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