Augustine (419, 1991), and Edmond Hill (Introduction, translation and notes), and John E Rotelle (editor), The Trinity, New City Press 399-419, 1991 Written 399 - 419: De Trinitate is a radical restatement, defence and development of the Christian doctrine of the Trinity. Augustine's book has served as a foundation for most subsequent work, particularly that of Thomas Aquinas.  
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Bergson (1911, 2009), Henri, Creative Evolution, General Books LLC 1911, 2009 ' Long absent from the center of discussion in Western philosophy, Bergson has recently made a reappearance. The Centennial Series of his works undertaken by Palgrave Macmillan thus comes at an opportune time, making it possible for those interested in Bergson's ideas to have access to newly annotated versions of several of his chief writings, freshly introduced and discussed. It is particularly good to see the republication of Mind-Energy, a treasure trove of Bergsonian insights long out of print.' - Pete A.Y. Gunter, Department of Philosophy and Religious Studies, University of North Texas 
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Cantor (1897, 1955), Georg, Contributions to the Founding of the Theory of Transfinite Numbers (Translated, with Introduction and Notes by Philip E B Jourdain), Dover 1895, 1897, 1955 Jacket: 'One of the greatest mathematical classics of all time, this work established a new field of mathematics which was to be of incalculable importance in topology, number theory, analysis, theory of functions, etc, as well as the entire field of modern logic.' 
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Cohen (1980), Paul J, Set Theory and the Continuum Hypothesis, Benjamin/Cummings 1966-1980 Preface: 'The notes that follow are based on a course given at Harvard University, Spring 1965. The main objective was to give the proof of the independence of the continuum hypothesis [from the Zermelo-Fraenkel axioms for set theory with the axiom of choice included]. To keep the course as self contained as possible we included background materials in logic and axiomatic set theory as well as an account of Gödel's proof of the consistency of the continuum hypothesis. . . .'  
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Dauben (1990), Joseph Warren, Georg Cantor: His Mathematics and Philosophy of the Infinite, Princeton University Press 1990 Jacket: 'One of the greatest revolutions in mathematics occurred when Georg Cantor (1843-1918) promulgated his theory of transfinite sets. . . . Set theory has been widely adopted in mathematics and philosophy, but the controversy surrounding it at the turn of the century remains of great interest. Cantor's own faith in his theory was partly theological. His religious beliefs led him to expect paradox in any concept of the infinite, and he always retained his belief in the utter veracity of transfinite set theory. Later in his life, he was troubled by attacks of severe depression. Dauben shows that these played an integral part in his understanding and defense of set theory.' 
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Hawking (1975), Steven W, and G F R Ellis, The Large Scale Structure of Space-Time, Cambridge UP 1975 Preface: Einstein's General Theory of Relativity . . . leads to two remarkable predictions about the universe: first that the final fate of massive stars is to collapse behind an event horizon to form a 'black hole' which will contain a singularity; and secondly that there is a singularity in our past which constitutes, in some sense, a beginning to our universe. Our discussion is principally aimed at developing these two results.' 
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Hopkins (2001), Keith, A World Full of Gods: The Strange Triumph of Christianity, Penguin Random House 2001 ' In this provocative, irresistibly entertaining book, Keith Hopkins takes readers back in time to explore the roots of Christianity in ancient Rome. Combining exacting scholarship with dazzling invention, Hopkins challenges our perceptions about religion, the historical Jesus, and the way history is written. He puts us in touch with what he calls “empathetic wonder”—imagining what Romans, pagans, Jews, and Christians thought, felt, experienced, and believed-by employing a series of engaging literary devices. These include a TV drama about the Dead Sea Scrolls; the first-person testimony of a pair of time-travelers to Pompeii; a meditation on Jesus’ apocryphal twin brother; and an unusual letter on God, demons, and angels.' 
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Jech (1997), Thomas, Set Theory, Springer 1997 Jacket: 'This book covers major areas of modern set theory: cardinal arithmetic, constructible sets, forcing and Boolean-valued models, large cardinals and descriptive set theory. . . . It can be used as a textbook for a graduate course in set theory and can serve as a reference book.' 
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Nielsen (2016), Michael A., and Isaac L Chuang, Quantum Computation and Quantum Information, Cambridge University Press 2016 Review: A rigorous, comprehensive text on quantum information is timely. The study of quantum information and computation represents a particularly direct route to understanding quantum mechanics. Unlike the traditional route to quantum mechanics via Schroedinger's equation and the hydrogen atom, the study of quantum information requires no calculus, merely a knowledge of complex numbers and matrix multiplication. In addition, quantum information processing gives direct access to the traditionally advanced topics of measurement of quantum systems and decoherence.' Seth Lloyd, Department of Quantum Mechanical Engineering, MIT, Nature 6876: vol 416 page 19, 7 March 2002. 
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Teilhard de Chardin (1965), Pierre, The Phenomenon of Man, Collins 1965 Sir Julian Huxley, Introduction: 'We, mankind, contain the possibilities of the earth's immense future, and can realise more and more of them on condition that we increase our knowledge and our love. That, it seems to me, is the distillation of the Phenomenon of Man.'  
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Action (physics) - Wikipedia, Action (physics) - Wikipedia, the free encyclopedia, ' In physics, action is a numerical value describing how a physical system has changed over time. Action is significant because the equations of motion of the system can be derived through the principle of stationary action. In the simple case of a single particle moving with a specified velocity, the action is the momentum of the particle times the distance it moves, added up along its path, or equivalently, twice its kinetic energy times the length of time for which it has that amount of energy, added up over the period of time under consideration. For more complicated systems, all such quantities are added together. More formally, action is a mathematical functional which takes the trajectory, also called path or history, of the system as its argument and has a real number as its result. Generally, the action takes different values for different paths. Action has dimensions of energy × time or momentum × length, and its SI unit is joule-second (like the Planck constant h).' back

