Galileo in the first half of Vatican II

Below are three examples from the first half of Vatican II where Galileo is explicitly mentioned by name.

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Bp. André Charue of Namur, Belgium, on 17 Nov. 1962, regarding a revision (p. 114-115) of the schema De sacra liturgia, said (p. 145):

Attendite, venerabiles Patres, ad conditionem eorum omnium, qui cum fide catholica componere debent scientificum laborem in universitatibus, in omnibus scientiarum circulis. Exemplum Galilaei et alia exempla recentiora sufficiant! Immaturae declarationes alicuius Concilii, propter earum solemnitatem, onerare possent, dicamus in semisaeculum, conditionem scientificorum.

[Beware, venerable Fathers, of the condition of all those who with catholic faith must compose scientific work, in all scientific circles. Let Galileo and the other more recent examples suffice! The immature declarations of some in this Council, because of their solemnity, could aggravate—we speak in the mid-century—the condition of the sciences.]

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Bp. emeritus of Innsbruck, Austria, Paulus Rusch (1903-1986) explicitly mentioned Galileo during the 22^nd meeting, 19 Nov. 1962, in his intervention (p. 356-357) against ch. 2, #12 ("Inerrancy") of the first schema the fathers voted on: De fontibus revelationis. Cdl. Siri's intervention, which mentioned Pope St. Pius X and Modernism, is on p. 38-39. The very next day, 61% of the council fathers rejected the schema (cf. Ratzinger Reader pp. 258 ff.). John XXIII thereafter called upon a mixed commission (incl. Cdl. Frings, whom Fr. Ratzinger advised, and Rahner) to redraft it. Cdl. Frings said (p. 34-35) the original schema was too scholastic and professorial in tone, "nec aedificans nec vivificans" ("neither edifying nor vivifying")!

Here is De fontibus revelationis ch.2, #12 on inerrancy:

Because divine Inspiration extends to everything, the absolute immunity of all Holy Scripture from error [PTC had said "the infallibility and inerrancy"] follows directly and necessarily. For we are taught by the ancient and constant faith of the Church that it is utterly forbidden to grant that the sacred author himself has erred, since divine Inspiration of itself as necessarily excludes and repels any error in any matter, religious or profane, as it is necessary to say that God, the supreme Truth, is never the author of any error whatever. [Pius XII, Divino afflante (EB 539), using the words of Leo XIII, Providentissimus Deus (D 1950); see also EB 44, 46, 125, 420, 463, etc.]

After giving an example of how Matt. 27:9 allegedly errs by quoting Jeremiah when it apparently was really quoting the prophet Zachary, Bp. Rusch said (p. 357):

Accedit nostram Ecclesiam hac in re iam duram passam esse experientiam. Anno 1633 Galilei sub Urbano VIII damnatus est, quia defendit doctrinam contra Scripturam. Doctrinam autem quam defendit erat, sicut notissimum est, terram circa solem rotare et non viceversa. [Additionally, our church has already suffered a hard experience in this matter. In 1633 Galileo was condemned under Urban VIII because he defended a doctrine contrary to Scripture. But the doctrine that he defended was, as is well-known, that the earth revolves around the sun and not vice versa.]

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Bp. Michel Darmancier (1918-1984), titular of Augurus, commenting on the "De ecclesiæ magistero" section (p. 47-54) of the 23 Nov. 1962 schema De ecclesia (p. 12 ff.), wrote in his "written animadversion" (p. 452):

De illis enim contingentibus elementis sicut in fide et theologia proprie dicta consentire possunt theologi per saecula et per totum orbem catholicum, illa intimius coniungentes cum dogmatibus, quin exinde oriatur quaevis certitudo de illorum veritate, etsi concludi potest fidem ex illis detrimentum non timere. Sic, usque ad saeculum XVI, unanimiter docuerunt theologi terram centrum universorum esse, unde Galileus quidam satis notas difficultates cum sancta Inquisitione expertus est.

[The theologians can agree, throughout the ages and the whole catholic world, on those contingent elements in faith and theology properly speaking which are intimately connected with dogmas, which might not arise from any certainty of their truth, although to fear a loss of faith from them cannot be concluded. Thus, until the 16^th century, theologians unanimously taught that the earth was the center of the universe, whence Galileo experienced some well-known difficulties with the holy Inquisition.]

Was Galileo persecuted?

Before Copernicus, Bishop Nicole Oresme (d. 1382) advanced the hypothesis that the earth, not the heavens, rotates diurnally. He was not condemned because he did not reinterpret Holy Scripture to support his scientific view.

Galileo was condemned because he ventured into Scriptural exegesis—in, e.g., his 1615 Letter to the Grand Duchess Madame Christina Lorraine—contrary to the unanimous consent of the Fathers of the Church and the Council of Trent. Copernicus did not do Scriptural exegesis regarding heliocentrism.

Galileo was condemned as "vehemently suspected of heresy" for holding "The proposition that the Sun is the center of the world and does not move from its place[, which] is absurd and false philosophically and formally heretical, because it is expressly contrary to Holy Scripture." (1633 Condemnation).

To say Galileo was persecuted seems to imply he adhered to a different religion than Catholicism. He was Catholic, hence the Church had jurisdiction over him in moral or religious matters. His house arrest was quite unusual; it was really a paid retirement, during which he wrote his most important physics work, The Two New Sciences (1638).

As the Tuscan ambassador Francesco Niccolini wrote on 27 February 1633 (p. 225 of Maurice A. Finocchiaro's The Galileo Affair: A Documentary History):

His Holiness [Pope Urban VIII] answered that he had done Mr. Galilei a singular favor, not done to others, by allowing him to stay in this house [the Tuscan embassy] rather than at the Holy Office, and that this kind procedure had been used only because he is a dear employee of the Most Serene Patron [the Pope] and because of the regard due to His Highness [the Pope]; for a Knight of the House of Gonzaga, son of Ferdinando, had been not only placed in a litter and escorted to Rome under guard but was taken to the Castle and kept there for a long time til the end of the trial. I showed myself to be aware of the nature of the favor, and I humbly thanked His Holiness [the Pope];

and on 16 April 1633 (p. 250-51 of ibid.):

Indeed, there is no precedent of anyone ever having been interrogated during a trial without being detained in a prison cell, and in this regard he has profited from being employed by His Highness [Pope Urban VIII] and from being lodged at this house; nor is there knowledge of anyone else (whether bishop, prelate, or nobleman) who, immediately upon his arrival in Rome, has not been kept at the Castle or at the same palace of the Inquisition, subject to all rigor and strictness. Furthermore, they even allow his servant to wait on him, to sleep there, and, what is more, to come and go as he pleases, and they allow my own servants to bring him food to his room from here and to return to my house morning and evening.

This singular treatment can hardly be considered a persecution.

His house arrest began at the same Tuscan embassy on 24 June 1633. On 1 December 1633, the Pope allowed Galileo to return to his villa in Arcetri, near Florence, where he stayed for the rest of his life.

St. Robert Cardinal Bellarmine

On today's feast day of St. Robert Cardinal Bellarmine, I reproduce below his 12 April 1615 letter to Fr. Foscarini, who wrote a theology book trying to reconcile heliocentrism with Scriptures (The Essential Galileo p. 146-148; my emphases):

[171] To the Very Reverend Father Paolo Antonio Foscarini, Provincial of the Carmelites in the Province of Calabria:

  My Very Reverend Father,

 I have read with interest the letter in Italian and the essay in Latin which Your Paternity sent me; I thank you for the one and for the other and confess that they are all full of intelligence and erudition.  You ask for my opinion, and so I shall give it to you, but very briefly, since now you have little time for reading and I for writing.

 First, I say that it seems to me that Your Paternity and Mr. Galileo are proceeding prudently by limiting yourselves to speaking suppositionally and not absolutely, as I have always believed that Copernicus spoke. For there is no danger in saying that, by assuming the earth moves and the sun stands still, one saves all the appearances better than by postulating eccentrics and epicycles; and that is sufficient for the mathematician. However, it is different to want to affirm that in reality the sun is at the center of the world and only turns on itself without moving from east to west, and the earth is in the third heaven⁴ and revolves with great speed around the sun; this is a very dangerous thing, likely not only to irritate all scholastic philosophers and theologians, but also to harm the Holy Faith by rendering Holy Scripture false. For Your Paternity has well shown many ways of interpreting Holy Scripture, but has not applied them to particular cases; without a doubt you would have encountered very great difficulties if you had wanted to interpret all those passages you yourself cited.

