology, viz., that knowledge of immaterial things for us comes after that of material things:

30. And here it is well to note that our philosophy can only by the grossest injustice be accused of being opposed to the advance and development of natural science. For, when the Scholastics, following the opinion of the holy Fathers, always held in anthropology that the human intelligence is only led to the knowledge of things without body and matter by things sensible, they well understood that nothing was of greater use to the philosopher than diligently to search into the mysteries of nature and to be earnest and constant in the study of physical things. And this they confirmed by their own example; for St. Thomas, Blessed Albertus Magnus, and other leaders of the Scholastics were never so wholly rapt in the study of philosophy as not to give large attention to the knowledge of natural things; and, indeed, the number of their sayings and writings on these subjects, which recent professors approve of and admit to harmonize with truth, is by no means small. Moreover, in this very age many illustrious professors of the physical sciences openly testify that between certain and accepted conclusions of modern physics and the philosophic principles of the schools there is no conflict worthy of the name.

—Pope Leo XIII's Æterni Patris

Mathematics: Its Importance and Limitations

Mathematics is most co-natural to man and it is also the most exact science according to St. Thomas Aquinas, says Bernard I. Mullahy in his excellent thesis Thomism and Mathematical Physics. Armand Maurer on pg. xxxv of his translation of St. Thomas Aquinas's Division and methods of the sciences, a commentary on Boethius's De Trinitate questions V and VI, says that

St. Thomas also attributes a major role to reasoning in mathematics. In this respect it is like natural philosophy. The difference in their methods lies in the causes employed in reasoning. Mathematical demonstrations begin with definitions and principles, from which conclusions are deduced by way of formal causality. For example, a certain property of the triangle is shown to follow from its very definition. Unlike natural philosophy, mathematics does not demonstrate through final or efficient causes.

Fr. McCool, S.J., wrote in his book on the history of 20th century Thomism that (pg. 154-155):

A new edition of St. Thomas' In Librum Boethii de Trinitate, Questiones quinta et sexta, published in 1948, led to a major revision of the accepted understanding of St. Thomas' theory of abstraction [which that of Boethius inspired]. Apart from the abstractio totius, abstraction of a sensible whole from its particulars required for any form of conceptual thought, the only other type of abstraction proposed by St. Thomas confines itself to the level of mathematics. This is an abstractio formae, the mind's separation of the form of quantity from the rest of the sensible whole which the mind disregards in mathematics.

Thus we can see that medieval philosophers recognized the great importance and certainty of mathematics. Yet, according to Armand Maurer,

St. Thomas saw that there is a particular temptation to single out the mathematical method for this role [of being a common method for all the sciences, as Descartes wished], since it is the most exact and certain. But he warns against this, insisting on the specificity of method in each of the sciences [natural philosophy (physics in the broad sense), mathematics, and metaphysics; modern physics is a natural philosophy / mathematics hybrid, a scientia media or "middle science"].

St. Thomas warns about this in In II Meta. lect. 5, n. 335-337, which says, commenting on Aristotle's answer regarding "The Method to Be Followed in the Search for Truth:"

ARISTOTLE’S TEXT Chapter 3: 994b 32-995a 20

171. The way in which people are affected by what they hear depends upon the things to which they are accustomed; for it is in terms of such things that we judge statements to be true, and anything over and above these does not seem similar but less intelligible and more remote. For it is the things to which we are accustomed that are better known.

172. The great force which custom has is shown by the laws, in which legendary and childish elements prevail over our knowledge of them, because of custom.

173. Now some men will not accept what a speaker says unless he speaks in mathematical terms; and others, unless he gives examples; while others expect him to quote a poet as an authority. Again, some want everything stated with certitude, while others find certitude annoying, either because they are incapable of comprehending anything, or because they consider exact inquiry to be quibbling; for there is some similarity. Hence it seems to some men that, just as liberality is lacking in the matter of a fee for a banquet, so also is it lacking in arguments.

174. For this reason one must be trained how to meet every kind of argument; and it is absurd to search simultaneously for knowledge and for the method of acquiring it; for neither of these is easily attained.

175. But the exactness of mathematics is not to be expected in all cases, but only in those which have no matter. This is why its method is not that of natural philosophy; for perhaps the whole of nature contains matter. Hence we must first investigate what nature is; for in this way it will become evident what the things are with which natural philosophy deals, and whether it belongs to one science or to several to consider the causes and principles of things.

that

[St. Thomas's] COMMENTARY

335. For this reason one must be trained (174).

He exposes the proper method of investigating the truth. Concerning this he does two things. First (335), he shows how a man can discover the proper method of investigating the truth. Second (336), he explains that the method which is absolutely the best should not be demanded in all matters (“But the exactness of mathematics”) .

He says, first, that since different men use different methods in the search for truth, one must be trained in the method which the particular sciences must use to investigate their subject. And since it is not easy for a man to undertake two things at once (indeed, so long as he tries to do both he can succeed in neither), it is absurd for a man to try to acquire a science and at the same time to acquire the method proper to that science. This is why a man should learn logic before any of the other sciences, because logic considers the general method of procedure in all the other sciences. Moreover, the method appropriate to the particular sciences should be considered at the beginning of these sciences.

336. But the exactness of mathematics (175).

He shows that the method which is absolutely the best should not be demanded in all the sciences. He says that the “exactness,” i.e., the careful and certain demonstrations, found in mathematics should not be demanded in the case of all things of which we have science, but only in the case of those things which have no matter; for things that have matter are subject to motion and change, and therefore in their case complete certitude cannot be had. For in the case of these things we do not look for what exists always and of necessity, but only for what exists in the majority of cases.