Ad Gentes (Vatican II), Decree on the Mission Activity of the Church, 'Divinely sent to the nations of the world to be unto them "a universal sacrament of salvation," the Church, driven by the inner necessity of her own catholicity, and obeying the mandate of her Founder (cf. Mark 16:16), strives ever to proclaim the Gospel to all men. The Apostles themselves, on whom the Church was founded, following in the footsteps of Christ, "preached the word of truth and begot churches." It is the duty of their successors to make this task endure "so that the word of God may run and be glorified (2 Thess. 3:1) and the kingdom of God be proclaimed and established throughout the world.' back

Aquinas, Summa, I, 27, 1, Is there procession in God?, 'As God is above all things, we should understand what is said of God, not according to the mode of the lowest creatures, namely bodies, but from the similitude of the highest creatures, the intellectual substances; while even the similitudes derived from these fall short in the representation of divine objects. Procession, therefore, is not to be understood from what it is in bodies, either according to local movement or by way of a cause proceeding forth to its exterior effect, as, for instance, like heat from the agent to the thing made hot. Rather it is to be understood by way of an intelligible emanation, for example, of the intelligible word which proceeds from the speaker, yet remains in him. In that sense the Catholic Faith understands procession as existing in God.' back

Aquinas, Summa, I, 75, 2, Is the human soul something subsistent?, ' I answer that, It must necessarily be allowed that the principle of intellectual operation which we call the soul, is a principle both incorporeal and subsistent. For it is clear that by means of the intellect man can have knowledge of all corporeal things. Now whatever knows certain things cannot have any of them in its own nature; because that which is in it naturally would impede the knowledge of anything else. . . .. Therefore the intellectual principle which we call the mind or the intellect has an operation per se apart from the body. Now only that which subsists can have an operation per se. For nothing can operate but what is actual: for which reason we do not say that heat imparts heat, but that what is hot gives heat. We must conclude, therefore, that the human soul, which is called the intellect or the mind, is something incorporeal and subsistent.' back

Aquinas, Summa, I, 75, 6, Is the human soul is incorruptible?, ' For it is clear that what belongs to a thing by virtue of itself is inseparable from it; but existence belongs to a form, which is an act, by virtue of itself. Wherefore matter acquires actual existence as it acquires the form; while it is corrupted so far as the form is separated from it. But it is impossible for a form to be separated from itself and therefore it is impossible for a subsistent form to cease to exist. . . .. Moreover we may take a sign of this from the fact that everything naturally aspires to existence after its own manner. Now, in things that have knowledge, desire ensues upon knowledge. The senses indeed do not know existence, except under the conditions of "here" and "now," whereas the intellect apprehends existence absolutely, and for all time; so that everything that has an intellect naturally desires always to exist. But a natural desire cannot be in vain. Therefore every intellectual substance is incorruptible.' back

Aristotle, Metaphysics book 1: 981b, ' The difference between art and science and the other kindred mental activities has been stated in the Ethics; the reason for our present discussion is that it is generally assumed that what is called Wisdom is concerned with the primary causes and principles, so that, as has been already stated, the man of experience is held to be wiser than the mere possessors of any power of sensation, the artist than the man of experience, the master craftsman than the artisan; and the speculative sciences to be more learned than the productive.' back