  [172] Second, I say that, as you know, the Council⁵ prohibits interpreting Scripture against the common consensus of the Holy Fathers; and if Your Paternity wants to read not only the Holy Fathers, but also the modern commentaries on Genesis, the Psalms, Ecclesiastes, and Joshua, you will find all agreeing in the literal interpretation that the sun is in heaven and turns around the earth with great speed, and that the earth is very far from heaven and sits motionless at the center of the world. Consider now, with your sense of prudence, whether the Church can tolerate giving Scripture a meaning contrary to the Holy Fathers and to all the Greek and Latin commentators. Nor can one answer that this is not a matter of faith, since if it is not a matter of faith “as regards the topic” [ex parte obiecti], it is a matter of faith “as regards the speaker” [ex parte dicentis]; and so it would be heretical to say that Abraham did not have two children and Jacob twelve, as well as to say that Christ was not born of a virgin, because both are said by the Holy Spirit through the mouth of the prophets and the apostles.

  Third, I say that if there were a true demonstration that the sun is at the center of the world and the earth in the third heaven, and that the sun does not circle the earth but the earth circles the sun, then one would have to proceed with great care in explaining the Scriptures that appear contrary, and say rather that we do not understand them than that what is demonstrated is false. But I will not believe that there is such a demonstration, until it is shown me. Nor is it the same to demonstrate that by assuming the sun to be at the center and the earth in heaven one can save the appearances, and to demonstrate that in truth the sun is at the center and the earth in heaven; for I believe the first demonstration may be available, but I have very great doubts about the second, and in case of doubt one must not abandon the Holy Scripture as interpreted by the Holy Fathers. I add that the one who wrote, “The sun riseth, and goeth down, and returneth to his place: and there rising again,”⁶ was Solomon, who not only spoke inspired by God, but was a man above all others wise and learned in the human sciences and in the knowledge of created things; he received all this wisdom from God; therefore it is not likely that he was affirming something that was contrary to truth already demonstrated or capable of being demonstrated. Now, suppose you say that Solomon speaks in accordance with appearances, since it seems to us that the sun moves (while the earth does so), just as to someone who moves away from the seashore on a ship it looks like the shore is moving. I shall answer that when someone moves away from the shore, although it appears to him that the shore is moving away from him, nevertheless he knows that this is an error and corrects it, seeing clearly that the ship moves and not the shore; but in regard to the sun and the earth, no scientist has any need to correct the error, since he clearly experiences that the earth stands still and that the eye is not in error when it judges that the sun moves, as it also is not in error when it judges that the moon and the stars move.  And this is enough for now.

  With this I greet dearly Your Paternity, and I pray to God to grant you all your wishes.

  At home, 12 April 1615.
  To Your Reverend Paternity.

As a Brother,
Cardinal Bellarmine.

Notes
⁴“In the third heaven” just means in the third orbit around the sun.
⁵The Council of Trent (1545–63). [Session the Fourth, Decree concerning the Canonical Scriptures; reiterated in Vatican I's Dei Filius]
⁶Ecclesiastes 1:5 [Douay-Rheims version]

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Also, from his entry in the Dictionary of Scientific Biography:

In his Système du monde, Duhem suggests that in one respect, at least, Bellarmine had shown himself a better scientist than Galileo by disallowing the possibility of a “strict proof” of the earth’ motion, on the grounds that an astronomical theory merely “saves the appearances” without necessarily revealing what “really happens.”

The Coming Paradigm Shift in Cosmology (interview #2)

New Science Internet Radio with Forward Boldly on BlogTalkRadio

The Coming Paradigm Shift in Cosmology

"The Principle" Documentary Trailer

http://www.theprinciplemovie.com/
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John Philoponus ("The Grammarian")

John Philoponus (late 5th, 2nd ½ of 6th century A.D.)

Philoponus’ main significance for the history of science lies in his being, at the close of antiquity, the first thinker to undertake a comprehensive and massive attack on the principal tenets of Aristotle’s physics and cosmology, an attack unequaled in thoroughness until Galileo.

He argued that the sun is fire and of terrestrial-like, corruptible matter. He devised a precursor to the notion of impetus which Buridan later developed, that which keeps moving bodies in motion even after the mover ceases being in contact with them; air does not keep projectiles in motion. He discovered that light rays travel the same both backwards and forwards. He invented functions of variables and their "courses" (what we'd call "first derivatives" in modern calculus). He discovered the law of inertia, that bodies in motion remain in motion unless something impedes their movement, literally a thousand years before Galileo, Newton, et al.!

He's certainly one of the "grands génies de l'Antiquité" ("great geniuses of Antiquity") and "principaux précurseurs de la Science moderne" ("principle precursers to modern Science"), as Pierre Duhem wrote.

Philoponus's arguments on the non-eternity of the world were interesting. From the Encyclopedia of Time: Science, Philosophy, Theology, & Culture (see also his Dict. of Sci. Bio. entry):

Philoponus and Simplicius

The beginning or the eternity of the world and infinity or finitude of time is a central topic in the philosophy of late antiquity, especially in the debate between Christians and pagans. This quarrel started for the first time in the Neoplatonic school of Alexandria in the 6th century CE between John Philoponus and Simplicius, who were the philosophically most talented pupils of Ammonius Hermeiou. Simplicius preserved the orthodox Neoplatonic doctrine (Ammonius and his master Proclus always held to the eternity of the world), whereas the Christian Philoponus opposed this view. It is astonishing that the grammarian Philoponus (he called himself John the Grammarian and edited most of Ammonius's lectures on Aristotle's writings) argued without Christian presuppositions and personal Philoponus and disparagement; Simplicius, however, usually a very modest and well-educated philosopher, very rudely called Philoponus's arguments “rubbish” and accused him of “bragging and contentiousness.” Obviously, they had never met personally (most probably, Simplicius had been working in Athens long before 529 CE, when the academy was closed by Justinian; Philoponus apparently never left Alexandria). Philoponus argued against the eternity of the world in his commentaries on Aristotle's Physics (probably written in 517 CE) and Meteorology, then in On the Eternity of the World, Against Proclus (De aeternitate mundi contra Proclum, written in 529 CE; this treatise refutes 18 arguments from a lost treatise written by Proclus about the eternity of the world). The writing Against Aristotle (Contra Aristotelem), which can be dated between approximately 530 CE and 534 CE, is preserved only in fragments. The first five books contained Philoponus's criticism of Aristotle's theory of the fifth element, the sixth book his criticism of Aristotle's theory of eternal movement, and at least two further books contained reflections about a Christian theory of divine creation. Simplicius's answer to Philoponus can be found mainly in his commentary on Aristotle's De caelo I and Physics VIII

Philoponus attacks the eternity of the world by demonstrating inner contradictions in Aristotle's theory of time and eternity and by refuting Aristotle through Aristotle himself. One argument goes as follows: The eternity of the world is incompatible with Aristotle's definition of movement, because movement is the act of what is movable in potency, that is, the movable in potency exists prior to the movement. This implies that the eternal movements (e.g., the heavens' circular movements) have some movable in potency prior to them (e.g., the heavens), if the movable in potency is always anterior to the movement. Philoponus concludes that the Aristotelian definition of movement is not universal. Simplicius defends the universality of Aristotle's definition of movement by making a difference between infinite and finite movement: In the case of finite movement, the movable is still there, if the movement has finished; in the case of infinite, eternal movement, only one state of movement is prior to another state. For instance, if the sun is in Aries, then it is the movable, which is potentially in Taurus.

Further, if any first movement is excluded, Philoponus argues that all present movements become unintelligible, because every movement presupposes an infinite number of previous movements; we could not avoid a regressus in infinitum. Moreover, all present movements are added to those of the past; that leads to the evidently absurd notion of an infinite constantly increasing. The same problem arises concerning the future: If time and movement infinitely continue in the future, there would be an infinite body with infinite power. But that is not possible, so the world could not exist indefinitely in the future. The core of this argument is Philoponus's attack on Aristotle's notion of infinity: Aristotle contends that infinity is merely potential and never actual. For if you divide a line or a duration, you can actually mark off only a finite number of divisions, either physically or mentally. There is only a potential infinity of divisions, inasmuch as infinity exists through a process of dividing one point (or one now) after another; it is the same with the infinity of numbers.

