Feynman on The Relation of Mathematics & Physics and on Probability & Uncertainty in Quantum

Lectures in 1964:

Cf. Thomism & Mathematical Physics.


Interestingly, although he says quantum is nothing like anything we have seen before, he later goes on saying that we can understand it in analogy to what we do know (cf. The interpretation of St. Thomas Aquinas of Aristotle, Physica 191a7-8: "The underlying nature is known by analogy.", available from ProQuest Theses). New knowledge must be party based on what we already know (cf. Expositio Posteriorum, lib. 1 l. 1 n. 1: "The need for pre-existent knowledge in all learning").

Work of a "learned Benedictine philosopher-scientist"

John Deely calls Joseph Gredt a "learned Benedictine philosopher-scientist." Here is his major work:



Go here for an online version of the latest edition of Gredt:
Elementa philosophiae Aristotelico-Thomisticae vol. 1 (logica & philosophia naturalis) and vol. 2 (metaphysica, theologia naturalis, ethica).

There's a "full screen" option, and you can even download a PDF if you register for free with Gloria.tv.

Another manual-style series similar to Gredt's is Édouard Hugon's:
Cursus Philosophiæ Thomisticæ I (PDF)
Cursus Philosophiæ Thomisticæ II (PDF)
Cursus Philosophiæ Thomisticæ III (PDF)

Nov. 15: Albertus Magnus

I am a day late posting about St. Albert the Great (Albertus Magnus), but here it is:

Albertus Magnus, Saint

also known as Albert the Great and Universal Doctor

(b. Lauingen, Bavaria, ca. 1200; d. Cologne, Prussia, 15 November 1280). Proficient in all branches of science, he was one of the most famous precursors of modern science in the High Middle Ages.

Albert was born in the family castle and probably spent his childhood at the family manor in nearby Bollstädt—whence he is variously referred to as Albert of Lauingen and Albert of Bollstädt. His birth date could have been as early as 1193 or as late as 1206 or 1207. His family was wealthy and powerful, of the military nobility, and he received a good education.

He studied liberal arts at Padua, where, over strong opposition from his family, he was recruited into the Dominican Order by its master general, Jordan of Saxony—identified by some (but probably falsely) as Jordanus de Nemore, the mechanician. He likely studied theology and was ordained a priest in Germany, where he also taught in various priories before being sent to the University of Paris ca. 1241. In Paris he was the first German Dominican to become a master of theology and to lecture in the chair “for foreigners” (1245–1248). In the summer of 1248 he went to Cologne to establish a studium generale: among his students were Thomas Aquinas, Ulrich of Strassburg, and Giles (Aegidius) of Lessines.

He began the administrative phase of his career as provincial of the German Dominicans (1253–1256). Subsequently he became bishop of Regensburg (1260), a post he resigned in 1226. in 1262. The latter part of his life was spent in preaching and teaching, mainly at Cologne. He took part in the Council of Lyons (1274) and journeyed to Paris in an unsuccessful attempt to block the famous condemnation of 1277, where some of Aquinas’ teachings were called into question. His health was good and he had great powers of physical endurance, even to old age, although his eyesight failed during the last decade of his life. Albert was canonized by Pope Pius XI on 16 December 1931 and was declared the patron of all who cultivate the natural sciences by Pope Pius XII on 16 December 1941.

Albert’s principal importance for the history of modern science derives from the role he played in rediscovering Aristotle and introducing Greek and Arab science into the universities of the Middle Ages. Before his time, what was to become the subject matter of modern science was usually treated in encyclopedias, which assembled a curious mélange of fact and fable about nature, or in theological treatises, which described the cosmos in terms of the six days of creation, as recounted in Genesis and variously analyzed by the church fathers. Aristotle, of course, had already made his entry into the Latin West through the translations of Gerard of Cremona and James of Venice, among others; but Christendom was generally hostile to the teachings of this pagan philosopher, particularly as contained in his libri naturales (“books on natural science”). In 1210, the ecclesiastical authorities at Paris had condemned Aristotle’s works on natural philosophy and had prohibited their being taught publicly or privately under pain of excommunication. Although this condemnation was revoked by 1234, it had a general inhibiting effect on the diffusion of Greek science in the schools of the Middle Ages.

Albert seems to have become acquainted with the Aristotelian corpus while at the Paris priory of St. Jacques in the 1240’s. Here too he probably began his monumental paraphrase of all the known works of Aristotle and Pseudo-Aristotle, to which are allotted seventeen of the forty volumes in the Cologne critical edition of Albert’s works (see Bibliography). The project was undertaken by Albert, then studying and teaching theology, at the insistence of his Dominican brethren, who wished him to explain, in Latin, the principal physical doctrines of the Stagirite so that they could read his works intelligently. Albert went far beyond their demands, explaining not only the natural sciences but also logic, mathematics, ethics, politics, and metaphysics, and adding to Aristotle’s exposition the discoveries of the Arabs and of whole sciences that were not available to him. The gigantic literary production that this entailed was recognized as one of the marvels of his age and contributed in no small measure to Albert’s outstanding reputation. Roger Bacon, a contemporary who was not particularly enamored of the German Dominican, complained of Master Albert’s being accepted as an authority in the schools on an equal footing with Aristotle, Avicenna, and Averroës—an honor, he protested, “never accorded to any man in his own lifetime.”

Like all medieval Aristotelians, Albert incorporated considerable Platonic thought into his synthesis, and even commented on a number of Neoplatonic treatises. In several places he represents himself as merely reporting the teachings of the Peripatetics and not as proposing anything new; some historians charge him, on this basis, with being a compiler who was not too judicious in his selection of source materials. Those who have studied his works, however, detect there a consistent fidelity to Aristotle’s basic theses, a clear indication of his own views when he thought Aristotle in error, a repudiation of erroneous interpretations of Aristotle’s teaching, and an explicit rejection of Platonic and Pythagorean physical doctrines—all of which would seem to confirm his Aristotelianism. J. A. Weisheipl, in particular, has stressed the differences between thirteenth-century Oxford masters such as Robert Grosseteste, Robert Kilwardby, and Roger Bacon (all of whom were more pronouncedly Platonist in their scientific views) and Paris masters such as Albert and Aquinas (who were more purely Aristotelian). Whereas the former held that there is a successive subalternation between physics, mathematics, and metaphysics (so that the principles of natural science are essentially mathematical, and the principle of mathematics is the unity that is identical with Being), the latter held for the autonomy of these sciences, maintaining that each has its won proper principles, underived from any other discipline.

