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St. Thomas on Mathematics's Certitude

St. Thomas Aquinas attests to mathematics's certitude:

1. In I An. Post. l. 42 n. 8: "For these ["first things," e.g., axioms, demonstrations, definitions, constructions, etc.] are understood in virtue of themselves; and such knowledge of these things is more certain than any science, because it is from such knowledge that science acquires its certitude."
2. In II De Anima l. 3 n. 245: "In…mathematics…what is the more knowable is such both in itself and relatively to us." (Mathematics is thus most "co-natural" to the human intellect.)
3. In I An. Post. l. 1 n. 8: "Of these (demonstrations) the best are the mathematical sciences because of their most certain manner of demonstrating."
4. In II Met. l. 5 n. 336: "[T]he things with which mathematics deals are abstracted from matter, they do not surpass our understanding; and therefore in their case most certain reasoning is demanded."
5. In I Eth. l. 3 n. 36: "Mathematics is concerned with matter in which perfect certitude is found."
6. In X Eth. l. 7 n. 2043: "[G]eometricians who take pleasure in the study of geometry can grasp more clearly each problem of this science because their mind is detained longer by that which is pleasant." (Thus, mathematics is beautiful because of its certitude.)

(cf. "Cap. XII. La certeza matematica" of the excellent Filosofía de las Matemáticas en Santo Tomás, pp. 125 ff., by José Alvarez Laso, C.M.F.)

Freeman Dyson's Jaki lecture

Kevin O'Brien impersonates Dom Stanley Jaki. ☺

“Kevin O'Brien as Father Stanley Jaki”
by Kevin O'Brien.

The Portsmouth Institute (RI) asked Kevin O'Brien to impersonate Father Jaki, during their 2012 (June 22-24) Conference on Modern Science, Ancient Faith. Kevin prepared his talk reading a lot of books of Father Jaki, and looking at the talks of him in the Internet. The result is truly impressive. The text which Kevin used as a basis for his talk is mostly made of quotes from various books of Father Jaki. It is available here. Kevin O'Brien, founder and directore of Theater of the Word Inc., recently started a new project named Grunky. The term Grunky comes from Chesterton: "A word I invented at the age of five to express my religious sentiments". About Kevin O'Brien activity, in his own words: "My wife and I run two theatrical companies, Upstage Productions, in which we perform comedy murder mysteries around the country—that's how we make our money; and The Theater of the Word Incorporated, in which we travel the country evangelizing through drama—that's how we lose our money."

New York Times obituary:

April 12, 2009

The Rev. Stanley L. Jaki, Physicist and Theologian, Dies at 84

By BRUCE WEBER

The Rev. Stanley L. Jaki, a physicist and theologian whose prolific writings parsed the histories of science and religion and the intertwining of faith and reason, died on Tuesday in Madrid, where he had traveled from Rome after delivering a lecture. He was 84 and lived in Princeton, N.J.

The cause was complications after a heart attack, said Holly Wojcik, a spokeswoman for Seton Hall University, where Father Jaki, a Benedictine priest, was a professor of physics.
Father Jaki (pronounced YAH-kee) held doctoral degrees in physics and theology. A relentless scholar, he wrote more than 40 books, including studies of the religious thinking of G. K. Chesterton, the works of the French physicist and historian of science Pierre Duhem and the life of Cardinal John Henry Newman, the 19th-century theologian who famously converted from Anglicanism to Roman Catholicism.

He is probably best known, however, for works like “The Relevance of Physics” (1966) and “Science and Creation” (1974), in which he argued that the scientific enterprise did not become viable and self-sustaining until its incarnation in Christian medieval Europe, and that the advancement of science was indebted to the Christian understanding of creation.
In later works Father Jaki explored the boundary between science and religion; he believed the two were compatible and mutually reinforcing, and in 1987 he received the Templeton Prize, the annual award given for advancing the quest to understand God.

“I believe there is a basic misunderstanding which has existed for hundreds of years and will continue to persist about the ‘creationist problem,’ ” he said in an interview with The New York Times after receiving the prize, “because in intellectual life we do not solve such dilemmas to the satisfaction of everybody.”

Stanley Ladislas Jaki was born in Gyor, Hungary, on Aug. 17, 1924. He attended local schools run by the Benedictines and joined the order in 1942, living in the Archabbey of Pannonhalma, which had been established in the 10th century, during World War II. He was ordained in 1948.