Philoponus attacks this notion of infinity by several arguments. First, the universe must have had a beginning, or it would by now have traversed an actual infinity of years. The second argument is this: If you suppose an actual infinite number of years up to this year, next year will be an infinity plus one year. So the infinity is increasing. Simplicius says Aristotle had already anticipated Philoponus's objections, for he had pointed out that the past years have finished, so you do not get an actual infinity of them existing. That implies that time and movement are not an actually infinite quantity, but their infinity means there is a possibility of transcending every given limitation. The most fundamental difference between Philoponus and Simplicius is this: Whereas, Simplicius's infinite time is a circular indefinite repetition of finite times, Philoponus's notion of time is linear. However, the rejection of Philoponus's argument appears difficult in the context of Aristotle's philosophy of nature if you want to preserve the singularity of the individual parts of time, for instance, days or hours.

Philoponus's arguments against the eternity of the world were repeated by Bonaventure in the 13th century, after the arguments had been elaborated by Islamic philosophers. Finally, the dispute between Philoponus and Simplicius has an equivalent in Kant's doctrine of the “antinomy of pure reason” in his Critique of Pure Reason, especially the “first conflict of transcendental ideas.” One branch of the antinomy is equivalent to Philoponus's argument (in Kant's words, “The world has a beginning in time”); this and the opposite argument (“the world has no beginning in time”) is equivalent to Simplicius. Probably, there is not any “ immediate effective historical connection” between the Alexandrian school quarrel and Kant's cosmo-logical antinomy, but it shows that in this quarrel, “Greek thinking comes to the limits of its own presuppositions.”

Michael Schramm

St. Robert Bellarmine

Today is the feast day of St. Robert Bellarmine, famously involved in the "Galileo affair:"

In his Système du monde, Duhem suggests that in one respect, at least, Bellarmine had shown himself a better scientist than Galileo by disallowing the possibility of a “strict proof” of the earth’ motion, on the grounds that an astronomical theory merely “saves the appearances” without necessarily revealing what “really happens.”

Duhem said in ΣΩZEIN TA ΦAINOMENA: Essai sur la notion de théorie physique de Platon à Galilée

that logic was on the side of Osiander, Bellarmine, and Urban VIII, and not on the side of Kepler and Galileo; that the former had understood the exact import of the experimental method; and that, in this regard, the latter were mistaken

"Faith, Reason, and Science" by Clifford Simske, MD

From the Tucson Catholic Physician Guild's September 2011 meeting:

Click here to download an OCRed version Dr. Simske's notes.

Galileo Affair

(source)

Further reading:
Aristotle's Aether and Contemporary Science by Christopher A. Decaen

1. Cf. Steven Baldner's "Thomas Aquinas on Celestial Matter;" this and Decaen's article are crucial for understanding the Galileo affair and
2. Decaen's lecture "Galileo Galilei, Scriptural Exegete, and the Church of Rome, Advocate of Science."

Medieval Scholars Applied Math to Physics

The Medieval scholars had no aversion to applying mathematics to physics, which they classified as a "middle sciences," and which, because of their "conclusions about physical matter from mathematical principles, are reckoned rather among the mathematical sciences, though, as to their matter they have more in common with physical [i.e., natural-philosophical] sciences." (Summa Theologica II-II, q. 9, a. 2 ad 3).

Here are some physicists we rarely hear about because of the myth that the Middle Ages were "dark ages":

• The medieval scientist Thomas Bradwardine determined in 1300 that for uniformly accelerated objects, d = ½ a t², which Fr. de Soto, O.P., (b. ca. 1494) applied to free-falling objects. (Before Galileo!)
• Jean Buridan (d. ca. 1359) invented the momentum equation: p = m v. Some have proposed naming the unit of momentum after him, where 1 B = 1 kg m/s.
• The French Bishop Nicole Oresme (d. 1382) determined mean speed theorem of uniformly accelerated body: v_avg = v_f / 2.
• Bishop Oresme posed the famous Gedankenexperiment: “I posit that the Earth is pierced clear through and that we can see through a great hole farther and farther right up to the other end where the antipodes [poles] would be if the whole of this Earth were inhabited; I say, first of all, that if we dropped a stone through this hole, it would fall and pass beyond the center of the earth, going straight on toward the other side for a certain limited distance, and that then it would turn back going beyond the center on this side of the Earth; afterward, it would fall back again, going beyond the center but not so far as before; it would go and come this way several times with a reduction of its reflex motions until finally it would come to rest as the center of the Earth....” Quoted by K. V. Magruder from Le Livre du Ciel et due Monde (Madison: University of Wisconsin Press, 1968), translated by D. Menut, pg. 573.
• Bishop Oresme wrote (before Galilean relativity): “If air were enclosed in a moving ship, it would seem to the person situated in this air that it was not moved.” Book of the Heavens, Book II chapter 25, from Grant, A Source Book of Medieval Science, pg. 505, Harvard, 1974

Superluminal Neutrinos?

Are neutrino's really going faster than the speed of light?...Does this completely undermine all previous science? How do we answer those who suggest our knowledge is not stable, open to complete change overnight?
Ave Maria radio host Al Kresta interviews Dr. Anthony Rizzi, Director of the Institute for Advanced Physics.

This is the paper they speak about: "Measurement of the neutrino velocity with the OPERA detector in the CNGS beam"

Newton the First Modernist?

Newton wrote at least as much theology as he did physics and mathematics, yet he believed in the Arian heresy that Jesus Christ is not truly divine. Newton also had a great contempt for the 13th century scholastic St. Thomas Aquinas (cf. his entry in the Complete Dictionary of Scientific Biography). But why? St. Thomas was crucial in advancing science and paving the way for the discoveries of Galileo et al.

Newton does not refute St. Thomas on his own grounds; he just says in "Two Notable Corruptions of Scripture (part 1: ff. 1-41):"

[...] but to us Thomas Aquinas is no Apostle; we are seeking for the authority of greek manuscripts.

(Cf. Fr. Ramírez, O.P.'s The Authority of St. Thomas Aquinas.) This "ressourcement" or "going back to the [supposedly] more authoritative sources" is what Modernist theologians say today. Modernism is detrimental to the advancement of science. In Standing on the Sholders of Giants, David Boyd Haycock writes (my emphasis and [comments]):

If Baconianism, Newtonianism and the Royal Society were three of the most significant influences upon the development of science in seventeenth- and early eighteenth-century England, then a fourth requiring full and equal consideration is religion. As we have seen, Baconian scientific methodology advocated a split from the earlier, uncritical Aristotelianism of the scholastics. However, in the Middle Ages Aristotelian philosophy and Christian theology had become thoroughly assimilated through the apologetics [He did pure philosophy and theology, too.] of the medieval scholar Thomas Aquinas, so that at least one cautious seventeenth-century religious commentator, writing as 'S. P.' (possibly Simon Patrick, later the bishop of Ely), feared that since 'philosophy and divinity [i.e., theology] are so interwoven by the schoolmen ... it cannot be safe to separate them; new philosophy will bring in new divinity.' [Yes, St. Thomas's doctrine on faith and reason will never be superseded.] It was this very fear which had led the Catholic Church to its persecution of both the former Dominican friar and philosopher Giordano Bruno [Suspected of the Arian heresy, he was a pantheist and materialist who said "Matter is not without its forms, but contains them all; and since it carries what is wrapped up in itself, it is in truth all nature and the mother of all the living." (C. Gutberlet).] (who was burnt at the stake [by civil authorities, not clerics] in 1600), and the Italian astronomer Galileo Galilei. Though English Protestants considered themselves well above such Papist extremes, Newton's critic Dr Edwards castigated his contemporaries for their practice of 'coining ... New Systems in Divinity.' He observed how 'this vain Apprehension [Yes, it certainly is vain. What is their justification of it?] possesses them, that, because in this Learned Age some parts of Humane Knowledge are censur'd [Such as?], and the very Principles of some Arts, especially those that relate to Natural Philosophy, have undergone a great Alteration [But not so great that, e.g., quidquid movetur ab alio movetur ("that which is moved is moved by another") is no longer true.]; therefore they may venture to advance some unheard-of doctrines in Divinity, to new model our Religion, to mend the Gospel, and to present us as it were with a New Christianity'. [So basically they changed "Divinity" in order to advance their supposedly greatly altered "Natural Philosophy," based on which they would try to justify the "New Christianity"?] Bacon had attempted to defend his new method from any such criticism by arguing that 'we do not presume by the contemplation of nature to attain to the mysteries of God.' [Cf. Romans 1:20: "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."] But it was impossible that a science based upon the empirical study of a world considered to be divine handiwork would not inevitably lead to questions relating to the very nature of the divine itself. [This is why by their very nature "philosophy and divinity are so interwoven," so, with Dr. Edwards, I reiterate: "Why the need for a 'new philosophy' and 'new divinity'?"]