Now immaterial things are most certain by their very nature because they are unchangeable, although they are not certain to us because our intellectual power is weak, as was stated above (279). The separate substances are things of this kind. But while the things with which mathematics deals are abstracted from matter, they do not surpass our understanding; and therefore in their case most certain reasoning is demanded.

Again, because the whole of nature involves matter, this method of most certain reasoning does not belong to natural philosophy. However, he says “perhaps” because of the celestial bodies, since they do not have matter in the same sense that lower bodies do.

337. Now since this method of most certain reasoning is not the method proper to natural science, therefore in order to know which method is proper to that science we must investigate first what nature is; for in this way we will discover the things which natural philosophy studies. Further, we must investigate “whether it belongs to one science,” i.e., to natural philosophy, or to several sciences, to consider all causes and principles; for in this way we will be able to learn which method of demonstration is proper to natural philosophy. He deals with this method in Book II of the Physics, as is obvious to anyone who examines it carefully.

Heisenberg: "concept of the soul [...] more natural and less forced"

Heisenberg said in his Physics and Philosophy that the probability wave concept in quantum mechanics "was a quantitative version of the concept of 'potentia' in Aristotelian philosophy" (p. 41) and that the "concept of the soul for instance in the philosophy of Thomas Aquinas was more natural and less forced than the Cartesian concept of 'res cogitans,' even if we are convinced that the laws of physics and chemistry are strictly valid in living organisms." (p. 80).

Crisis of Faith in Science

The Crisis of the Faith in Science

The resistance of creation to its manipulation by men has become a new factor in the intellectual situation in the last decade. It is impossible to evade the question of the limits of science and of the criteria it must follow. The change in the way in which the case of Galileo is evaluated seems to me characteristic of the change of climate. This event, to which little attention was paid in the seventeenth century, was elevated in the following century to nothing less than the my of the Enlightenment: Galileo appears as the victim of the medieval obscurantism in which the Church persists. Good and evil stand in a distinct confrontation: on the one side, we find the Inquisition as the power of superstition, as the opponent of freedom and knowledge; on the other side stand the natural sciences, represented by Galileo, as the power of progress and of the liberation of man from the fetters of ignorance that kept him powerless vis-à-vis nature. The star of the modern period arises over the darkness of the Middle Ages.

Strangely enough, Ernst Bloch with his romantic Marxism was one of the first to oppose this myth openly and to offer a new interpretation of the events. For him, the heliocentric world-system, just like the geocentric system, rests on unprovable presuppositions, including above all the supposition of motionless space, which has since been shattered by the theory of relativity. He states:

Consequently, since an empty motionless space no longer exists, no movement toward it occurs, but merely a relative movement of bodies toward one another, the determination of which depends on the choice made of the body that is to be taken to be at rest. Thus, if it were not for the fact that the complexity of the calculations involved makes this appear infeasible, the earth could continue to be taken as stable and the sun as moving. [E. Bloch, Das Prinzip Hoffnung (frankfurt am Main, 1959), 920]

According to this view, the advantage of the heliocentric system over the geocentric does not consist in a greater degree of objective truth but merely in an easier calculability for us. Up to this point Bloch is doing no more than expressing the insight of the modern natural sciences; but the conclusion he derives from this now is astonishing:

Since the relativity of the motion is beyond doubt, an older man-centered Christian reference system does not indeed have the right to involve itself in the astronomical calculations and their heliocentric simplification; but it does have its own methodological right to hold fast to the earth as far as the question of the importance of mass is concerned and to impart an ordered structure to the world around what happens and has happened on the earth. [Bloch, 920f.]

The two methodological spheres are clearly distinguished from one another here, and the rights, as well as the limitations, of each are acknowledged. But the summary of the skeptical agnostic philosopher P. Feyerabend sounds much more aggressive when he writes:

The Church at the time of Galileo kept much more closely to reason than did Galileo himself, and she took into consideration the ethical and social consequences of Galileo's teaching too. Her verdict against Galileo was rational and just, and the revision of his verdict can be justified only on grounds of what is politically opportune. [P. Feyerabend, Wider den Methodenzwang (Against Method) (Frankfurt am Main, 1976, 1983), 206.]

C. F. von Weizäcker (to take one example) goes even one step farther in considering the prictical effects when he sees a "perfectly straight path" leading from Galileo to the the atomic bomb. To my surprise, when I was interviewed recently about the case of Galileo, I was not asked (for instance) why the church had presumed to hinder the knowledge of the natural sciences but, quite to the contrary, why the Church had not taken up a clearer position against the disasters that were bound to result when Galileo opened Pandora's box. It would be foolish to construct an impulsive apologetic on the basis of such views; faith does not grow out of resentment and skepticism with respect to rationality, but only out of a fundamental affirmation and a spacious reasonableness; we shall come back to this point. I mention all this only as a symptomatic case that permits us to see how deep the self-doubt of the modern age, of science and of technology goes today.

—Then-Cardinal Ratzinger, now Pope Benedict XVI, A Turning Point for Europe, pg. 95-98 (Cf. "Ratzinger's 1990 remarks on Galileo")

Albertus Magnus' Feast Day

Deus, qui beatum Albertum Pontificem tuum atque Doctorem in humana sapientia divinae fidei subicienda magnum effecisti: da nobis, quaesumus; ita eius magisterii inhaerere vestigiis ut luce perfecta fruamur in caelis.

O God, who didst make blessed Albert, thy bishop and doctor, great in subjecting human wisdom to divine faith, grant we pray, that we may so adhere to the footprints of his authorative teaching that in heaven we may enjoy perfect life.

—today's collect for St. Albertus Magnus

Vide also James A. Weisheipl, O.P., "Albert the Great and Medieval Culture," The Thomist 44 (1980) 500, cited here.

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