Aristotle - On the Soul, On the Soul - The Internet Classics Archive, ' Holding as we do that, while knowledge of any kind is a thing to be honoured and prized, one kind of it may, either by reason of its greater exactness or of a higher dignity and greater wonderfulness in its objects, be more honourable and precious than another, on both accounts we should naturally be led to place in the front rank the study of the soul. The knowledge of the soul admittedly contributes greatly to the advance of truth in general, and, above all, to our understanding of Nature, for the soul is in some sense the principle of animal life. Our aim is to grasp and understand, first its essential nature, and secondly its properties; of these some are taught to be affections proper to the soul itself, while others are considered to attach to the animal owing to the presence within it of soul.' back

Astrology - Wikipedia, Astrology - Wikipedia, the free encyclopedia, 'Astrology is the study of the movements and relative positions of celestial objects as a means for divining information about human affairs and terrestrial events. Astrology has been dated to at least the 2nd millennium BCE, and has its roots in calendrical systems used to predict seasonal shifts and to interpret celestial cycles as signs of divine communications.' back

Axiom of power set - Wikipedia, Axiom of power set - Wikipedia, the free encyclopedia, 'In mathematics, the axiom of power set is one of the Zermelo–Fraenkel axioms of axiomatic set theory. . . . succinctly: for every set x there is a set P(x) consisting precisely of the subsets of x. . . . The axiom of power set appears in most axiomatizations of set theory. back

Calculus - Wikipedia, Calculus - Wikipedia, the free encyclopedia, '. . . Calculus is the study of change, in the same way that geometry is the study of shape and algebra is the study of operations and their application to solving equations. . . .' back

Cantor's paradox - Wikipedia, Cantor's paradox - Wikipedia, the free encyclopedia, 'In set theory, Cantor's paradox is derivable from the theorem that there is no greatest cardinal number, so that the collection of "infinite sizes" is itself infinite. The difficulty is handled in axiomatic set theory by declaring that this collection is not a set but a proper class; in von Neumann–Bernays–Gödel set theory it follows from this and the axiom of limitation of size that this proper class must be in bijection with the class of all sets. Thus, not only are there infinitely many infinities, but this infinity is larger than any of the infinities it enumerates.' back

Cantor's theorem - Wikipedia, Cantor's theorem - Wikipedia, the free encyclopedia, ' In mathematical set theory, Cantor's theorem is a fundamental result which states that, for any set A , the set of all subsets of A, the power set of A, has a strictly greater cardinality than A itself. For finite sets, Cantor's theorem can be seen to be true by simple enumeration of the number of subsets. Counting the empty set as a subset, a set with n elements has a total of n ² subsets, and the theorem holds because n² > n for all non-negative integers. Much more significant is Cantor's discovery of an argument that is applicable to any set, and shows that the theorem holds for infinite sets also.' back

Cartesian coordinate system - Wikipedia, Cartesian coordinate system - Wikipedia, the free encyclopedia, ' In geometry, a Cartesian coordinate system in a plane is a coordinate system that specifies each point uniquely by a pair of real numbers called coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, called coordinate lines, coordinate axes or just axes (plural of axis) of the system. The point where they meet is called the origin and has (0, 0) as coordinates.' back

Christopher Shea (2012), Why Power Corrupts, ' “Power tends to corrupt,” said Lord Acton, the 19th-century British historian. “Absolute power corrupts absolutely.” His maxim has been vividly illustrated in psychological studies, notably the 1971 Stanford Prison Experiment, which was halted when one group of students arbitrarily assigned to serve as “prison guards” over another group began to abuse their wards. But new scholarship is bringing fresh subtlety to psychologists’ understanding of when power leads people to take ethical shortcuts—and when it doesn’t. Indeed, for some people, power seems to bring out their best. After all, good people do win elective office, says Katherine A. DeCelles, a professor of management at the University of Toronto, and no few business executives want to do good while doing well. “When you give good people power,” DeCelles says she wondered, are they more able than others “to enact that moral identity, to do what’s right?” back