"Do not block the way of inquiry!", C. S. Peirce would say.

God, Modern Life, and Physics: Science's Challenge to the Faith with Dr. Rizzi & Fr. Pacwa

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")

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

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.

Science's Light Ages

One often hears today that everything before Galileo (1564-1642), including science, lived in the "Dark Ages" where people were unenlightened and apparently wasted their time studying theology. Yet Galileo was not alone; he indeed did "stand on the shoulders of giants." Who were some of them? What did they say? Certainly they were not theologians, or were they?

Besides Aristotle (382-322 B.C.), the first physicist, as mentioned before, there was St. Augustine (354-430 A.D.), whose theory of time even today is mentioned in the quantum cosmology literature (e.g., in Rev. Mod. Phys. 61, 1 (1989) pg. 15). He said:

For what is time? Who can easily and briefly explain it? Who even in thought can comprehend it, even to the pronouncing of a word concerning it? But what in speaking do we refer to more familiarly and knowingly than time? And certainly we understand when we speak of it; we understand also when we hear it spoken of by another. What, then, is time? If no one ask of me, I know; if I wish to explain to him who asks, I know not. Yet I say with confidence, that I know that if nothing passed away, there would not be past time; and if nothing were coming, there would not be future time; and if nothing were, there would not be present time. Those two times, therefore, past and future, how are they, when even the past now is not; and the future is not as yet? But should the present be always present, and should it not pass into time past, time truly it could not be, but eternity. If, then, time present—if it be time—only comes into existence because it passes into time past, how do we say that even this is, whose cause of being is that it shall not be—namely, so that we cannot truly say that time is, unless because it tends not to be?

—St. Augustine's Confessions XI, ch. 14

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Much later (1225-1274) St. Thomas Aquinas unified Greek, principally Aristotelean, thought with that of Christendom. Some of his scientific contributions were to describe the

1. relation of mathematics to the natural sciences,
2. relativity of locomotion,
3. nature of light in optics,
4. motion of falling bodies, and
5. foundations of the modern, Galileo-like scientific method,

among many other things.

1. Relation of Mathematics to Natural Sciences

St. Thomas commented on question V of Boethius's De Trinitate, saying:

By its very nature motion is not in the category of quantity, but it partakes somewhat of the nature of quantity from another source, namely, according as the division of motion derives from either the division of space or the division of the thing subject to motion. So it does not belong to the mathematician to treat of motion, although mathematical principles can be applied to motion. Therefore, inasmuch as the principles of quantity are applied to motion, the natural scientist treats of the division and continuity of motion, as is clear in the Physics. And the measurements of motions are studied in the intermediate sciences between mathematics and natural science: for instance, in the science of the moved sphere and in astronomy.

Simple bodies and their properties remain in composite bodies although in a different way, as the proper qualities of the elements and their proper movements are found in a mixed body. What is proper to composite bodies, however, is not found in simple bodies. And so it is that the more abstract and simple the objects of a science are, the more applicable its principles are to the other sciences. Thus the principles of mathematics are applicable to natural things, but not visa versa, because physics presupposes mathematics; but the converse is not true, as is clear in the De Caelo et Mundo. So there are three levels of sciences concerning natural and mathematical entities. Some are purely natural and treat of the properties of natural things as such, like physics, agriculture, and the like. Others are purely mathematical and treat of quantities absolutely, as geometry considers magnitude and arithmetic numbers. Still others are intermediate, and these apply mathematical principles to natural things; for instance, music, astronomy, and the like. These sciences, however, have a closer affinity to mathematics, because in their thinking that which is physical is, as it were, material, whereas that which is mathematical is, as it were, formal. For example, music considers sounds, not inasmuch as they are sounds, but inasmuch as they are proportionable according to numbers; and the same holds in other sciences. Thus they demonstrate their conclusions concerning natural things, but by means of mathematics. Therefore nothing prevents their being concerned with sensible matter insofar as they have something in common with natural science, but insofar as they have something in common with mathematics they are abstract.

—In Boethium De Trinitate, q. 5, a. 3 ad 5 et ad 6

Commenting on Aristotle's Physics 193b22, St. Thomas also wrote:

161. Next where he says, ‘That is why he separates ...’(193 b 33), he concludes to a sort of corollary from what he has just said. Because the mathematician does not consider lines, and points, and surfaces, and things of this sort, and their accidents, insofar as they are the boundaries of a natural body, he is said to abstract from sensible and natural matter. And the reason why he is able to abstract is this: according to the intellect these things are abstracted from motion.

As evidence for this reason we must note that many things are joined in the thing, but the understanding of one of them is not derived from the understanding of another. Thus white and musical are joined in the same subject, nevertheless the understanding of one of these is not derived from an understanding of the other. And so one can be separately understood without the other. And this one is understood as abstracted from the other. It is clear, however, that the posterior is not derived from the understanding of the prior, but conversely. Hence the prior can be understood without the posterior, but not conversely. Thus it is clear that animal is prior to man, and man is prior to this man (for man is had by addition to animal, and this man by addition to man). And because of this our understanding of man is not derived from our understanding of animal, nor our understanding of Socrates from our understanding of man. Hence animal can be understood without man, and man without Socrates and other individuals. And this is to abstract the universal from the particular.

In like manner, among all the accidents which come to substance, quantity comes first, and then the sensible qualities, and actions and passions, and the motions consequent upon sensible qualities. Therefore quantity does not embrace in its intelligibility the sensible qualities or the passions or the motions. Yet it does include substance in its intelligibility. Therefore quantity can be understood without matter, which is subject to motion, and without sensible qualities, but not without substance. And thus quantities and those things which belong to them are understood as abstracted from motion and sensible matter, but not from intelligible matter, as is said in Metaphysics, VII:10.

Since, therefore, the objects of mathematics are abstracted from motion according to the intellect, and since they do not include in their intelligibility sensible matter, which is a subject of motion, the mathematician can abstract them from sensible matter. And it makes no difference as far as the truth is concerned whether they are considered one way or the other. For although the objects of mathematics are not separated according to existence, the mathematicians, in abstracting them according to their understanding, do not lie, because they do not assert that these things exist apart from sensible matter (for this would be a lie). But they consider them without any consideration of sensible matter, which can be done without lying. Thus one can truly consider the white without the musical, even though they exist together in the same subject. But it would not be a true consideration if one were to assert that the white is not musical.

162. Next where he says, “The holders of the theory...’ (193 b 35), he excludes from what he has said an error of Plato.

Since Plato was puzzled as to how the intellect could truly separate those things which were not separated in their existence, he held that all things which are separated in the understanding are separated in the thing. Hence he not only held that mathematical entities are separated, because of the fact that the mathematician abstracts from sensible matter, but he even held that natural things themselves are separated, because of the fact that natural science is of universals and not of singulars. Hence he held that man is separated, and horse, and stone, and other such things. And he said these separated things are ideas, although natural things are less abstract than mathematical entities. For mathematical entities are altogether separated from sensible matter in the understanding, because sensible matter is not included in the understanding of the mathematicals, neither in the universal nor in the particular. But sensible matter is included in the understanding of natural things, whereas individual matter is not. For in the understanding of man flesh and bone is included, but not this flesh and this bone.