Albert’s early identification as a precursor of modern science undoubtedly stemmed from his empiricist methodology, which he learned from Aristotle but which he practiced with a skill unsurpassed by any other Schoolman. From boyhood he was an assiduous observer of nature, and his works abound in descriptions of the phenomena he noted, usually in great detail. Considering that his observations were made without instruments, they were remarkably accurate. Some of the “facts” he reported were obviously based on hearsay evidence, although he was usually at pains to distinguish what he had himself seen from what he had read or been told by others. Fui et midi experiri (“I was there and saw it happen”) was his frequent certification for observations. Sometimes, as Lynn Thorndike has well illustrated in his A History of Magic and Experimental Science, even these certifications test the reader’s credulity; what is significant in them, however, is Albert’s commitment to an empiricist program. He stated that evidence based on sense perception is the most secure and is superior to reasoning without experimentation. Similarly, he noted that a conclusion that is inconsistent with the evidence cannot be believed and that a principle that does not agree with sense experience is really no principle at all. He was aware, however, that the observation of nature could be difficult: much time, he remarked, is required to conduct an experiment that will yield foolproof results, and he suggested that it be repeated under a variety of circumstances so as to assure its general validity.

On the subject of authority, he pointed out that science consists not in simply believing what one is told but in inquiring into the causes of natural things. He had great respect for Aristotle, but disagreed with the Averroists of his day on the Stagirite’s infallibility. “Whoever believes that Aristotle was a god, must also believe that he never erred. But if one believes that he was a man, then doubtless he was liable to error just as we are.” His Summa theologica, for example, contains a section listing the errors of Aristotle, and in his Meteorology he observes that “Aristotle must have spoken from the opinions of his predecessors and not from the truth of demonstration or experiment,”

Albert recognized the importance of mathematics for the physical sciences and composed treatises (unfortunately lost) on its pure and applied branches. Yet he would not insist that the book of nature is written in the language of mathematics, as Galileo was later to do, and as Roger Bacon intimated in his own lifetime. Rather, for Albert, mathematics had only a subsidiary role to play in scientific activity, insofar as it assisted in the discovery of physical causes. Mathematics is itself an abstract science, prescinding from motion and sensible matter, and thus its applications must be evaluated by the science that studies nature as it really exists, in motu et inabstracta (“in motion and in concrete detail”).

The mechanics of Albert was basically that of Aristotle, with little innovation in either its kinematical or its dynamical aspects. One part of Albert’s teaching on motion, however, did assume prominence in the late medieval period and influenced the emerging new science of mechanics. This was his use of the expressions fluxus formae and forma fhtens to characterize the scholastic dispute over the entitative status of local motion. Arab thinkers such as Avicenna and Averroës had pursued the question whether this motion, or any other, could be located in the Aristotelian categories; the question quickly led to an argument whether motion is something really distinct from the terminus it attains. Local motion, in this perspective, could be seen in one of two ways: either it was a fluxus formae (the “flowing” of successive forms, or locations) or a forma fluens (a form, or absolute entity, that is itself a process). Although Albert made no clear dichotomy between these two views and allowed that each described a different aspect of motion, later writers came to be sharply divided over them. Nominalists, such as William of Ockham, defended the first view: this equivalently denied the reality of local motion, equating it simply with the distance traversed and rejecting any special causality in its production or continuance—a view that stimulated purely kinematical analyses of motion. Realists, such as Walter Burley and Paul of Venice, on the other hand, defended the second view: for them, local motion was an entity really distinct from the object moved and from its position, and thus had its own proper causes and effects—a view that stimulated studies of its more dynamical aspects.

Albert mentioned the term impetus when discussing projectile motion, but spoke of it as being in the medium rather than in the projectile, thus defending the original Aristotelian teaching; certainly he had no treatment of the concept to match that found in the work of fourteenth-century thinkers. His analysis of gravitational motion was also Aristotelian: he regarded the basic mover as the generator of the heavy object, giving it not only its substantial form but also its gravity and the motion consequent on this. He knew that bodies accelerate as they fall, and attributed this to their increasing propinquity to their natural place.

The cause of sound, for Albert, is the impact of two hard bodies, and the resulting vibration is propagated in the form of a sphere whose center is the point of percussion. He speculated also on the cause of heat, studying in detail how light from the sun produces thermal effects; here his use of simple experiments revealed a knowledge of the method of agreement and difference later to be formulated by J.S. Mill. He knew of the refraction of solar rays and also of the laws of refraction of light, although he employed the term reflexio for both refraction and reflection, as, for example, when discussing the burning lens and the burning mirror. His analysis of the rainbow was diffuse in its historical introduction, but it made an advance over the theory of Robert Grosseteste in assigning individual raindrops a role in the bow’s formation, and undoubtedly prepared for the first correct theory of the rainbow proposed by another German Dominican, Dietrich von Freiberg, who was possibly Albert’s student. In passing, he corrected Aristotle’s assertion that the lunar rainbow occurs only twice in fifty years: “I myself have observed two in a single year.”

Although he had no telescope, he speculated that the Milky Way is composed of stars and attributed the dark spots on the moon to configurations on its surface, not to the earth’s shadow. His treatise on comets is notable for its use of simple observation to verify or falsify theories that had been proposed to explain them. He followed Grosseteste in correlating the occurrence of tides with the motion of the moon around its deferent. He favored the mathematical aspects of the Ptolemaic theory of the structure of the solar system, contrasting it with that of al-Bịtrūjī, although he acknowledged the superiority of the latter’s theory in its physical aspects. Albert accepted the order of the celestial spheres commonly taught by Arabian astronomers; he knew of the precession of the equinoxes, attributing knowledge of this (falsely) to Aristotle also. Like most medieval thinkers, Albert held that heavenly bodies are moved by separated substances, but he denied that such substances are to be identified with the angels of Christian revelation, disagreeing on this point with his celebrated disciple Thomas Aquinas.