Christopher Shields (Stanford Encyclopedia of Philosophy a), Aristotle's Psychology, ' In De Anima, Aristotle makes extensive use of technical terminology introduced and explained elsewhere in his writings. He claims, for example, using vocabulary derived from his physical and metaphysical theories, that the soul is a “first actuality of a natural organic body” (De Anima ii 1, 412b5–6), that it is a “substance as form of a natural body which has life in potentiality” (De Anima ii 1, 412a20–1) and, similarly, that it “is a first actuality of a natural body which has life in potentiality” (De Anima ii 1, 412a27–8), all claims which apply to plants, animals and humans alike.' back

Christopher Shields (Stanford Encyclopedia of Philosophy b), The Active Mind of De Anima III 5 , ' After characterizingnous the mind (nous) and its activities in De Animaiii 4, Aristotle takes a surprising turn. In De Anima iii 5, he introduces an obscure and hotly disputed subject: the active mind or active intellect (nous poiêtikos). Controversy surrounds almost every aspect of De Anima iii 5, not least because in it Aristotle characterizes the active mind—a topic mentioned nowhere else in his entire corpus—as ‘separate and unaffected and unmixed, being in its essence actuality’ (chôristos kai apathês kai amigês, tê ousia energeia; DA iii 5, 430a17–18) and then also as ‘deathless and everlasting’ (athanaton kai aidion; DA iii 5, 430a23). This comes as no small surprise to readers of De Anima, because Aristotle had earlier in the same work treated the mind (nous) as but one faculty (dunamis) of the soul (psuchê), and he had contended that the soul as a whole is not separable from the body (DA ii 1, 413a3–5). back

Christopher Shields (Stanford Encyclopedia of Philosophy), Aristotle, First published Thu Sep 25, 2008; substantive revision Tue Aug 25, 2020 'Aristotle (384–322 B.C.E.) numbers among the greatest philosophers of all time. Judged solely in terms of his philosophical influence, only Plato is his peer: . . . A prodigious researcher and writer, Aristotle left a great body of work, perhaps numbering as many as two-hundred treatises, from which approximately thirty-one survive. His extant writings span a wide range of disciplines, from logic, metaphysics and philosophy of mind, through ethics, political theory, aesthetics and rhetoric, and into such primarily non-philosophical fields as empirical biology, where he excelled at detailed plant and animal observation and taxonomy. In all these areas, Aristotle's theories have provided illumination, met with resistance, sparked debate, and generally stimulated the sustained interest of an abiding readership.' back

Combination - Wikipedia, Combination - Wikipedia, the free encyclopedia, ' In mathematics, a combination is a selection of items from a set that has distinct members, such that the order of selection does not matter (unlike permutations). For example, given three fruits, say an apple, an orange and a pear, there are three combinations of two that can be drawn from this set: an apple and a pear; an apple and an orange; or a pear and an orange. More formally, a k-combination of a set S is a subset of k distinct elements of S. So, two combinations are identical if and only if each combination has the same members. (The arrangement of the members in each set does not matter.) ' back

Constantine the Great and Christianity - Wikipedia, Constantine the Great and Christianity - Wikipedia, the free encyclopedia, ' During the reign of the Roman Emperor Constantine the Great (AD 306–337), Christianity began to transition to the dominant religion of the Roman Empire. Historians remain uncertain about Constantine's reasons for favoring Christianity, and theologians and historians have often argued about which form of early Christianity he subscribed to. . . . Constantine's decision to cease the persecution of Christians in the Roman Empire was a turning point for early Christianity, sometimes referred to as the Triumph of the Church, the Peace of the Church or the Constantinian shift. In 313, Constantine and Licinius issued the Edict of Milan decriminalizing Christian worship. The emperor became a great patron of the Church and set a precedent for the position of the Christian emperor within the Church and raised the notions of orthodoxy, Christendom, ecumenical councils, and the state church of the Roman Empire declared by edict in 380. He is revered as a saint and is apostolos in the Eastern Orthodox Church, Oriental Orthodox Church, and various Eastern Catholic Churches for his example as a "Christian monarch”.' back

Crusades - Wikipedia, Crusades - Wikipedia, the free encyclopedia, ' The Crusades were a series of intermittent military campaigns in the years from 1096 to 1487, sanctioned by various Popes. In 1095 the Byzantine Emperor, Alexios I, sent an ambassador to Pope Urban II requesting military support in the Byzantines' conflict with the westward migrating Turks in Anatolia. The Pope responded by calling Catholics to join what later became known as the First Crusade. One of Urban's stated aims was to guarantee pilgrims access to the holy sites in the Holy Land that were under Muslim control while his wider strategy was to reunite the Eastern and Western branches of Christendom, divided after their split in 1054, and establish himself as head of the united Church. This initiated a complex 200-year struggle in the region.' back