163. Next where he says, ‘This becomes plain ...’ (194 a 1), he clarifies the solution he has given in two ways, first by means of the difference in the definitions which the mathematician and the natural philosopher assign, and secondly by means of the intermediate sciences, where he says, ‘Similar evidence ...’ (194 a 7 #164).

He says, therefore, first that what has been said of the different modes of consideration of the mathematician and the natural philosopher will become evident if one attempts to give definitions of the mathematicals, and of natural things and of their accidents. For the mathematicals, such as equal and unequal, straight and curved, and number, and line, and figure, are defined without motion and matter, but this is not so with flesh and bone and man. Rather the definition of these latter is like the definition of the snub in which definition a sensible subject is placed, i.e., nose. But this is not the case with the definition of the curved in which definition a sensible subject is not placed.

And thus from the very definitions of natural things and of the mathematicals, what was said above [#160ff] about the difference between the mathematician and the natural philosopher is apparent.

164. Next where he says, ‘Similar evidence...’ (194 a 7), he proves the same thing by means of those sciences which are intermediates between mathematics and natural philosophy.

Those sciences are called intermediate sciences which take principles abstracted by the purely mathematical sciences and apply them to sensible matter. For example, perspective applies to the visual line those things which are demonstrated by geometry about the abstracted line; and harmony, that is music, applies to sound those things which arithmetic considers about the proportions of numbers; and astronomy applies the consideration of geometry and arithmetic to the heavens and its parts.

However, although sciences of this sort are intermediates between natural science and mathematics, they are here said by the Philosopher to be more natural than mathematical, because each thing is named and takes its species from its terminus. Hence, since the consideration of these sciences is terminated in natural matter, then even though they proceed by mathematical principles, they are more natural than mathematical sciences.

He says, therefore, that sciences of this sort are established in a way contrary to the sciences which are purely mathematical, such as geometry or arithmetic. For geometry considers the line which has existence in sensible matter, which is the natural line. But it does not consider it insofar as it is in sensible matter, insofar as it is natural, but abstractly, as was said [#160ff]. But perspective conversely takes the abstract line which is in the consideration of mathematics, and applies it to sensible matter, and thus treats it not insofar as it is a mathematical, but insofar as it is a physical thing.

Therefore from this difference between intermediate sciences and the purely mathematical sciences, what was said above is clear. For if intermediate sciences of this sort apply the abstract to sensible matter, it is clear that mathematics conversely separates those things which are in sensible matter.

165. And from this it is clear what his answer is to the objection raised above [#158] concerning astronomy. For astronomy is a natural science more than a mathematical science. Hence it is no wonder that astronomy agrees in its conclusions with natural science.

However, since it is not a purely natural science, it demonstrates the same conclusion through another method. Thus, the fact that the earth is spherical is demonstrated by natural science by a natural method, e.g., because its parts everywhere and equally come together at the middle. But this is demonstrated by astronomy from the figure of the lunar eclipse, or from the fact that the same stars are not seen from every part of the earth.

—In II Phys. lect. 3, nn. 5-9

He also mentioned in his Summa Theologica that:

As stated above (Question 1, Article 1), every cognitive habit regards formally the mean through which things are known, and materially, the things that are known through the mean. And since that which is formal, is of most account, it follows that those sciences which draw conclusions about physical matter from mathematical principles, are reckoned rather among the mathematical sciences, though, as to their matter they have more in common with physical sciences: and for this reason it is stated in Phys. ii, 2 that they are more akin to physics. Accordingly, since man knows God through His creatures, this seems to pertain to "knowledge," to which it belongs formally, rather than to "wisdom," to which it belongs materially: and, conversely, when we judge of creatures according to Divine things, this pertains to "wisdom" rather than to "knowledge."

—II-II, q. 9, a. 2 ad 3

2. Relativity of Locomotion

Commenting on Aristotle's De Cælo II., St. Thomas preceded Galilean relativity by writing:

396. First he considers the first one [297], and says that it is impossible that both, i.e., the star and its orb, be at rest if we assume that the earth is also at rest. For the apparent motion of the stars cannot be saved if both the stars which appear to be in motion are at rest, and the men who see them. For, that motion should appear, this must be caused either by the motion of the thing seen or of the one seeing. For this reason, some, positing the stars and the whole heaven to be at rest, posited the earth on which we live to be moved from west to east around the equinoxial poles [i.e., its axis] once a day. According to this, it is due to our own motion that the stars seem to move in a contrary direction. This is said to have been the opinion of Heraclitus of Pontus and Aristarchus. However, Aristotle is supposing for the present that the earth is at rest —which fact he will later prove. Hence it remains, the first member, in which the heaven and the stars were assumed to be at rest, having been set aside, to verify one of the two others —namely, that stating that both, i.e., the star and the orb, are in motion, or that stating one to be in motion and the other at rest.

—In II De Cælo, lect. 11, n. 2

405. Then he shows that the motion seen in the stars is due to neither of these two motions. First he shows that the motion seen in the stars is not one of circumgyration; and he proves this in two ways. First, because if the stellar bodies were being moved with the motion of circumgyration, then, even though the parts of the star exchanged places as to subject, the star as a whole would have to remain in the same place as to subject, the place being varied only according to notion, as is clear from what was proved in Physics VI. For that is the way things turn out for a spherical motion due to its relation to a center and to poles that are stationary. But we cannot admit such a situation in the stars, since the contrary is evident to sense —for we see stars sometimes in the east and sometimes in the west. Likewise, everyone says that the stars do not remain always in the same place but are transferred from one place to another. Therefore, the motion that appears to be in the stars is not one of circumgyration.

—In II De Cælo, lect. 12, n. 4

3. Nature of Light in Optics

Commenting on Aristotle's De Anima II., St. Thomas wrote this about light, which is reminiscent of field of view or the inverse square law in optics:

§ 433. [...] For if anything is to be seen it must actually affect the organ of sight. Now it has been shown that this organ as such is not affected by an immediate object—such as an object placed upon the eye. So there must be a medium between organ and object. But a vacuum is not a medium; it cannot receive or transmit effects from the object. Hence through a vacuum nothing would be seen at all.

§ 434. Democritus went wrong because he thought that the reason why distance diminishes visibility was that the medium is of itself an impediment to the action of the visible object upon sight. But it is not so. The transparent medium as such is not in the least incompatible with luminosity or colour; on the contrary, it is proximately disposed to their reception; a sign of which is that it is illumined or coloured instantaneously. The real reason why distance diminishes visibility, is that everything seen is seen within the angle of a triangle, or rather pyramid, whose base is the object seen and apex in the eye that sees.

§ 435. It makes no difference whether seeing takes place by a movement from the eye outwards, so that the lines enclosing the triangle or pyramid run from the eye to the object, or e converso, so long as seeing does involve this triangular or pyramidal figure; which is necessary because, since the object is larger than the pupil of the eye, its effect upon the medium has to be scaled down gradually until it reaches the eye. And, obviously, the longer are the sides of a triangle or pyramid the smaller is the angle at the apex, provided that the base remains the same. The further away, then, is the object, the less does it appear—until at a certain distance it cannot be seen at all.

—In II De Anima lect. 15, §433-§435

Long before the Italian physicist Macedonio Melloni (1798-1854) discovered that heat and light share similar properties, St. Thomas wrote this:

[L]ux [...] semper est effectiva caloris; etiam lux lunæ. ["Light always is effected of heat; even moonlight."]

—Super Sent., lib. 2 d. 15 q. 1 a. 2 ad 5

4. Motion of Falling Bodies

Previously, many adopted Aristotle's theory that the medium—e.g., air—is what keeps a falling object in motion. Commenting on Aristotle's Physics III., St. Thomas distinguished for the first time these three things: weight, mass, and the resisting medium:

535. [...] This resistance can arise from three sources: First, from the situs of the mobile; for from the very fact that the mover intends to transfer the mobile to some certain place, the mobile, existing in some other place, resists the intention of the mover. Secondly, from the nature of the mobile, as is evident in compulsory motions, as when a heavy object is thrown upwards. Thirdly, from the medium. All three are taken together as one resistance, to constitute one cause of slowing up in the motion. Therefore when the mobile, considered in isolation as different from the mover, is a being in act, the resistance of the mobile to the mover can be traced either to the mobile only, as happens in the heavenly bodies, or to the mobile and medium together, as happens in the case of animate bodies on this earth. But in heavy and light objects, if you take away what the mobile receives from the mover, viz., the form which is the principle of motion given by the generator, i.e., by the mover, nothing remains but the matter which can offer no resistance to the mover. Hence in light and heavy objects the only source of resistance is the medium. Consequently, in heavenly bodies differences in velocity arise only on account of the ratio between mover and mobile; in animate bodies from the proportion of the mover to the mobile and to the resisting medium—both together. And it is in these latter cases that the given objection would have effect, viz., that if you remove the slowing up caused by the impeding medium, there still remains a definite amount of time in the motion, according to the proportion of the mover to the mobile. But in heavy and light bodies, there can be no slowing up of speed, except what the resistance of the medium causes—and in such cases Aristotle’s argument applies.