On the structure of matter, when discussing the presence of elements in compounds, Albert attempted to steer a middle course between the opposed positions of Avicenna and Averroës, thereby preparing for Aquinas’ more acceptable theory of “virtual” presence. In a similar vein, he benignly viewed Democritus’ atoms as equivalent to the minima naturalia of the Aristotelians. He seems to have experimented with alchemy and is said to have been the first to isolate the element arsenic. He compiled a list of some hundred manerals, giving the properties of each. During his many travels, he made frequent sidetrips to mines and excavations in search of specimens. He was acquainted with fossils, and made accurate observations of “animal impressions” and improved on Avicenna’s account of their formation. Albert suggested the possibility of the transmutation of metals, but he did not feel that alchemists had yet found the method to bring this about.

Extensive as was Albert’s work in the physical sciences, it did not compare with his contributions to the biological sciences, where his powers of observation and his skill at classification earned for him an unparalleled reputation. Some aspects of his work have been singled out by A.C. Crombie as “unsurpassed form Aristotle and Theophrastus to Cesalpino and Jung,” His De vegetabilibus et plantis, in particular, is a masterpiece for its independence of treatment, its accuracy and range of detailed description, its freedom from myth, and its innovation in systematic classification. His comparative study of plants extended to all their, parts and his digressions show a remarkable sense of morphology and ecology. He drew a distinction between thorns and prickles on the basis of their formation and structure, classified flowers into the celebrated three types (bird-form, bell-form, and star-form), and made an extensive comparative study of fruits. His general classification of the vegetable kingdom followed that proposed by Theophrastus: he ranged plants on a scale reaching from the fungi to the flowering types, although, among the latter, he did not explicitly distinguish the monocotyledons from the dicotyledons. He seems to have been the first to mention spinach in Western literature, the first to note the influence of light and heat on the growth of trees, and the first to establish that sap (which he knew was carried in veins—like blood vessels, he said, but without a pulse) is tasteless in the root and becomes flavored as it ascends.

On plant evolution, Albert proposed that existing types were sometimes mutable and described five ways of transforming one plant into another; he believed, for example, that new species could be produced by grafting. Here he registered an advance over most medieval thinkers, who accounted for the succession of new species not by modification but by generation from a common source such as earth.

Albert’s De animalibus includes descriptions of some fabulous creatures, but it also rejects many popular medieval myths (e.g., the pelican opening its breast to feed its young) and is especially noteworthy for its sections on reproduction and embryology. Following Aristotle. Albert distinguished four types of reproduction; in sexual reproduction among the higher animals he taught that the material produced by the female was like a seed (a humor seminalis), differentiating it from the catamenia (menstruum) in mammals and the yolk of the egg in birds, but incorrectly identifying it with the white of the egg. The cause of the differentiation of the sexes, in his view, was that the male “vital heat” could “concoct” semen out of surplus blood, whereas the female was too cold to effect the change.

He studied embryology by such simple methods as opening eggs at various intervals of time and tracing the development of the embryo from the appearance of the pulsating red speck of the heart to hatching. He was acquainted, too, with the development of fish and mammals, and understood some aspects of fetal nutrition. His studies on insects were especially good for their descriptions of insect mating, and he correctly identified the insect egg. He showed that ants lose their sense of direction when their antennae are removed, but concluded (wrongly) that the antennae carry eyes.

Among the larger animals, he described many northern types unknown to Aristotle, noting changes of coloration in the colder climates, and speculating that if any animals inhabited the poles they would have thick skins and be of a white color. His knowledge of internal anatomy was meager, but he did dissect crickets and observed the ovarian follicles and tracheae. His system of classification for the animal kingdom was basically Aristotelian; occasionally he repeated or aggravated the Stagirite’s mistakes, but usually he modified and advanced Aristotle’s taxonomy, as in his treatment of the ten genera of water animals. His anthropology was more philosophical than empirical in intent, but some have detected in it the adumbration of methods used in experimental psychology.

Apart from these more speculative concerns, Albert made significant contributions also to veterinary and medical science, dentistry included. In anatomy, for example, he took the vertebral column as the basis for structure, whereas in his day and for long afterward most anatomists began with the skull. He was reported to have cures for all manner of disease, and despite his own repudiation of magic and astrology came to be regarded as something of a magician. Many spurious works, some utterly fantastic, were attributed to him or published under his name to assure a wide diffusion—among these are to be included the very popular De secretis mulierum (“On the Secrets of Women”) and other occult treatises.

Albert’s productivity in science was matched by a similar output in philosophy and theology. In these areas his teachings have been overshadowed by those of his most illustrious disciple, Thomas Aquinas. The latter’s debt to Albert is, of course, considerable, for Aquinas could well attribute the extent of his own vision to the fact that he stood on the shoulders of a giant.

BIBLIOGRAPHY

I. Major Works and Writings. Standard editions include Omnia opera, B. Geyer, ed. (Cologne, 1951), a critical edition, in progress, 40 vols.; Vol, XII (1955) is the only work of direct scientific interest to appear thus far; it contains the Quaestiones super de animalibus and other treatises related to Alberdt’s work in zoology; Omnia opera. A. Borgnet, ed. (Paris, 1890–1899), 38 quarto vols.; Omnia opera, P. Jammy, ed. (Lyons, 1651), 21 folio vols., available on microfilm positives from the Vatican Library; his Book of Minerals is translated from the Latin by Dorothy Wychoff (Oxford, 1967). Special texts include H. Stadler, ed., “Albertus Magnus De animalibus libri XXVI,” in Beiträge zur Geschichte der Philosophie des Mittelalters, 15–16 (Münster, 1916; 1921); L. Thorndike, Latin Treatises on Comets Between 1238 and 1368 A.D. (Chicago, 1950), pp. 62–76; J.A. Weisheipl, “The Problema Determinata XLIII ascribed to Albertus Magnus (1271),” in Mediaeval Studies, 22 (1960), 303–354.