In 1950, he received a doctorate in theology from the Pontifical Institute of San Anselmo, Rome, and came to the United States, where he taught at a seminary in Pennsylvania. When complications after a tonsillectomy deprived him of his voice — he would not regain it for a number of years — he gave up teaching and enrolled in Fordham University’s graduate program in physics, where he studied with the Nobel laureate Victor F. Hess, the discoverer of cosmic rays. He received a doctorate in 1957.

He joined the faculty of Seton Hall in 1965 and was made distinguished university professor in 1975. Father Jaki was a visiting professor at universities all over the world and delivered the prestigious Gifford Lectures at the University of Edinburgh.

He is survived by two brothers, both Benedictine priests, the Rev. Zeno Jaki and the Rev. Theodose Jaki, who live at the Archabbey of Pannonhalma.

Ariew on Duhem

Science, God & Creation

Fr. Spitzer, S.J. of the Magis Center of Reason and Faith holds a PhD whose thesis is entitled: A Study of Objectively Real Time.

It must be noted that he argues entirely dialectically, since otherwise Fr. Spitzer would disagree with St. Thomas's article: Summa Theologica I q. 46 a. 2 "Whether it is an article of faith that the world began?" (answer: YES! It's de Fide divina.) or De Æternitate Mundi (I liked the examples taken from St. Augustine toward the end, which are also mentioned in the Summa article's replies to the objections), in which he argues there is

1. nothing contradictory in the notion that God could have created an eternal universe
2. no way we could know the eternity (or not) of the world from natural reason (which goes for the Trinity, too).
   

Essentially, Fr. Spitzer is using the Kalam argument, which relies on scientific theories to prove the premise that the universe is not eternal.

Science, Truth, & Morality

Just as Einstein noted that a physicist must not restrict himself solely to physics but must also be a philosopher so that he can "make clear in his own mind just how far the concepts which he uses are justified, and are necessities," Pope Benedict XVI, in his 2009 encyclical letter Caritas in Veritate ("Charity in Truth"), relates the importance of combating a segmentation of knowledge to that of economic prosperity (my emphasis and [comments]):

30. In this context, the theme of integral human development takes on an even broader range of meanings: the correlation between its multiple elements requires a commitment to foster the interaction of the different levels of human knowledge in order to promote the authentic development of peoples. Often it is thought that development, or the socio-economic measures that go with it, merely require to be implemented through joint action. This joint action, however, needs to be given direction, because “all social action involves a doctrine”. In view of the complexity of the issues, it is obvious that the various disciplines have to work together through an orderly interdisciplinary exchange. Charity does not exclude knowledge, but rather requires, promotes, and animates it from within. Knowledge is never purely the work of the intellect. It can certainly be reduced to calculation and experiment, but if it aspires to be wisdom capable of directing man in the light of his first beginnings and his final ends, it must be “seasoned” with the “salt” of charity. Deeds without knowledge are blind, and knowledge without love is sterile. [Summa Theologiæ, Iª q. 12 a. 13 ad 3: "[Faith is] a kind of knowledge, inasmuch as the intellect is determined by faith to some knowable object." Cf. this.] Indeed, “the individual who is animated by true charity labours skilfully to discover the causes of misery, to find the means to combat it, to overcome it resolutely”. Faced with the phenomena that lie before us, charity in truth requires first of all that we know and understand, acknowledging and respecting the specific competence of every level of knowledge. Charity is not an added extra, like an appendix to work already concluded in each of the various disciplines: it engages them in dialogue from the very beginning. The demands of love do not contradict those of reason. Human knowledge is insufficient and the conclusions of science cannot indicate by themselves the path towards integral human development. There is always a need to push further ahead [This is what Einstein means, too, by saying: "At a time like the present, when experience forces us to seek a newer and more solid foundation..."]: this is what is required by charity in truth. Going beyond, however, never means prescinding from the conclusions of reason, nor contradicting its results. Intelligence and love are not in separate compartments: love is rich in intelligence and intelligence is full of love.