Deferent and epicycle - Wikipedia, Deferent and epicycle - Wikipedia, the free encyclopedia, ' In the Hipparchian, Ptolemaic, and Copernican systems of astronomy, the epicycle (from Ancient Greek ἐπίκυκλος (epíkuklos) 'upon the circle', meaning "circle moving on another circle")[1] was a geometric model used to explain the variations in speed and direction of the apparent motion of the Moon, Sun, and planets. In particular it explained the apparent retrograde motion of the five planets known at the time. Secondarily, it also explained changes in the apparent distances of the planets from the Earth.' back

Eamonn Wooster & Erick Liundgren, From meerkat school to whale-tail slapping and oyster smashing, how clever predators shape their world, ' In the 1980s a single humpback whale in the Gulf of Maine developed the “lobtail feeding method”. This unique hunting method of slapping the water’s surface appears to drive fish into dense schools, making it easier to consume them. Lobtail feeding caught on. Now many humpback whales are doing it. Ecologists have long thought animals acted on instinct alone. But a growing body of evidence shows many animals, much like us, have complex brains and social lives. In our new research, we argue the science of ecology can learn a great deal from the study of animal cognition and culture. Cognition is what goes on in the mind, which determines how animals perceive and respond to the world around them. Culture is the development and spread of socially learned behaviours. These are important – but generally overlooked – mechanisms influencing ecosystems.' back

Electron microscope - Wikipedia, Electron microscope - Wikipedia, the free encylopedia, ' An electron microscope is a microscope that uses a beam of accelerated electrons as a source of illumination. As the wavelength of an electron can be up to 100,000 times shorter than that of visible light photons, electron microscopes have a higher resolving power than light microscopes and can reveal the structure of smaller objects. A scanning transmission electron microscope has achieved better than 50 pm resolution in annular dark-field imaging mode and magnifications of up to about 10,000,000× whereas most light microscopes are limited by diffraction to about 200 nm resolution and useful magnifications below 2000×.' back

English versions of the Nicene Creed - Wikipedia, English versions of the Nicene Creed - Wikipedia, the free encyclopedia, 'The Nicene Creed, composed in part and adopted at the First Council of Nicaea (325) and revised with additions by the First Council of Constantinople (381), is a creed that summarizes the orthodox faith of the Christian Church and is used in the liturgy of most Christian Churches. This article endeavours to give the text and context of English-language translations.' back

Ethan Siegel, The 13 scales that define our physical Universe, ' The visible Universe extends 46.1 billion light-years from us, while we've probed scales down to as small as ~10^-19 meters.. . .. From macroscopic scales down to subatomic ones, the sizes of the fundamental particles play only a small role in determining the sizes of composite structures. Whether the building blocks are truly fundamental and/or point-like particles is still not known, but we do understand the Universe from large, cosmic scales down to tiny, subatomic ones. The scale of quarks and gluons is the limit to how far we’ve ever probed nature. On the right, the gauge bosons, which mediate the three fundamental quantum forces of our Universe, are illustrated. There is only one photon to mediate the electromagnetic force, there are three bosons mediating the weak force, and eight mediating the strong force. This suggests that the Standard Model is a combination of three groups: U(1), SU(2), and SU(3), whose interactions and particles combine to make up everything known in existence. With gravity thrown into the mix, there are a total of 26 fundamental constants required to explain our Universe, with four big questions still awaiting explanation. back

Eugene Wigner (1960), The Unreasonable Effectiveness of Mathematics in the Natural Sciences, 'The first point is that the enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and that there is no rational explanation for it. Second, it is just this uncanny usefulness of mathematical concepts that raises the question of the uniqueness of our physical theories.' back

European wars of religion - Wikipedia, European war of religion - Wikipedia, the free encyclopedia, ' The conflicts began with the minor Knights' Revolt (1522), followed by the larger German Peasants' War (1524–1525) in the Holy Roman Empire. Warfare intensified after the Catholic Church began the Counter-Reformation in 1545 against the growth of Protestantism. The conflicts culminated in the Thirty Years' War, which devastated Germany and killed one-third of its population, a mortality rate twice that of World War I. The Peace of Westphalia broadly resolved the conflicts by recognising three separate Christian traditions in the Holy Roman Empire: Roman Catholicism, Lutheranism, and Calvinism.' back