—In IV Physica lect. 12, n. 535

5. Foundations of the Modern Scientific Method

Commenting on Aristotle's De Cælo II., St. Thomas notes that there can be multiple theories explaining given observations:

Yet it is not necessary that the various suppositions which [the astronomers] hit upon be true—for although these suppositions save the appearances, we are nevertheless not obliged to say that these suppositions are true, because perhaps there is some other way men have not yet grasped by which the things which appear as to the stars are saved.

—In II De cælo, lect. 17, n. 451

Similarly, St. Thomas writes, when considering whether one can know the Trinity by natural means:

Reason may be employed in two ways to establish a point: firstly, for the purpose of furnishing sufficient proof of some principle, as in natural science, where sufficient proof can be brought to show that the movement of the heavens is always of uniform velocity. Reason is employed in another way, not as furnishing a sufficient proof of a principle, but as confirming an already established principle, by showing the congruity of its results, as in astrology the theory of eccentrics and epicycles is considered as established, because thereby the sensible appearances of the heavenly movements can be explained; not, however, as if this proof were sufficient, forasmuch as some other theory might explain them. [...]

—Summa Theologica, I, q. 32, a. 1 ad 2

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Following St. Thomas Aquinas came these people:

Robert Grosseteste (c. 1168-1253) did experiments (not yet of course with modern rigor) and was keen on using mathematics; he is known for his work on understanding the rainbow. Thomas of Bradwardine (c. 1295-1349) at Merton College Oxford introduced the distinction between mean velocity (x/t) and instantaneous velocity (dx/dt) [and he was the first to write a physics equation]. Bradwardine had an enthusiasm for empiriometric physics that started a whole school called the Merton school (his successors include: William Heytesbury, Richard Swineshead, and John Dumbleton) that was extremely influential throughout Europe. Among other things, they were known for the Merton mean speed theorem, by which they proved the correct formula for free fall distance was given by s=1/2 a t². Interestingly, both Bradwardine and Grosseteste at some point in their lives were Archbishops of Canterbury. Nicole Oresme (<1348-1382) and Giovanni di Casali (c. 1350) independently developed use of 2-D graphs [long before Descartes (1596-1650)]. Oresme described all change using these graphs in particular local motion, including calculating area (integrating) under velocity curves to get distance. Oresme's arguments for the sun-centered and moving earth were widely known: he said, for example, that "...not only is the earth so moved diurnally, but with it the water and the air, as was said, in such a way that the water and the lower air are moved differently than they are by winds and other causes. It is like this situation If air were enclosed in a moving ship, it would seem to the person situated in this air that it was not moved." (p. 133, Dales.)

—A. Rizzi's Science Before Science pgs. 199-200

Roger Bacon (1214-1294) advocated mathematics in the experimental sciences:

The neglect [of mathematics] for the past thirty or forty years has nearly destroyed the entire learning of Latin Christendom. For he who does not know mathematics cannot know any of the other sciences.

—Opus maius IV.1.1. (ed. J.H. Bridges [Oxford 1897], I, 97-98)

Quantity is the first property of anything, so to neglect that would indeed be to miss a lot. St. Thomas said that mathematics is most connatural to man, hence its development—not the introduction of experimentation, which already existed—was what has driven the scientific boom in the past 400 years. Card. Thomas of Bradwardine said this about mathematics in the sciences:

[Mathematics] reveals every genuine truth, for it knows every hidden secret, and bears the key to every subtlety of letters; whoever, then, has the effrontery to study physics while neglecting mathematics, should know from the start that he will never make his entry through the portals of wisdom.

—Tractatus de continuo MS Erfurt Amplon Q.385, fol. 31v.

Fathers of Modern Mathematics and Physics

Noting both the difficulty and the ease in investigating the truth, as does science (from Latin scire, "to know" or "to understand"), Aristotle says "that we should be grateful" to those thinkers before us, our scientific heritage:

The investigation of the truth is in one way hard, in another easy. An indication of this is found in the fact that no one is able to attain the truth adequately, while, on the other hand, we do not collectively fail, but every one says something true about the nature of things, and while individually we contribute little or nothing to the truth, by the union of all a considerable amount is amassed. Therefore, since the truth seems to be like the proverbial door, which no one can fail to hit, in this respect it must be easy, but the fact that we can have a whole truth and not the particular part we aim at shows the difficulty of it. Perhaps, too, as difficulties are of two kinds, the cause of the present difficulty is not in the facts but in us. For as the eyes of bats are to the blaze of day, so is the reason in our soul to the things which are by nature most evident of all. It is just that we should be grateful, not only to those with whose views we may agree, but also to those who have expressed more superficial views; for these also contributed something, by developing before us the powers of thought. It is true that if there had been no Timotheus we should have been without much of our lyric poetry; but if there had been no Phrynis there would have been no Timotheus. The same holds good of those who have expressed views about the truth; for from some thinkers we have inherited certain opinions, while the others have been responsible for the appearance of the former. It is right also that philosophy should be called knowledge of the truth. For the end of theoretical knowledge is truth, while that of practical knowledge is action (for even if they consider how things are, practical men do not study the eternal, but what is relative and in the present). Now we do not know a truth without its cause; and a thing has a quality in a higher degree than other things if in virtue of it the similar quality belongs to the other things as well (e.g. fire is the hottest of things; for it is the cause of the heat of all other things); so that that causes derivative truths to be true is most true. Hence the principles of eternal things must be always most true (for they are not merely sometimes true, nor is there any cause of their being, but they themselves are the cause of the being of other things), so that as each thing is in respect of being, so is it in respect of truth.

—Metaphysics 993^a30-993^b19

Who are the analogous Phrynises in science, the giants on whose shoulders we stand? Besides the obvious—e.g., Galileo, Copernicus, Newton, Kepler, Einstein—let us note some lesser-known characters. First among these is Aristotle, the first physicist (Physics) and developer of the scientific method of knowing causes through their effects (Posterior Analytics). We have mentioned him already, e.g., in this post on the dehellenization of modern science. Second is St. Thomas Aquinas, student of the pro-science patron saint St. Albert the Great, both scholastics. St. Thomas's contributions to modern scientific thought, such as his knowledge of Euclid's Elements and the empiriological sciences of at his time, display a profound respect for the scientific method and methodological naturalism. In discussing how one cannot know by natural reason that God is triune (three in one), he reflects his support of the modern scientific method, often attributed to Galileo yet more deservingly to Aristotle's Posterior Analytics. St. Thomas mentions that one can outmode scientific theories for better, truer ones, i.e., for ones that conform with reality better.

Reason may be employed in two ways to establish a point: firstly, for the purpose of furnishing sufficient proof of some principle, as in natural science, where sufficient proof can be brought to show that the movement of the heavens is always of uniform velocity. Reason is employed in another way, not as furnishing a sufficient proof of a principle, but as confirming an already established principle, by showing the congruity of its results, as in astrology the theory of eccentrics and epicycles is considered as established, because thereby the sensible appearances of the heavenly movements can be explained; not, however, as if this proof were sufficient, forasmuch as some other theory might explain them. In the first way, we can prove that God is one; and the like. In the second way, reasons avail to prove the Trinity; as, when assumed to be true, such reasons confirm it. We must not, however, think that the trinity of persons is adequately proved by such reasons. This becomes evident when we consider each point; for the infinite goodness of God is manifested also in creation, because to produce from nothing is an act of infinite power. For if God communicates Himself by His infinite goodness, it is not necessary that an infinite effect should proceed from God: but that according to its own mode and capacity it should receive the divine goodness. Likewise, when it is said that joyous possession of good requires partnership, this holds in the case of one not having perfect goodness: hence it needs to share some other's good, in order to have the goodness of complete happiness. Nor is the image in our mind an adequate proof in the case of God, forasmuch as the intellect is not in God and ourselves univocally. Hence, Augustine says (Tract. xxvii. in Joan.) that by faith we arrive at knowledge, and not conversely.