31. This means that moral evaluation and scientific research must go hand in hand [Morality involves determining what the greatest good is in a given situation. It involves much more than resolving never to kill anybody, to "be nice," etc. It guides even questions in science such as "How should I approach this problem?", "What methodology should I use?", "Where is it taking me?", "It is worth it?", etc.; consequently, morality is vitally important for those who seek truth (cf. Veritatis Splendor).], and that charity must animate them in a harmonious interdisciplinary whole, marked by unity and distinction. The Church's social doctrine, which has “an important interdisciplinary dimension”, can exercise, in this perspective, a function of extraordinary effectiveness. It allows faith, theology, metaphysics and science to come together in a collaborative effort in the service of humanity. It is here above all that the Church's social doctrine displays its dimension of wisdom. Paul VI had seen clearly that among the causes of underdevelopment there is a lack of wisdom and reflection, a lack of thinking capable of formulating a guiding synthesis, for which “a clear vision of all economic, social, cultural and spiritual aspects” is required. The excessive segmentation of knowledge [Cf. John Paul II, Encyclical LetterFides et Ratio (14 September 1998), 85: AAS 91 (1999), 72-73.], the rejection of metaphysics by the human sciences [Cf. ibid., 83: loc. cit., 70-71.], the difficulties encountered by dialogue between science and theology are damaging not only to the development of knowledge, but also to the development of peoples, because these things make it harder to see the integral good of man in its various dimensions. The “broadening [of] our concept of reason and its application” [Benedict XVI, Address at the University of Regensburg, 12 September 2006.] is indispensable if we are to succeed in adequately weighing all the elements involved in the question of development and in the solution of socio-economic problems.

An excellent book that tackles this problem is The Way toward Wisdom (vide this excerpt and this article) by Benedict Ashley, O.P., a proponent of River Forest Thomism.

The Assumption & Unity of Knowledge

KNOLLER, Martin
Assumption of the Virgin
c. 1774
Oil on canvas, 220 x 82 cm
Musée du Louvre, Paris

The definition of the Dogma of the Bodily Assumption into Heaven of Our Blessed Mother was given on All Saints Day, November, 1950, just a few months after the promulgation of Humani Generis on August 12, 1950. Pope Pius XII writes in Munificentissimus Deus: "Now, just like the present age, our pontificate is weighed down by ever so many cares, anxieties, and troubles, by reason of very severe calamities that have taken place [such as WWII] and by reason of the fact that many have strayed away from truth and virtue." What is underlined is certainly Humani Generis's concern, too.

Intellectuals like the great Canadian philosopher of science Charles de Koninck, who wrote the excellent philosophico-theological short work "Ego Sapientia: The Wisdom that is Mary," noted that the bodily Assumption reaffirms the unity of man (contra, e.g., Cartesian dualism, which splits body and soul) and thus also the unity of knowledge (as Our Lady is the highest form of knowledge: Wisdom Herself).

Pierre Duhem on Philosophers Pretending to Know about Physics

Pierre Duhem gave an "intervention" during the philosopher Père Bulliot's presentation at the Third International Scientific Congress of Catholics in Bruxelles (1894). It caused quite a stir, but it's excellent advice:

Only the principles of the different positive sciences are of interest to philosophers; but, in order to know these principles, it is not enough to read a book of popularization, not even the first chapters of a treatise written by a competent scientist. One does not comprehend the meaning and bearing of the principles on which a science rests except when one has studied that science for years, applied in a thousand ways those principles to particular cases, and mastered in depth the technique of what the Germans call the materials of science.

For example, the obvious sense of Euclid's [parallel] postulate is accessible to a child who studies the first book of geometry. But in order to understand the exact sense of that postulate, to grasp the reasons which give it a special place among the truths of geometry, to see clearly what would become of geometry if that postulate were to be abandoned, one must have a complete mathematical training which requires years of work.

If therefore we want to handle with competence and fruitfully the questions which are of the domain common to metaphysics and to positive science, let us begin with studying the latter for ten, for fifteen years; let us study it, first of all, in itself and for itself, without seeking to put it in harmony with such and such philosophical assertion; then, as we have mastered its principles, applied it in a thousand ways, we can search for its metaphysical meaning which will not fail to accord with true philosophy.

Anyone who would find exaggerated a similar labor must not forget that every hasty, scientifically incorrect solution of one of the problems relating to the common frontiers of science and philosophy, would result in the greatest prejudice against our cause. The philosophers must imitate the patience of scientists. Once a problem is posed, scientists devote centuries, if necessary, to solving it. They accept only a precise and rigorous solution.

At any rate, the schools we are combatting give us example. The positivist school, the critical school, publish numerous works on the philosophy of science. These works carry the names of the greatest names of European science. We cannot triumph over these schools except by opposing them with researches done by people who, too, are masters of the positive sciences.

(source: Jaki, Stanley L. Uneasy Genius the Life and Work of Pierre Duhem. Boston: The Hague, 1984, pp. 113-4.)