Exodus 32, The Lord orders Moses to slaughter the worshippers of the Golden Calf, '27 Then he said to them, “This is what the Lord, the God of Israel, says: ‘Each man strap a sword to his side. Go back and forth through the camp from one end to the other, each killing his brother and friend and neighbour'.” 28 The Levites did as Moses commanded, and that day about three thousand of the people died. 29 Then Moses said, “You have been set apart to the Lord today, for you were against your own sons and brothers, and he has blessed you this day”.' back

Formalism (mathematics) - Wikipedia, Formalism (mathematics) - Wikipedia, the free encyclopedia, ' In foundations of mathematics, philosophy of mathematics, and philosophy of logic, formalism is a theory that holds that statements of mathematics and logic can be thought of as statements about the consequences of certain string manipulation rules. For example, Euclidean geometry can be seen as a game whose play consists in moving around certain strings of symbols called axioms according to a set of rules called "rules of inference" to generate new strings. In playing this game one can "prove" that the Pythagorean theorem is valid because the string representing the Pythagorean theorem can be constructed using only the stated rules.' back

Fourier analysis - Wikipedia, Fourier analysis - Wikipedia, the free encyclopedia, ' In mathematics, Fourier analysis is the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions. Fourier analysis grew from the study of Fourier series, and is named after Joseph Fourier, who showed that representing a function as a sum of trigonometric functions greatly simplifies the study of heat transfer. Today, the subject of Fourier analysis encompasses a vast spectrum of mathematics. In the sciences and engineering, the process of decomposing a function into oscillatory components is often called Fourier analysis, while the operation of rebuilding the function from these pieces is known as Fourier synthesis.' back

Galileo affair - Wikipedia, Galileo affair - Wikipedia, the free encyclopedia, ' The Galileo affair (Italian: il processo a Galileo Galilei) began around 1610 and culminated with the trial and condemnation of Galileo Galilei by the Roman Catholic Inquisition in 1633. Galileo was prosecuted for his support of heliocentrism, the astronomical model in which the Earth and planets revolve around the Sun at the centre of the Solar System. ' back

Galileo Galilei, Recantation of Galileo (June 22, 1633), ' Therefore, desiring to remove from the minds of your Eminences, and of all faithful Christians, this vehement suspicion, justly conceived against me, with sincere heart and unfeigned faith I abjure, curse, and detest the aforesaid errors and heresies, and generally every other error, heresy, and sect whatsoever contrary to the said Holy Church, and I swear that in the future I will never again say or assert, verbally or in writing, anything that might furnish occasion for a similar suspicion regarding me; ' back

Galileo Galilei - Wikipedia, Galileo Galilei - Wikipedia, the free encyclopedia, 'Galileo Galilei (. . . 15 February 1564 – 8 January 1642), commonly known as Galileo, was an Italian physicist, mathematician, astronomer, and philosopher who played a major role in the Scientific Revolution. His achievements include improvements to the telescope and consequent astronomical observations and support for Copernicanism. Galileo has been called the "father of modern observational astronomy", the "father of modern physics", the "father of science", and "the Father of Modern Science".' back

Genesis 1:27, God creates humans, ' 27: So God created man in his own image, in the image of God created he him; male and female created he them. And God blessed them, and God said unto them, Be fruitful, and multiply, and replenish the earth, and subdue it: and have dominion over the fish of the sea, and over the fowl of the air, and over every living thing that moveth upon the earth. ' back

Georg Cantor - Wikipedia, Georg Cantor - Wikipedia, the free encyclopedia, Georg Ferdinand Ludwig Philipp Cantor (March 3 [O.S. February 19] 1845 – January 6, 1918) was a German mathematician, born in Russia. He is best known as the creator of set theory, which has become a fundamental theory in mathematics. Cantor established the importance of one-to-one correspondence between sets, defined infinite and well-ordered sets, and proved that the real numbers are "more numerous" than the natural numbers. In fact, Cantor's theorem implies the existence of an "infinity of infinities". He defined the cardinal and ordinal numbers and their arithmetic. Cantor's work is of great philosophical interest, a fact of which he was well aware of.' back

Human brain - Wikipedia, Human brain - Wikipedia, the free encyclopedia, 'The human brain is the central organ of the human nervous system, and with the spinal cord makes up the central nervous system. The brain consists of the cerebrum, the brainstem and the cerebellum. It controls most of the activities of the body, processing, integrating, and coordinating the information it receives from the sense organs, and making decisions as to the instructions sent to the rest of the body.' back