II.Secondary Literature. For a compact summary of Albert’s life and works, with bibliography, see J.A. Weisheipl, “Albert the Great (Albertus Magnus), St.,” in the New Catholic Encyclopedia (New York, 1967). Biographies include S.M. Albert, Albert the Great (Oxford, 1948) and T. M. Schwertner, St. Albert the Great (Milwaukee. 1932), a fuller biography with indication of sources. Works concerned with scientific teachings include H. Balss, Albertus Magnus als Biologe (Stuttgart, 1947); M. Barbado, Introduction á la psychologie expérimentale, P. Mazoyer, trans. (Paris, 1931), pp. 114–189; C.B. Boyer, The Rainbow: From Myth to Mathematics (New York, 1959), esp. pp.94–99; A.C. Crombie, Medieval and Early Modern Science, I (New York, 1959), esp. 147–157; A.C. Crombie. Robert Grosseteste and the Origins of Experimental Science (Oxford, 1953), esp. pp. 189–200; E.J. Dijksterhuis, The Mechanization of the World Picture, C., Dikshoorn, trans, (Oxford, 1961); P. Duhem, Le systéme du monde, III (Paris, 1914; reprinted, 1958), 327–345; A. Maier, Die Vorlaüfer Galileis im 14. Jahrhundert, Edizioni di Storia e Letteratura, 22 (Rome, 1949), 11–16, 183–184; L. Thorndike, A History of Magicand Experimental Science II (New York, 1923), esp. pp. 517–592 J.A. Weisheipl, The Development of Physical Theory in the Middle Ages (London, 1959); J.A. Weisheipl “Celestial Movers in Medival Physics” in The Thomist, 24 (1961), 286–326 See also Serta Albertina, a special issue of the Roman periodical Angelicum, 21 (1944), 1–336, devoted to all branches of Albert’s science: includes a bibliography classified by field.

William A. Wallace, O.P.

—"Albertus Magnus, Saint." Complete Dictionary of Scientific Biography. 2008.

Protestantism: Reason is Devil's Greatest Whore

The arch-heretic Martin Luther wrote (Erlangen Edition v. 16, pp. 142‐148):

Reason is the Devil’s greatest whore; by nature and manner of being she is a noxious whore; she is a prostitute, the Devil’s appointed whore; whore eaten by scab and leprosy who ought to be trodden under foot and destroyed, she and her wisdom… Throw dung in her face to make her ugly. She is and she ought to be drowned in baptism… She would deserve, the wretch, to be banished to the filthiest place in the house, to the closets.

If by "reason" he means so-called "reason"—really vain philosophy and deceit (cf. Col. 2:8)—that contradicts the true faith, then he is correct, but this is not the way many have interpreted him, such as G. K. Chesterton.

This is one of many reasons why Protestantism is a heresy according to the Roman Catholic Church; Protestantism teaches the heresy of fideism, viz., that reason and faith are opposed to one another. The Catholic Church infallibly teaches the contrary in Dei Filius:

not only can faith and reason never be opposed to one another, but they are of mutual aid one to the other; for right reason demonstrates the foundations of faith, and, enlightened by its light cultivates the science of things divine; while faith frees and guards reason from errors, and furnishes it with manifold knowledge. So far, therefore, is the Church from opposing the cultivation of human arts and sciences, that it in many ways helps and promotes it. For the Church neither ignores nor despises the benefits of human life which result from the arts and sciences, but confesses that, as they came from God, the Lord of all science, so, if they be rightly used, they lead to God by the help of his grace. Nor does the Church forbid that each of these sciences in its sphere should make use of its own principles and its own method; but, while recognizing this just liberty, it stands watchfully on guard, lest sciences, setting themselves against the divine teaching, or transgressing their own limits, should invade and disturb the domain of faith.

"What about the Galileo affair?", you might object. To which I would reply, "The Lutherans, in agreement with their arch-heretic founder's calling reason the devil's greatest whore, excommunicated Kepler a hundred years before the Galileo affair. The Catholic Church, fighting their Counter-Reformation against the anti-reason Protestants, merely put Galileo in 'house arrest', which was nothing more than a paid retirement during which he composed his greatest scientific work, The Two New Sciences."

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.

St. Thomas a Preformationist

From De Principiis Naturæ you can clearly tell that—contrary to many claims that St. Thomas agreed with Aristotle that a human fetus temporally first has a vegetative, sensitive, then intellectual soul—St. Thomas was a "preformationist" as opposed to an "epigeneticist" (cf. this), viz., he argues that man is a substance, a substantial whole, more than just a sum of his parts, more than a collection of accidental forms:

4. [...] matter differs from subject because the subject is that which does not have existence by reason of something which comes to it, rather it has complete existence of itself (per se); just as man does not have existence through whiteness [or through any other accidental forms that comprise man, e.g., his bones, brain, etc.].

[...]

6. [...] Generation simpliciter corresponds to the substantial form [that man is generated simpliciter corresponds to preformationism] and generation secundum quid [This is how epigeneticists think man is generated.] corresponds to the accidental form. When a substantial form is introduced we say that something comes into being simpliciter, for example we say that man comes into being or man is generated [something]. But when an accidental form is introduced, we do not say that something comes into being simpliciter, but that it comes into being as this; for example when man comes into being as white, we do not say simpliciter that man comes into being or is generated, but that he comes into being or is generated as white [somehow].

Ptolemy & Homer

Some people think Copernicus's model of planetary orbits was able to "save the appearances" of elliptical orbits where the older theory of Ptolemy's epicycles was not and this was why the Copernican model gained scientific consensus. This is not true, especially since there were at least five competing theories at the time. In fact Kepler's 3 Laws were originally mathematical approximations of Ptolemy's epicycles. Epicycles can reproduce any orbit, even this complex one, which required 1,000 epicycles:

What the ancients called epicycles we would today call a complex Fourier series. For the mathematical formalism, see Hanson's Isis article; cf. also Christián Carman's “Deferentes, epiciclos y adaptaciones.”

We can understand why

Reason may be employed in two ways to establish a point: firstly, for the purpose of furnishing sufficient proof of some principle [...]. 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 astronomy 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

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

Relatively Relativist

From a real conversation at 1 min. 20 sec. into the video:

"Why is natural law and homosexuality relative? It's completely self-evident."
"You want me to become a relativist. I don't want to become a relativist."
"No, I don't even agree with the fact that you're saying I'm a relativist."
"So you're relatively relativist?"
"Yeah."

Cf. Searle's "Refutation of Relativism."

Atheism & its Scientific Pretensions by David Belinski

Six 24-Hour Days?