—Summa Theologica Iª q. 32 a. 1 ad. 2

St. Thomas also mentions the interplay between physics and mathematics, shedding light on the mystery of the connection between mathematics and the physical world, a topic fascinating to Einstein, who wrote:

How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality? Is human reason, then, without experience, merely by taking thought, able to fathom the properties of real things?

To the latter question, no; we have no knowledge without prior sense experience. In the former question, we can see Kant's idealism—i.e., agnosticism of an objective reality—creeping into his thought when says that mathematics is independent of experience. Our ideas of it may be independent of external sense experience, but mathematical properties of matter such as quantity exist in the objective reality outside one's mind ("intellectual soul" or simply "soul"). As Boethius says in his De Trinitate II., "Mathematics does not deal with motion and it is not abstract, for it inquires into the forms of bodies apart from matter and therefore apart from motion [viz., change], which forms, however, since they exist in matter, cannot be separated from bodies." This is how St. Thomas explains how mathematics and physics differ:

By its very nature motion is not in the category of quantity, but it partakes somewhat of the nature of quantity from another source, namely, according as the division of motion derives from either the division of space or the division of the thing subject to motion. So it does not belong to the mathematician to treat of motion, although mathematical principles can be applied to motion. Therefore, inasmuch as the principles of quantity are applied to motion, the natural scientist treats of the division and continuity of motion, as is clear in the Physics. And the measurements of motions are studied in the intermediate sciences between mathematics and natural science: for instance, in the science of the moved sphere and in astronomy. Simple bodies and their properties remain in composite bodies although in a different way, as the proper qualities of the elements and their proper movements are found in a mixed body. What is proper to composite bodies, however, is not found in simple bodies. And so it is that the more abstract and simple the objects of a science are, the more applicable its principles are to the other sciences. Thus the principles of mathematics are applicable to natural things, but not vice versa, because physics presupposes mathematics; but the converse is not true, as is clear in the De Caelo et Mundo. So there are three levels of sciences concerning natural and mathematical entities. Some are purely natural and treat of the properties of natural things as such, like physics, agriculture, and the like. Others are purely mathematical and treat of quantities absolutely, as geometry considers magnitude and arithmetic number. Still others are intermediate, and these apply mathematical principles to natural things; for instance, music, astronomy, and the like. These sciences, however, have a closer affinity to mathematics, because in their thinking that which is physical is, as it were, material, whereas that which is mathematical is, as it were, formal. For example, music considers sounds, not inasmuch as they are sounds, but inasmuch as they are proportionable according to numbers; and the same holds in other sciences. Thus they demonstrate their conclusions concerning natural things, but by means of mathematics. Therefore nothing prevents their being concerned with sensible matter insofar as they have something in common with natural science, but insofar as they have something in common with mathematics they are abstract.

—Super De Trinitate, pars 3 q. 5 a. 3 ad 5 et 6

Modern physics is what St. Thomas would call an intermediate science because it is intermediate between a truly physical science—physics as Aristotle conceived it—and mathematics, which abstracts from physical matter.

Those sciences are called intermediate sciences which take principles abstracted by the purely mathematical sciences and apply them to sensible matter. For example, perspective applies to the visual line those things which are demonstrated by geometry about the abstracted line; and harmony, that is music, applies to sound those things which arithmetic considers about the proportions of numbers; and astronomy applies the consideration of geometry and arithmetic to the heavens and its parts. However, although sciences of this sort are intermediates between natural science and mathematics, they are here said by the Philosopher to be more natural than mathematical, because each thing is named and takes its species from its terminus. Hence, since the consideration of these sciences is terminated in natural matter, then even though they proceed by mathematical principles, they are more natural than mathematical sciences. He says, therefore, that sciences of this sort are established in a way contrary to the sciences which are purely mathematical, such as geometry or arithmetic. For geometry considers the line which has existence in sensible matter, which is the natural line. But it does not consider it insofar as it is in sensible matter, insofar as it is natural, but abstractly, as was said. But perspective conversely takes the abstract line which is in the consideration of mathematics, and applies it to sensible matter, and thus treats it not insofar as it is a mathematical, but insofar as it is a physical thing. Therefore from this difference between intermediate sciences and the purely mathematical sciences, what was said above is clear. For if intermediate sciences of this sort apply the abstract to sensible matter, it is clear that mathematics conversely separates those things which are in sensible matter.

—In Physic., lib. 2 l. 3 n. 8

What makes the Catholic philosophy of St. Thomas so efficacious to the advancement of science? Catholics embrace the physical world—especially through the necessarily physical Sacraments, the physical manifestations of a hidden reality—because it is with the world, through our five external senses, that one obtains knowledge of God, a human's first Beginning and ultimate End. Catholics do not despise the human body nor do they consider it intrinsically evil. From a review of the popular science book The Tao of Physics, a book about how modern physics and Eastern thought relate:

But it is least of all to history that we should look for confirmation of Capra's thesis. In the early chapters he blames Aristotle and Christianity for the ensuing "lack of interest in the material world" (p. 22). But what cultures ever displayed a more profound and studious disregard for the material world than the Eastern mystical traditions? And why would they hold in high regard something that is at best a creation of the human mind and at worst a deceptive illusion?

Hence the philosophies of the Eastern religions are fundamentally at odds with understanding the physical world. The philosophy of the Greeks is better. E.g., the word "science" in English is equivocal; however, the Greeks distinguished ἐπιστήμη, "knowledge of an event or a thing through its causes" (Weisheipl 183), from τέχνη (art, skill, craft; root of the word "technology"), νόος (verbal: νοέω; "understood" in Rom. 1:20), and σοφία (wisdom). Thus scientific knowledge as we moderns conceive it, the ἐπιστήμη, is not the only form of knowing. Fr. Georges-Henri Lemaître—with his background in the supreme science, theology—recognized this. He was the inventor of the Big Bang theory and pupil of the cosmologist Fr. Désiré Nys at the University of Louvain, a university Pope Leo XIII established to promote St. Thomas's philosophy in the context of modern scientific discoveries. From The Heavens Proclaim: Astronomy and the Vatican:

Astronomy has long featured in Christian theology. Indeed, astronomy was one of the seven subjects of the medieval university that all scholars were expected to master before they could begin their studies of philosophy and theology. At the beginning of this book we examined two specific instances in the history of the Church and astronomy: the successful reform the calendar under Pope Gregory XIII in 1582, and the tragic conflict just fifty years later between the Church and Galileo. Here, however, we would like to take a look at more recent statements of Popes concerning the modern science of astronomy. Much of the Church’s interest has had an overt apologetic slant, using science to support its philosophical ideas or using its support of science to refute those who would accuse the Church of opposing progress and fearing newly-discovered truths. Even in Roman times, the apologetic need for the Church’s teachers to have an up-to-date knowledge of the physical universe, to give credibility to the theological truths of the Church, was evident to St. Augustine. Writing in AD 400, he commented:

Even a non-Christian knows something about the Earth, the heavens, and the other elements of this world, about the motion and orbit of the stars and even their size and relative positions, about the predictable eclipses of the Sun and Moon, the cycles of the years and the seasons... and this knowledge he holds to as being certain from reason and experience. Now, it is a disgraceful and dangerous thing for an infidel to hear a Christian, presumably giving the meaning of Holy Scripture, talking nonsense on these topics; and we should take all means to prevent such an embarrassing situation, in which people show up vast ignorance in a Christian and laugh it to scorn.