Hylomorphism - Wikipedia, Hylomorphism - Wikipedia, the free encyclopedia, 'Hylomorphism (Greek ὑλο- hylo-, "wood, matter" + -morphism < Greek μορφή, morphē, "form") is a philosophical theory developed by Aristotle, which analyzes substance into matter and form. Substances are conceived of as compounds of form and matter.' back

On the Trinity - Wikipedia, On the Trinity - Wikipedia, the free encyclopedia, 'On the Trinity (Latin: De Trinitate) is a Latin book written by Augustine of Hippo to discuss the Trinity in context of the logos. Although not as well known as some of his other works, it is arguably his masterpiece and of more doctrinal importance than the Confessions or City of God. . . . Arthur West Haddan inferred from [the] evidence that it was written between 400, when he was forty-six years old and had been Bishop of Hippo about four years, and 428 at the latest; but it probably had been published ten or twelve years earlier, in around 417.' back

Infallibility - First Vatican Council, The Latin Text of Denzinger: Enchiridion Symbolorum, Definitionum et Declarationum de Rebus Fidei et Morum, Denzinger 3074: 'Romanum Pontificem, cum ex cathedra loquitur, id est, cum omnium Christianorum pastoris et doctoris munere fungens pro suprema sua Apostolica auctoritate doctrinam de fide vel moribus ab universa Ecclesia tenendam definit, per assistentiam divinam ipsi in beato Petro promissam, ea infallibilitate pollere, qua divinus Redemptor Ecclesiam suam in definienda doctrina de fide vel moribus instructam esse voluit; ideoque eiusmodi Romani Pontificis definitiones ex sese, non autem ex consensu Ecclesiae, irreformabiles esse.
Si quis autem huic Nostrae definitioni contradicere, quod Deus avertat: anathema sit.' back

Irrational number - Wikipedia, Irrational number - Wikipedia, the free encyclopedia, 'In mathematics, an irrational number is any real number that cannot be expressed as a ratio a/b, where a and b are integers, with b non-zero, and is therefore not a rational number. Informally, this means that an irrational number cannot be represented as a simple fraction. Irrational numbers are those real numbers that cannot be represented as terminating or repeating decimals. As a consequence of Cantor's proof that the real numbers are uncountable (and the rationals countable) it follows that almost all real numbers are irrational.' back

Isaac Newton (1736), Method of Fluxions and Infinite Series with its Application to the Geometry of Curve-Lines, 'The method of fluxions and infinite series with its application to the geometry of curve-lines by the inventor Sir Isaac Newton ... ; translated from the author's Latin original not yet made publick. To which is subjoin'd, A perpetual comment upon the whole work, consisting of annotations, illustrations, and supplements, to make this treatise a compleat institution for the use of learners. back

Karl Weierstrass - Wikipedia, Karl Weierstrass - Wikipedia. the free encyclopedia, ' Karl Theodor Wilhelm Weierstrass (German: Weierstraß 31 October 1815 – 19 February 1897) was a German mathematician often cited as the "father of modern analysis". Despite leaving university without a degree, he studied mathematics and trained as a teacher, eventually teaching mathematics, physics, botany and gymnastics. Weierstrass formalized the definition of the continuity of a function, proved the intermediate value theorem and the Bolzano–Weierstrass theorem, and used the latter to study the properties of continuous functions on closed bounded intervals.' back

Limit of a function - Wikipedia, Limit of a function - Wikipedia, the free encyclopedia, ' The notion of a limit has many applications in modern calculus. In particular, the many definitions of continuity employ the concept of limit: roughly, a function is continuous if all of its limits agree with the values of the function. . . . In 1861, Weierstrass first introduced the epsilon-delta definition of limit in the form it is usually written today. back

Lumen Gentium (Vatican II), Dogmatic Constitution on the Church, 'THE MYSTERY OF THE CHURCH 1. Christ is the Light of nations. Because this is so, this Sacred Synod gathered together in the Holy Spirit eagerly desires, by proclaiming the Gospel to every creature, to bring the light of Christ to all men, a light brightly visible on the countenance of the Church. Since the Church is in Christ like a sacrament or as a sign and instrument both of a very closely knit union with God and of the unity of the whole human race, it desires now to unfold more fully to the faithful of the Church and to the whole world its own inner nature and universal mission.' back

Medieval university - Wikipedia, Medieval university - Wikipedia, the free encyclopedia, ' A medieval university was a corporation organized during the Middle Ages for the purposes of higher education. The first Western European institutions generally considered to be universities were established in present-day Italy, including the Kingdoms of Sicily and Naples, and the Kingdoms of England, France, Spain, Portugal, and Scotland between the 11th and 15th centuries for the study of the arts and the higher disciplines of theology, law, and medicine. These universities evolved from much older Christian cathedral schools and monastic schools,[3][4] and it is difficult to define the exact date when they became true universities, though the lists of studia generalia for higher education in Europe held by the Vatican are a useful guide.' back