Many scientists are justifiably scandalized by Christian Fundamentalists' assertion that the world had to have begun ~10,000 years ago and that it only took six 24-hour periods to come into existence. This assertion is wrong in two respects: (a) The Hebrew word םוי ("yom") in Genesis can either mean a 24-hour period or an indefinite length of time, and (b) if God did stop creating the universe after six days, it would no longer exist today; this is because God creates with creatio ex nihilo ("creation out of nothing"), creation in its true sense and proper only to God, Who sustains everything in existence. So these Fundamentalists have an incorrect understanding both of the literal sense of Genesis and of creation.

Dr. Ludwig Ott summarizes the Catholic perspective, which opposes that of Fundamentalist Christians, in his Fundamentals of Catholic Dogma (pp. 93-94):

The Divine Work of Creation

chapter 1

Revealed Doctrine concerning Material Things, i.e., Christian Cosmology

§ 11. The Biblical Hexahemeron (The Six Days of Creation)

1. General Principles

In order to solve the difficulties deriving from the apparent contradiction between the results of natural science and the Biblical narrative of the Creation the following general principles are to be observed:

a) Even though all Holy Writ is inspired and is the Word of God, still, following St. Thomas (Sent. II d. 12 q. 1 a. 2), a distinction must be made between that which is inspired per se, and that which is inspired per accidens. As the truths of Revelation laid down in Holy Writ are designed to serve the end of religious and moral teaching, inspiration per se extends only to the religious and moral truths. The profane facts of natural science and history contained in Holy Writ are not inspired per se, but only per accidens, that is, by virtue of their relation to the religious-moral truths. The data inspired per accidens is also the Word of God, and consequently without error. However, as the hagiographers in profane things make use of a popular, that is, a non-scientific form of exposition suitable to the mental perception of their times, a more liberal interpretation, is possible here. The Church gives no positive decisions in regard to purely scientific questions, but limits itself to rejecting errors which endanger faith. Further, in these scientific matters there is no value in a consensus of the Fathers since they are not here acting as witnesses of the Faith, but merely as private scientists.

b) Since the findings of reason and the supernatural knowledge of Faith go back to the same source, namely to God, there can never be a real contradiction between the certain discoveries of the profane sciences and the Word of God properly understood. The Vatican Council declared: Nulla unquam inter fidem et rationem vera dissensio esse potest. D 1797.

2. Decisions of the Bible Commission (30/6/1909)

a) The first three Chapters of Genesis contain narratives of real events (rerum vere gestarum narrationes quae scilicet obiectivae realitati et historicae veritati respondeant), no myths, no mere allegories or symbols of religious truths, no legends. D 2122.

b) In regard to those facts, which touch the foundations of the Christian religion (quae christianae religionis fundamenta attingunt), the literal historical sense is to be adhered to. Such facts are, inter alia, the creation of all things by God in the beginning of time, and the special creation of humanity. D 2123.

c) It is not necessary to understand all individual words and sentences in the literal sense (sensu proprio). Passages which are variously interpreted by the Fathers and by theologians, may be interpreted according to one’s own judgment with the reservation, however, that one submits one’s judgment to the decision of the Church, and to the dictates of the Faith. D 2124 et seq.

d) As the Sacred Writer had not the intention of representing with scientific accuracy the intrinsic constitution of things, and the sequence of the works of creation but of communicating knowledge in a popular way suitable to the idiom and to the pre-scientific development of his time, the account is not to be regarded or measured as if it were couched in language which is strictly scientific (proprietas scientifici sermonis). D 2127.

e) The word “day” need not be taken in the literal sense of a natural day of 24 hours, but can also be understood in the improper sense of a longer space of time. D 2128. Cf. the whole letter of the Secretary of the Bible Commission to Cardinal Suhard, dated 16th January, 1948 (D 3002).

3. Explanation of the Work of the Six Days

The Biblical account of the duration and order of Creation is merely a literary clothing of the religious truth that the whole world was called into existence by the creative word of God. The Sacred Writer utilised for this purpose the pre-scientific picture of the world existing at the time. The numeral six of the days of the Creation is to be understood as an anthropomorphism. God’s work of creation represented in schematic form (opus distinctionis—opus ornatus) by the picture of a human working week, the termination of the work by the picture of the Sabbath rest. The purpose of this literary device is to manifest Divine approval of the working week and the Sabbath rest. Cf. Ex. 20:8 et seq.

The many theories which have been evolved to explain the Biblical Hexahemeron (the six days of Creation), fall into two groups. The former regard Gn. 1, as giving a historical account of the duration and sequence of the works of creation (realistic theories). The second group sacrifices the historicity of the narrative concerning the duration and sequence of the works of the Creation, and in order to avoid conflict with natural science, assumes that the division of the six working days derives from the imagination of the Sacred Writers (idealistic theories). To the former group belong those who hold the “Verbal Theory,” which is expounded by most of the Fathers and Schoolmen, the “Restitution Theory,” the “Sin Flood Theory,” and the various “Concordance Theories,” which explain the six days of Creation as six periods of creation. To the second group belong the “Allegorism of St. Augustine,” “The Vision Theory,” “Poetism,” “The Anthropomorphistic Explanation,” mentioned above, and “Mythism,” which has been rejected by the Church (D 2122).

§ 12. The Doctrine of Evolution in the Light of the Revelation

1. The materialist doctrine of evolution (E. Haeckel) which assumes the eternal existence of uncreated material, and which explains the emergence of all living creatures, of plants and animals and also of men, both body and soul, through purely mechanical evolution out of this material, is contrary to Revelation, which teaches the creation of the material and its formation by God in time.

2. The doctrine of evolution based on the theistic conception of the world, which traces matter and life to God’s causality and assumes that organic being, developed from originally created seed-powers (St. Augustine) or from stemforms (doctrine of descent), according to God’s plan, is compatible with the doctrine of Revelation. However, as regards man, a special creation by God is demanded, which must extend at least to the spiritual soul (creatio hominis peculiaris D 2123). Individual Fathers, especially St. Augustine, accepted a certain development of living creatures. Proceeding from the assumption that God created everything at the one time (cf. Ecclus. 18:1), they taught that God brought a certain part of His creatures into existence in a finished state, while He created others in the form of primitive seeds (rationes, seminales or causales) from which they were gradually to develop. Those Fathers and Schoolmen who accepted a development, conceived a development of the individual species of living things each from a particular primitive form created by God; but modern theories of evolution (descendence theory) conceives the development as from one species to another. According as these give priority to evolution from a plurality of original forms or from one single stem-form (primitive form) one speaks of a many-stemmed (polyphyletic) or single-stemmed (monophyletic) development. From the standpoint of the doctrine of evolution, either form is possible. From the standpoint of natural science, F. Birkner says: “A single-stemmed monophyletic development of living beings is to be rejected, as the transitions from one group to the other are missing. Everything seems to favour a many-stemmed, polyphyletic development. Unfortunately, up to the present it has not been possible to determine how many primitive forms or basic organisations of living beings existed.”