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

Peirce's concise refutation of Kant

From The Philosophy of Peirce: Selected Writings, a very concise refutation of Kant (pg. 15, his "Fixation of Belief" article, CP 5.358-87), Kant believes that

An opinion that something is universally true clearly goes further than experience can warrant. An opinion that something is necessarily true (that is, not merely is true in the existing state of things, but would be true in every state of things) equally goes further than experience will warrant.
…
Kant proceeds to reason as follows:

• Geometrical propositions are held to be universally true.
• Hence, they are not given by experience.
• Consequently, it must be owing to an inward necessity of man's nature that he sees everything in space.
• Ergo, the sum of the angles of a triangle will be equal to two right angles for all the objects of our vision.

But the dry-rot of reason in the seminaries has gone to the point where such stuff is held to be admirable argumentation.

Quantum Mechanics (an embarrassment)

See the full paper here.
100% of the problems with QM are philosophical/metaphysical.

St. Thomas Aquinas in the Dictionary of Scientific Biography

Happy feast day of
Aquinas, Saint Thomas
from the Dictionary of Scientific Biography.

One of a handful a chants he composed in Orvieto, Italy:

SACRIS solemniis iuncta sint gaudia, et ex praecordiis sonent praeconia; recedant vetera, nova sint omnia, corda, voces, et opera.	AT this our solemn feast let holy joys abound, and from the inmost breast let songs of praise resound; let ancient rites depart, and all be new around, in every act, and voice, and heart.
Noctis recolitur cena novissima, qua Christus creditur agnum et azyma dedisse fratribus, iuxta legitima priscis indulta patribus.	Remember we that eve, when, the Last Supper spread, Christ, as we all believe, the Lamb, with leavenless bread, among His brethren shared, and thus the Law obeyed, of all unto their sire declared.
Post agnum typicum, expletis epulis, Corpus Dominicum datum discipulis, sic totum omnibus, quod totum singulis, eius fatemur manibus.	The typic Lamb consumed, the legal Feast complete, the Lord unto the Twelve His Body gave to eat; the whole to all, no less the whole to each did mete with His own hands, as we confess.
Dedit fragilibus corporis ferculum, dedit et tristibus sanguinis poculum, dicens: Accipite quod trado vasculum; omnes ex eo bibite.	He gave them, weak and frail, His Flesh, their Food to be; on them, downcast and sad, His Blood bestowed He: and thus to them He spake, "Receive this Cup from Me, and all of you of this partake."
Sic sacrificium istud instituit, cuius officium committi voluit solis presbyteris, quibus sic congruit, ut sumant, et dent ceteris.	So He this Sacrifice to institute did will, and charged His priests alone that office to fulfill: tn them He did confide: to whom it pertains still to take, and the rest divide.
Panis angelicus fit panis hominum; dat panis caelicus figuris terminum; O res mirabilis: manducat Dominum pauper, servus et humilis.	Thus Angels' Bread is made the Bread of man today: the Living Bread from heaven with figures dost away: O wondrous gift indeed! the poor and lowly may upon their Lord and Master feed.
Te, trina Deitas unaque, poscimus: sic nos tu visita, sicut te colimus; per tuas semitas duc nos quo tendimus, ad lucem quam inhabitas.	Thee, therefore, we implore, o Godhead, One in Three, so may Thou visit us as we now worship Thee; and lead us on Thy way, That we at last may see the light wherein Thou dwellest aye.

(lyrics and translation of Sacris Solemnis, from the Feast of Corpus Christi)

From the matins of the feast:

That splendid adornment of the Christian world and light of the Church, blessed Thomas of Aquino, was the son of Landulph, Earl of Aquino, and Theodora of Naples, his wife, being nobly descended on both sides. (He was born in the year of salvation 1226,) and even as an infant gave token of the love which he afterwards bore to the Mother of God. He found a little bit of paper upon which was written the Angelic Salutation, and held it firm in his hand in spite of the efforts of his wet-nurse; his mother took it away by force, but he cried and stretched out for it, and when she gave it back to him, he swallowed it. When he was only four years old, he was given into the keeping of the Benedictine monks of Monte Cassino. He was thence sent to Naples to study, and there, while very young, entered the Order of Friars Preachers. This displeased his mother and brothers, and he left Naples for Paris. When he was on his journey his brothers met him, and carried him off by force to the castle of Monte San Giovanni, where they imprisoned him in the keep. Here they used every means to break him of his intention, and at last brought a woman into his room to try to overcome his purity. The lad drove her out with a fire-brand. When he was alone he knelt down before the figure of the Cross, and there he fell asleep. As he slept, it seemed to him that angels came and girded his loins and from this time he never felt the least sexual inclination. His sisters came to the castle to beseech him to give up his purpose of leaving the world, but he so worked on them by his godly exhortations, that both of them ever after set no value on earthly things, and busied themselves rather with heavenly.