—St. Augustine's The Literal Meaning of Genesis, pgs. 42-43

The irony is, of course, that the cosmology the learned men of Rome knew so well, was the very Ptolemaic cosmology later overthrown by Copernicus and Galileo! But through the writings of these modern Popes one begins to see developing a second realization: that, as the Psalmist knew, the Heavens themselves do proclaim the greatness of the Creator. The simple act of seeking truth in the natural sciences is in and of itself a religious act, independent of any apologetic agenda. from AETERNI PATRIS, 1879 (POPE LEO XIII) In an encyclical letter proclaimed in 1879, subtitled “On the Restoration of Christian Philosophy in Catholic Schools in the Spirit (ad mentem) of the Angelic Doctor, St. Thomas Aquinas,” Pope Leo XIII endorsed the study of scholastic philosophy and ignited a new interest in the rational understanding of the faith. In passing, he reflects on the role of the physical sciences, in a way that foreshadows his establishment, twelve years later, of the Vatican Observatory itself:

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.

THE REFOUNDATION AND RESTRUCTURING OF THE VATICAN OBSERVATORY, 1891 (POPE LEO XIII) Here is the text of Leo XIII’s Motu Proprio [Ut mysticam Sponsam], a personal decree that re-established the Vatican Observatory. In it he explains the apologetic need for supporting a scientific institution at that time, and also outlines the previous history of papal support for astronomy.

So that they might display their disdain and hatred for the mystical Spouse of Christ, who is the true light, those borne of darkness are accustomed to calumniate her to unlearned people and they call her the friend of obscurantism, one who nurtures ignorance, an enemy of science and of progress, all of these accusations being completely contrary to what in word and deed is essentially the case. Right from its beginnings all that the Church has done and taught is an adequate refutation of these impudent and sinister lies. In fact, the Church, besides her knowledge of divine realities, in which she is the unique teacher, also nourishes and gives guidance in the practice of philosophy which is essential to understanding the scientific foundations of knowing – to make its principles clear, to suggest the criteria necessary for rigorous research and for a systematic presentation of the results, to investigate the soul’s faculties, to study life and human behavior – and she does this so well that it would be difficult to add anything worth mentioning and it would be dangerous to dissociate oneself from her teachings. Furthermore, it is to the great merit of the Church that the legal code has been completed and perfected, nor can we ever forget how much she has contributed through her doctrine, her example and her institutions to addressing the complex issues arising in the so-called social sciences and in economics. In the meantime the Church has not neglected those disciplines which investigate nature and its forces. Schools and museums have been founded so that young scholars might have a better opportunity to deepen those studies. Among the Church’s children and ministers there are some illustrious scientists whom the Church has honored and assisted as much as she could by encouraging them to apply themselves with complete dedication to such studies. Among all of these studies astronomy holds a preeminent position. It proposes to investigate those inanimate creatures which more than all others proclaim the glory of God and which gave marvelous delight to the wisest of beings, the one who exulted in his divinely inspired knowledge, especially of the yearly cycles and of the positions of the heavenly bodies (Wisdom VII.19). The Church’s pastors were motivated, among other considerations, to see to progress in this science and to support its followers by the possibility that it alone offered to establish with certainty those days on which the principal religious solemnities of the Christian mystery should be celebrated. So it was that the Fathers at Trent, well aware that the calendar reform done by Julius Caesar had not been perfect so that time calculations had changed, urgently requested that the Roman Pontiff would, after consulting experts in the field, prepare a new and more perfect reform of the calendar. It is well known from historical documents how zealously and generously committed was Our Predecessor Gregory XIII in responding to this request. He saw to it that at the place judged to be best for an observatory within the confines of the existing Vatican buildings an observing tower was constructed and he equipped it with the best instruments of those days. It was here that he held the meetings of the experts he had selected for the reform of the calendar. This tower still exists today and it brings back the memory of its illustrious and generous founder. The meridian constructed by Ignazio Danti from Perugia is to be found there. Along the meridian line there is a round marble tablet whose lines are designed with such wisdom that when the suns rays fall on them it becomes obvious how necessary it was to reform the old calendar and how well the reform conformed to nature. That tower, a splendid memory to a Pontiff who is to be much praised for his contribution to the progress of literary and scientific studies, was, toward the end of the last century after a long period of inactivity, restored to its original use as an astronomical observatory by the auspicious orders of Pius VI. Through the initiatives of a Roman Monsignor Filippo Gilii, other types of research were also undertaken on terrestrial magnetism, meteorology and botany. But, after the death in 1821 of this very capable scientist, this monument to astronomical research went into neglect and was abandoned. Right after this Pius VII died and the energies of Leo XII were completely taken up with the reform of studies in the worldwide Church, a huge undertaking aimed at promoting all branches of learning. Such a reform, which had already been planned by his immediate and immortal predecessor, came by his efforts to a happy ending with the Apostolic Letter, Quod divina sapientia. In this letter he established certain rules with respect to astronomical observatories, the observations which were to be made regularly, the daily list of data to be made, and the information that was to be distributed internally concerning discoveries made by others. The fact that the tower in the Vatican was no longer used as an observatory, after others in Rome had been equipped for that very purpose, came about because those who were competent to judge were of the opinion that the nearby buildings, and especially the dome which crowns the Vatican basilica, would have obstructed observations. And so it was deemed preferable to have observatories in other higher places where unobstructed observations could be carried out. It then happened that, after those observing sites along with the whole city of Rome fell into the hands of others, we were given, on the occasion of our 51st anniversary as a priest, many excellent instruments for research in astronomy, meteorology, and earth physics, as well as other gifts. It was the opinion of the experts that no place was better to house them than the Vatican tower, where, it seems, Gregory XIII had already in some way made preparations. After having evaluated this proposal and having examined the structure itself of the building, the history of its past glories, and the equipment already gathered there, as well as the opinions of persons renowned for their knowledge and judgement, we were persuaded to give orders that the observatory be restored and that it be equipped with all that would be required to carry out research not only in astronomy but also in earth physics and in meteorology. As to the lack of an unobstructed view of the heavens in all directions from this Vatican tower, we saw fit to consider providing the nearby ancient and solid Leonine fortification where there is a quite high tower which, since it rises on the summit of the Vatican hill, provides for complete and perfect observation of the heavenly bodies. We, therefore, added this tower to the one of Gregory and we had installed there the large equatorial telescope for photographing the stars. To this purpose we chose conscientious men, prepared to do all that was necessary for such an undertaking, and we proposed to them a most competent scholar in astronomy and physics, Father Francesco Denza of the Clerks Regular of Saint Paul, also called the Barnabites. Relying on their dedicated work, we agreed wholeheartedly that the Vatican Observatory be chosen to collaborate with other renowned astronomical institutes in the project to reproduce from photographic plates an accurate map of the whole sky. Considering the fact that we wish this work of restoring the Specola to be a lasting one and not one that terminates after a short time, we have established bylaws for it with rules to be observed both for internal administration and for the services which others require of it. Furthermore, we have appointed a Board of carefully selected persons whose responsibility it is to govern the observatory and they have the highest authority after our own for all decisions respecting the internal administration. And so with the present letter we confirm those bylaws and that Board and we also assign the various jobs and all that, with our order or consent, has been done with respect to the Specola. And we desire that the Specola be considered at the same level as the other Pontifical Institutes founded to promote the sciences. In order to provide in a more secure way for the stability of this work, we even designate a sum of money which should suffice to cover the expenses required to keep it operating and to maintain it. Nevertheless, we trust that such a work will find its justification and support in the favor and help of Almighty God more than in what humans can do. In fact, in taking up this work we have become involved not only in helping to promote a very noble science which, more than any other human discipline, raises the spirit of mortals to the contemplation of heavenly events, but we have in the first place put before ourselves the plan which we have energetically and constantly sought to carry out right from the beginning of Our Pontificate in talks, writings, and deeds whenever we were provided the opportunity. This plan is simply that everyone might see clearly that the Church and her Pastors are not opposed to true and solid science, whether human or divine, but that they embrace it, encourage it, and promote it with the fullest possible dedication. We wish, therefore, that everything that has been established and announced in the present letter will remain into the future confirmed and ratified as it is proposed herein and we declare null and void any attempt at changes by whatsoever person. And it remains established and confirmed, despite any previous contrary declaration.

Given in Rome at St. Peter’s, 14 March 1891

Pope Leo XIII, through his establishing the Catholic University at Louvain and the Vatican Observatory, was a very pro-science pope. Even our current pope, Benedict XVI, has been very pro-science. Thus the fathers of modern mathematics and physics have been true (albeit ordained) Catholic fathers!