Duhem's Scientific Work Translated into English

Paul Needham has just produced the first full-length translation of one of Pierre Duhem's scientific works*: Commentary on the Principles of Thermodynamics by Pierre Duhem. From its preface:

Pierre Maurice Marie Duhem (1861–1916) held the chair of physics (changed to chair of theoretical physics in 1895) at Bordeaux from 1894 to his death. He established a reputation in both the history and philosophy of science as well as in science (physics and physical chemistry). His pioneering work in medieval science opened up the area as a new discipline in the history of science, and his La théorie physique (Duhem 1906) is a classic in the philosophy of science which is still read and discussed today. Although his work in these two fields is now well represented in English with a number of translations that have appeared in recent decades (Duhem 1892b, 1903, 1902, 1905–1906, 1906, 1908, 1915, 1985, 1996), there is little of his scientific work available in English. The original manuscript of Duhem (1898) was translated by J. E. Trevor, one of the editors of The Journal of Physical Chemistry, for its first issue. But his work almost invariably appeared in French. The present volume contains translations of some of his important early work in thermodynamics, which I hope will contribute to a more balanced picture in English of the breadth of Duhem’s publications and provide a further source of insight into his thought.

(*There is a textbook by Duhem translated into English called Thermodynamics and chemistry: A non-mathematical treatise for chemists and students of chemistry; but since it is a textbook, it is not a purely scientific contribution.)

The Wikipedia entry on Duhem has the most complete collection of links to online historical, scientific, and philosophical works of Duhem that I know of. Check them out! It makes me want to learn French.

Psychology

From the Catechism of the Summa of St. Thomas Aquinas by Fr. Thomas Pègues:

What is man?
Man is a composite of spirit and body, in whom the world of spirits and the world of bodies in some sort coalesce (LXXV.).

What is the spirit called that is in man?
It is called the soul (LXXV. 1-4).

Is man the only being in the world of bodies that has a soul?
No. Besides man plants and animals have souls.

What is the difference between the soul of man and the souls of plants and animals?
There is this difference, the soul of a plant has only vegetative life, the soul of an animal has both vegetative and sensitive life, whereas the soul of man has in addition an intellective life.

Is it then by intellective life that man is distinct from all other living beings in this world?
Yes

Is this intellective life of the soul of man, in itself, independent of his body?
Yes (LXXV. 2).

Can any reason be given to establish this truth?
Yes; and the reason is because the object of thought is something wholly immaterial.

But how does it follow from this that the human soul in its intellective life is, in itself, independent of body?
This follows because if the soul itself were not wholly immaterial it could not attain by thought to an object wholly immaterial (ibid.).

What follows from this truth?
It follows that the soul of man is immortal (LXXV. 6).

(B)

Can it be shown that the immortality of man's soul follows from this truth?
Yes. Because if in the soul there is an act wholly independent of bodily matter, it must itself be independent of bodily matter.

What follows from this truth that the soul is, in itself, independent of bodily matter?
It follows that if the body perishes by separation from the soul, the soul itself does not perish (ibid.).

Will the human soul live forever?
Yes.

Why then is the human soul united to a body?
The human soul is united to a body in order to make a substantial whole called man (LXXVI. 1).

Is it not then accidental that the soul is united to a body?
No, for the soul was made to be joined to a body (LXXVI. 1).

What are the effects of the soul upon the body to which it is united?
The soul gives to the body every perfection that the body has, that is it gives to it being, life, and sense; but thought it cannot give, for this is proper to the soul itself (LXXVI. 3, 4).

XIV. OF THE VEGETATIVE AND SENSITIVE POWERS

(A)

Are there in the soul divers powers corresponding to the divers acts it produces?
Yes, with the only exception of the first perfection which the soul gives to the body, namely, existence; but it gives this not through some power or faculty, but immediately, of itself (LXXVII.).

What powers of the soul give life to the body?
The vegetative powers.

What are these powers?
They are three in number, viz., the power of nutrition, of growth, and of reproduction (LXXVIII. 2).

(B)

What faculties of the soul give sense to the body?
The sensitive powers.

What are these powers?
They are twofold: the powers of knowing and the powers of loving.

What are the sensitive powers through which the body knows?
The five external senses (LXXVIII. 3).

What are these powers called?
They are called the powers of seeing, hearing, smelling, tasting, and touching.

And the five external senses, what are they called?
They are called sight, hearing, smell, taste, and touch (ibid.).

Are there also any internal sensitive powers of knowing that do not appear externally?
Yes, they are the common (or central) sense, the imagination, instinct (or estimative sense), and memory (LXXVIII. 4).

XV. OF THE MIND AND ITS ACT OF UNDERSTANDING

(A)

Are there any other powers of knowing in man?
Yes, there is another faculty of knowing, and it is man's chief power.

What is this chief power of knowing in man called?
It is called his reason or intellect (LXXIX. 1).

Is reason and intellect one and the same power of knowing in man?
Yes (LXXIX. 8).

Why are these two names given to the same power?
It is because in the act of knowing man sometimes understands at a glance as it were without reasoning, whereas at other times he must reason (ibid.).

Is reasoning an act proper to man?
Yes, because of all beings that are, man alone is able to reason, or has need of reasoning.

Is it a perfection in man to be able to reason?
Yes, but it is an imperfection to have need of reasoning.

Why is it a perfection in man to be able to reason?
Because in this wise man can attain to truth; whereas no creature inferior to man, such as animals which are without reason, can do this.

Why is it, on the other hand, an imperfection in man to have need of reasoning?
Because in this wise he attains to truth by slow degrees only, and he is thereby liable to err; whereas God and the angels who have no need of reasoning attain to truth straightway without fear of making a mistake.