Being let down from a window, Thomas escaped out of the castle of Monte San Giovanni, and returned to Naples. Thence he went first to Rome, and then to Paris, in company of Brother John the German, then Master-General of the Friars Preachers. At Paris he studied Philosophy and Theology under Albert the Great Doctor. At the age of twenty-five years he took the degree of Master, and gave public disquisitions on the Philosophers and Theologians with great distinction. He never set himself to read or write till he had first prayed, and when he was about to take in hand a hard passage of the Holy Scriptures, he fasted also. Hence he was wont to say to Brother Reginald his comrade, that whatever he knew, he had learnt, not so much from his own labour and study, as from the inspiration of God. At Naples he was once kneeling in very earnest prayer before an image of Christ Crucified, when he heard a voice which said Thomas, thou hast written well of Me what reward wilt thou that I give thee? He answered: Lord, thyself. He studied most carefully the works of the Fathers, and there was no kind of author in which he was not well read. His own writings are so wonderful, both because of their number, their variety, and the clearness of his explanations of hard things, that his rich and pure teaching, marvellously consonant with revealed truth, is an admirable antidote for the errors of all times.

The Supreme Pontiff Urban IV. A sent for him to Rome, and at his command he composed the Church Office for the feast of Corpus Christi. The Pope could not persuade him to accept any dignity. Pope Clement IV. also offered him the Archbishoprick of Naples, but he refused it. He did not neglect the preaching of the Word of God. Once while he was giving a course of sermons in the Basilica of St Peter, during the octave of Easter, a woman who had an issue of blood was healed by touching the hem of his garment. He was sent by blessed Gregory X. to the Council of Lyons, but fell sick on his way to the Abbey of Fossa Nuovo, and there during his illness he made an exposition of the Song of Songs. There he died on the th day of March, in the year of salvation 1274, aged fifty years. He was distinguished for miracles even after his death, and on proof of these Pope John XXII. added his name to those of the Saints in the year 1323. His body was afterwards carried to Toulouse by command of blessed Urban V. He has been compared to an angel, both on account of his innocency and of his intellectual power, and has hence been deservedly termed the Angelic Doctor. The use of which title as applied to him was approved by the authority of holy Pius V. Leo XIII. cheerfully agreeing to the prayers and wishes of nearly all the bishops of the Catholic world, and in conformity with a vote of the Congregation of Sacred Rites, by his Apostolic letters declared and recognised Thomas of Aquino as the patron in heaven of all Catholic schools, as an antidote to the plague of so many false systems, especially of philosophy, for the increase of scientific knowledge, and for the common good of all mankind.

Read G. K. Chesterton's St. Thomas Aquinas.

Everything is not Mathematics.

Regarding cosmologist Max Tegmark's "Mathematical Universe Hypothesis (MUH)" (cf. Is the Universe Actually Made of Math?, interview with me about Level IV in Discover Magazine, 6/16 2008), it seems he has an overly broad conception of what mathematics is.

• Mathematics is the study of discrete or continuous quantity;
• Mathematics is not the study of all relations.
• Semiotic is the general science of relations (signs).
• Physicist and America's greatest philosopher Charles Sanders Peirce said (CP 5.448) that "this universe is perfused with signs, if it is not composed exclusively of signs."
  
• Cf. John Deely's physiosemiosis, the action of signs in the physical universe, in his free bestseller Basics of Semiotics, ch. 6.
• Boethius's famous definition of mathematics is (De Trinitate q. 5):

"Mathematics does not deal with motion [change] and is not abstract [for this sense of abstract, see Armand Mauer's introduction to his translation of Thomas Aquinas's Division and Methods of the Sciences], for it investigates forms of bodies apart from matter, and therefore apart from movement, which forms being connected with matter cannot really be separated from bodies."

• Thomas Aquinas, in Division and Methods of the Sciences q. 5 a. 3, argues that mathematics treats "without motion [change] and matter, of what exists in matter."
• See also this question's 5th objection, regarding how "mathematics treats without motion," and his reply to it, where he says "it does not belong to the mathematician to treat of motion, although mathematical principles can be applied to motion." He also shows mathematical physics is an "intermediate science" (scientia media), since it's materially physical and formally mathematical.
  