(B)

What is it to know truth?
To know truth is to know things as they are.

What then is it not to know things as they are?
It is to be in ignorance or in error.

Is there any difference between being in ignorance and being in error?
Yes, there is a great difference; to be in ignorance is merely not to know things as they are; whereas to be in error is to affirm that a thing is, when it is not, or conversely.

Is it an evil for man to be in error?
Yes, it is a great evil, because man's proper good consists in knowledge of the truth which is the good of his intellect.

Has man a knowledge of the truth at birth?
No, at birth man has no knowledge of the truth; for though he then has an intellect it is in an entirely undeveloped state; its unfolding, necessary for the attainment of truth, awaits the development of the powers of sense which are its handmaids (LXXXIV. 5).

When then does man begin to know truth?
Man begins to know truth when he has attained the use of reason, that is at about the age of seven years.

(C)

Can man know all things by his reason?
No, man cannot know all by his reason adequately, that is if one considers his reason within the limits of its natural powers (XII. 4; LXXXVI. 2, 4).

What things can man know by the natural force of his reason?
By the natural power of his reason man can know all things attainable by his senses and all that these things manifest.

Can man know himself by the natural power of his reason?
Yes, because he himself is a thing attainable by the power of sense, and by the help of other things that fall within the scope of his senses, he is able, by reasoning, to come to a knowledge of himself (LXXXVI I.).

Mother Teresa on Abortion

Mother Teresa on Abortion:

I feel that the greatest destroyer of peace today is abortion, because it is a war against the child—a direct killing of the innocent child—murder by the mother herself. And if we accept that a mother can kill even her own child, how can we tell other people not to kill one another?

[...]

By abortion, the mother does not learn to love, but kills even her own child to solve her problems. And by abortion, the father is told that he does not have to take any responsibility at all for the child he has brought into the world. That father is likely to put other women into the same trouble. So abortion just leads to more abortion. Any country that accepts abortion is not teaching the people to love, but to use any violence to get what they want. That is why the greatest destroyer of love and peace is abortion.

—Bl. Mother Teresa, National Prayer Breakfast, Washington, D.C, February 5, 1994

Bioethics

The following is an excerpt from the textbook Ethical issues in modern medicine: contemporary readings in bioethics by Steinbock et al. which the UofA class on bioethics uses. It treats abortion, obligations to the unborn, and assisted reproduction like in vitro fertilization (IVF).

Section 1 : The morality of abortion --
The unspeakable crime of abortion [excerpt of Evangelium Vitæ] / Pope John Paul II --
Why abortion is immoral / Don Marquis --
Why most abortions are not wrong / Bonnie Steinbock --
The morality of abortion / Margaret Olivia Little --

Section 2 : Obligations to the not-yet-born --
The rights of "unborn children" and the value of pregnant women / Howard Minkoff and Lynn M. Paltrow --
Reproductive freedom and prevention of genetically transmitted harmful conditions / Allen Buchanan, Dan W. Brock, Norman Daniels, and Daniel Wikler --
Cheap listening? Reflections on the concept of wrongful disability / Richard J. Hull --

Section 3 : Assisted reproduction --
The presumptive primacy of procreative liberty / John Robertson --
Instruction on respect for human life in its origin and on the dignity of procreation [excerpt of Instruction on respect for human life in its origin and on the dignity of procreation] / Vatican, Congregation for the Doctrine of the Faith --
What are families for? Getting to an ethics of reproductive technology / Thomas H. Murray --
Grade A : the market for a Yale woman's eggs / Jessica Cohen --
Payment for egg donation / Bonnie Steinbock --

Reproduction bioethics

Physicsts Must Also Be Philosophers.

Einstein, in his Physics & Reality, says that physicists must also be philosophers:

It has often been said, and certainly not without justification, that the man of science is a poor philosopher. Why then should it not be the right thing for the physicist to let the philosopher do the philosophizing? Such might indeed be the right thing at a time when the physicist believes he has at his disposal a rigid system of fundamental concepts and fundamental laws which are so well established that waves of doubt can not reach them; but it can not be right at a time when the very foundations of physics itself have become problematic as they are now. At a time like the present, when experience forces us to seek a newer and more solid foundation, the physicist cannot simply surrender to the philosopher the critical contemplation of the theoretical foundations; for, he himself knows best, and feels more surely where the shoe pinches. In looking for a new foundation, he must try to make clear in his own mind just how far the concepts which he uses are justified, and are necessities.

And by being its philosophers, he does not mean being its undertakers; for, as Étienne Gilson observed, philosophy "always buries its undertakers." Hence the necessity for a Thomistic revival in modern mathematical physics, Thomism being the philosophical foundation of modern science.

TruthInspire » Blog Archive » REASON AND FAITH

TruthInspire » Blog Archive » REASON AND FAITH

Is Thomism Secular?

Considering St. Thomas Aquinas came in 9th in this poll of "Who are the most important philosophers of all time?", I was curious which of the universities in the Philosophical Gourmet Report's 2009 "ranking of the top facilities in the English-speaking world" is most Thomist. Here is how they performed, based on the number of Google results for "Aquinas" (cf. this, too) at each university's entire website:

Sorted by Google Hits (1st # shown)

1. University of Toronto 24400 6777.8
2. Yale University 6790 1741.0
3. University of Pennsylvania 5150 1775.9
4. University of Notre Dame 3650 1013.9
5. University of Colorado, Boulder 3590 1196.7
6. University of Michigan, Ann Arbor 2810 685.4
7. Cambridge University 2780 817.6
8. University of Chicago 2000 606.1
9. Stanford University 1920 505.3
10. University of Texas, Austin 1710 502.9
11. Oxford University 1040 221.3
12. City University of New York Graduate Center 981 272.5
13. Princeton University 942 219.1
14. Harvard University 860 215.0
15. Cornell University 801 228.9
16. Rutgers University, New Brunswick 782 170.0
17. Massachusetts Institute of Technology 734 183.5
18. University of Wisconsin, Madison 677 211.6
19. University of Massachusetts, Amherst 629 209.7
20. University of North Carolina, Chapel Hill 589 155.0
21. Columbia University 583 157.6
22. University of California, Los Angeles 493 129.7
23. Duke University 493 164.3
24. New York University 440 89.8
25. University of Pittsburgh 423 100.7
26. University of Western Ontario 385 142.6
27. Indiana University, Bloomington 383 119.7
28. University of Maryland, College Park 380 131.0
29. London School of Economics 380 135.7
30. University of California, Berkeley 339 89.2
31. University of California, Riverside 326 112.4
32. Australian National University 296 80.0
33. University of Southern California 295 84.3
34. University of California, San Diego 246 74.5
35. University College London 229 71.6
36. University of Miami 190 67.9
37. King's College, London 183 59.0
38. Syracuse University 181 64.6
39. University of Arizona 179 48.4
40. Washington University, St. Louis 173 59.7
41. Ohio State University 170 56.7
42. Brown University 155 44.3
43. University of Warwick 148 54.8
44. University of California, Irvine 143 44.7
45. University of Nottingham 121 44.8
46. University of Sheffield 66 22.8
47. University of Sydney 52 17.3
48. Birkbeck College, University of London 33 11.0
49. University of Reading 5 1.9

Sorted by Ratio (2nd # shown) of Hits to Mean Ranking

1. University of Toronto 24400 6777.8
2. University of Pennsylvania 5150 1775.9
3. Yale University 6790 1741.0
4. University of Colorado, Boulder 3590 1196.7
5. University of Notre Dame 3650 1013.9
6. Cambridge University 2780 817.6
7. University of Michigan, Ann Arbor 2810 685.4
8. University of Chicago 2000 606.1
9. Stanford University 1920 505.3
10. University of Texas, Austin 1710 502.9
11. City University of New York Graduate Center 981 272.5
12. Cornell University 801 228.9
13. Oxford University 1040 221.3
14. Princeton University 942 219.1
15. Harvard University 860 215.0
16. University of Wisconsin, Madison 677 211.6
17. University of Massachusetts, Amherst 629 209.7
18. Massachusetts Institute of Technology 734 183.5
19. Rutgers University, New Brunswick 782 170.0
20. Duke University 493 164.3
21. Columbia University 583 157.6
22. University of North Carolina, Chapel Hill 589 155.0
23. University of Western Ontario 385 142.6
24. London School of Economics 380 135.7
25. University of Maryland, College Park 380 131.0
26. University of California, Los Angeles 493 129.7
27. Indiana University, Bloomington 383 119.7
28. University of California, Riverside 326 112.4
29. University of Pittsburgh 423 100.7
30. New York University 440 89.8
31. University of California, Berkeley 339 89.2
32. University of Southern California 295 84.3
33. Australian National University 296 80.0
34. University of California, San Diego 246 74.5
35. University College London 229 71.6
36. University of Miami 190 67.9
37. Syracuse University 181 64.6
38. Washington University, St. Louis 173 59.7
39. King's College, London 183 59.0
40. Ohio State University 170 56.7
41. University of Warwick 148 54.8
42. University of Arizona 179 48.4
43. University of Nottingham 121 44.8
44. University of California, Irvine 143 44.7
45. Brown University 155 44.3
46. University of Sheffield 66 22.8
47. University of Sydney 52 17.3
48. Birkbeck College, University of London 33 11.0
49. University of Reading 5 1.9

The second sorted list gives one a good idea what are the best secular Thomist universities.

Law is a Teacher

The law is a teacher. Here is an example of why civil laws should outlaw abortion:

1. Women are generally ignorant about reproductive issues.
2. Abortion is a reproductive issue; therefore,
   
   1. women are generally ignorant about abortion.
   2. Women are less ignorant about the law; therefore,
      
      1. women know more about the law than abortion.
      2. The law tells one what is right or wrong; therefore,
         1. women know abortion's rightness or wrongness based on the law.
         2. The law currently makes it legal; therefore,
            1. the law teaches women that abortion is right.
            2. People more often than not do what they think is right; therefore,
               1. women more often than not choose abortion because they think it is right.
               2. Women choosing abortions more often than not is contrary to keeping abortions rare; therefore,
                  1. Abortion should be illegal.
                     

With what premise or conclusion do you disagree?

Learning Order

St. Thomas Aquinas, founder of Thomism (vide 24 Thomistic Theses and Pope St. Pius X's Doctoris Angelici), describes in his Sententia Ethic., lib. 6 l. 7 n. 17 [1211.] which subjects and in what order boys must learn (my emphases):

[T]he proper order of learning is that boys first be instructed in things pertaining to logic because logic teaches the method of the whole of philosophy. Next, they should be instructed in mathematics, which does not need experience and does not exceed the imagination. Third, in natural sciences, which, even though not exceeding sense and imagination, nevertheless require experience. Fourth, in the moral sciences, which require experience and a soul free from passions [...]. Fifth, in the sapiential and divine sciences, which exceed imagination and require a sharp mind.

Can you believe this? If St. Thomas thinks boys (pueri in the Latin of Sententia Ethic., lib. 6 l. 7 n. 17) should learn these, a fortiori college students must.

Master Advice

St. Thomas Aquinas said in De modo studendi: "non respicias a quo audias, sed quidquid boni dicatur" ("Do not heed by whom a thing is said, but rather what good is said").

Similarly, Fr. Sertillanges, O.P., said in his The Intellectual Life (p. 163-164):

    St. Thomas, whose idea I base myself on here, concludes from these observations that we owe gratitude even to those who have thus tested us, if because of them and their action we have made any kind of progress. Directly, we owe everything to truth alone, but indirectly we owe to those who are in error the mental development that, thanks to them, Providence provides for us. [In II. Metaphys. lect. I.]
    Think what the Church owes to heresies and philosophy to its great conflicts of opinion. If it had not been for Arius, Eutyches, Nestorius, Pelagius, Luther, Catholic dogma would not have been constituted. If Kant had not shaken the foundations of human knowledge, criteriology would still be in its childhood; and if Renan had not written on Christian origins, the Catholic clergy would be far from having the historical and exegetical formation they now possess.
    What is true collectively is true individually. We must learn right thinking principally by contact with the wise; but folly itself contains a lesson; he who escapes its contagion draws strength from it. "He who stumbles without falling makes a bigger step forward."

Hume vs. Aquinas on Transubstantiation

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

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

[...]

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

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

Benedict Ashley, O.P., responds:

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

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

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

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

[...]

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