• Cf. Peirce's "The Nature of Mathematics," ch. 10 (p. 135) of The Philosophy of Peirce.

• quantity does not comprise the substances of material things;
• Aristotle writes (Metaphysics 1017b16-22):

"substance means those parts which, being present in such things, limit them and designate them as individuals and as a result of whose destruction the whole is destroyed; for example, body is destroyed when surface is, as some say, and surface when line is. And in general it seems to some that number is of this nature; for [according to them] if it is destroyed, nothing will exist, and it limits all things."

Thomas Aquinas commentates (Sententia Metaphysicae, lib. 5 l. 10 n. 3 [900-1]):

"He gives a third meaning of substance, which is the one used by the Platonists and Pythagoreans. He says that all those parts of the foregoing substances which constitute their limits and designate them as individuals, according to the opinion of these thinkers, and by whose destruction the whole is destroyed, are also termed substances. For example, body is destroyed when surface is, as some say, and surface when line is. It is also clear that surface is the limit of body and line the limit of surface. And according to the opinion of the philosophers just mentioned the line is a part of surface and surface a part of body. For they held that bodies are composed of surfaces, surfaces of lines, and lines of points; and thus it would follow that the point is the substance of the line, the line the substance of surface, and so on for the rest. And according to this position number seems to constitute the entire substance of all things, because when number is destroyed nothing remains in the world; for what is not one is nothing. And similarly things which are not many are non-existent. And number is also found to limit all things, because all things are measured by number.

"But this sense of substance is not a true one. For that which is found to be common to all things and is something without which they cannot exist does not necessarily constitute their substance, but it can be some property flowing from the substance or from a principle of the substance. These philosophers also fell into error especially regarding unity and number because they failed to distinguish between the unity which is interchangeable with being and that which is the principle of number."

• rather, quantity presupposes a substance: "of all the accidents [properties of a substance] quantity is closest to substance" (Sententia Metaphysicae, lib. 5 l. 15 n. 7 [983]).
  
• ∴ everything is not mathematics.

A Sign is What?

"A Sign is What? A dialogue between a semiotist and a would-be realist" by John N. Deely, Presidential Address to the Semiotic Society of America

Published Works of C.S. Peirce

Published Works of C.S. Peirce just released today!

Benedict M. Ashley, O.P., RIP

Angelicum Newsletter Blog: Benedict M. Ashley, O.P., RIP

He wrote his last email to me when he just turned 97 years old!

See my Aristotelian Thomism page (he preferred that term to River Forest Thomism) and his page on MoreC.com. He assumed a special rôle in the review process of Physics for Realists by Dr. Anthony Rizzi of the Institute for Advanced Physics.

Requiescat in pace.

UPDATE: A close correspondent of Fr. Ashley just wrote to me what could be considered a good obituary, the beginning of which is below:

As you probably have heard by now, Father Ashley died on Saturday, only 69 days short of his 98th birthday. He is a tremendous loss to all of us. I am told that he was intellectually active until the end, and that a month before he died, he was able to receive into his hands the printed version of his autobiography [available online] published now by the New Priory Press. In one of my letters to him, I had written that in my opinion, that is his most important book, since it supplies the absolutely essential keys to understanding his whole philosophical and theological enterprize (the 'experimentum' which serves as both the ground and the terminus of all human knowing in this life). In reply to my letter of condolance, the provincial, Fr. Bouchard, told me that, at the time of his death, Ashley had several completed or almost completed manuscripts on his desk and that his confreres are now preparing them for publication. I don't know their content as yet, but I can hardly wait to see them.

C. S. Peirce

The 20th century philosopher Charles Sanders Peirce is America's greatest thinker so far. He was a logician, specialized in semiotics, a realist, renouncer of Kantianism, and was vigorously anti-Cartesian. See:

• C. S. Peirce's 5 famous The Monist papers
• John N. Deely's "Charles Sanders Peirce and the Recovery of the Signum" and "The Impact of Semiotics on Philosophy"
• Arisbe: The Peirce Gateway
• Dictionary of Peirce's Terms
• Institute for Studies in Pragmaticism
• Peirce.org
• physicist Peder Voetmann Christiansen's papers on applying Peirce's thought to physics (quantum semiotics)
• cf. also A Triadic Theory of Elementary Particle Interactions and Quantum
• and the related U.S. Patent 6819474.