Microscope - Wikipedia, Microscope - Wikipedia, the free encyclopedia, ' A microscope (from Ancient Greek μικρός (mikrós) 'small', and σκοπέω (skopéō) 'to look (at); examine, inspect') is a laboratory instrument used to examine objects that are too small to be seen by the naked eye. . . . .. back

Neuron - Wikipedia, Neuron - Wikipedia, the free encyclopedia, 'A neuron or nerve cell is an electrically excitable cell that communicates with other cells via specialized connections called synapses. It is the main component of nervous tissue in all animals except sponges and placozoa. Plants and fungi do not have nerve cells. . . . A typical neuron consists of a cell body (soma), dendrites, and a single axon. The soma is usually compact. The axon and dendrites are filaments that extrude from it. Dendrites typically branch profusely and extend a few hundred micrometers from the soma. The axon leaves the soma at a swelling called the axon hillock, and travels for as far as 1 meter in humans or more in other species.' back

Nicene Creed - Wikipedia, Nicene Creed - Wikipedia, the free encyclopedia, ' The Nicene Creed (Greek: Σύμβολον τῆς Νίκαιας, Latin: Symbolum Nicaenum) is the profession of faith or creed that is most widely used in Christian liturgy. It forms the mainstream definition of Christianity for most Christians. It is called Nicene because, in its original form, it was adopted in the city of Nicaea (present day Iznik in Turkey) by the first ecumenical council, which met there in the year 325. The Nicene Creed has been normative for the Catholic Church, the Eastern Orthodox Church, the Church of the East, the Oriental Orthodox churches, the Anglican Communion, and the great majority of Protestant denominations.' back

Organon - Wikipedia, Organon - Wikipedia, the free encyclopedia, 'The Organon (Greek: όργανον meaning instrument, tool, organ) is the standard collection of Aristotle's six works on logic. The name Organon was given by Aristotle's followers, the Peripatetics. They are as follows:
Categories
On Interpretation
Prior Analytics
Posterior Analytics
Topics
Sophistical Refutations. ' back

Permutation - Wikipedia, Permutation - Wikipedia, the free encyclopedia, 'In mathematics, the notion of permutation relates to the act of permuting, or rearranging, members of a set into a particular sequence or order (unlike combinations, which are selections that disregard order). For example, there are six permutations of the set {1,2,3}, namely (1,2,3), (1,3,2), (2,1,3), (2,3,1), (3,1,2), and (3,2,1). As another example, an anagram of a word, all of whose letters are different, is a permutation of its letters. The study of permutations of finite sets is a topic in the field of combinatorics.' back

Permutation group - Wikipedia, Permutation group - Wikipedia, the free encyclopedia, 'In mathematics, a permutation group is a group G whose elements are permutations of a given set M and whose group operation is the composition of permutations in G (which are thought of as bijective functions from the set M to itself). The group of all permutations of a set M is the symmetric group of M, often written as Sym(M). The term permutation group thus means a subgroup of the symmetric group. If M = {1,2,...,n} then, Sym(M), the symmetric group on n letters is usually denoted by S_n. The way in which the elements of a permutation group permute the elements of the set is called its group action. Group actions have applications in the study of symmetries, combinatorics and many other branches of mathematics, physics and chemistry.' back

Pierre Teilhard de Chardin - Wikipedia, Pierre Teilhard de Chardin - Wikipedia, the free encyclopedia, ' Pierre Teilhard de Chardin SJ 1 May 1881 – 10 April 1955) was a French Jesuit priest, scientist, paleontologist, theologian, philosopher and teacher. He was Darwinian in outlook and the author of several influential theological and philosophical books. He took part in the discovery of Peking Man. He conceived the vitalist idea of the Omega Point. With Vladimir Vernadsky he developed the concept of the noosphere. In 1962, the Congregation for the Doctrine of the Faith condemned several of Teilhard's works based on their alleged ambiguities and doctrinal errors. Some eminent Catholic figures, including Pope Benedict XVI and Pope Francis, have made positive comments on some of his ideas since. The response to his writings by scientists has been divided. ' back

Planck constant - Wikipedia, Planck constant - Wikipedia, the free encyclopedia, ' Since energy and mass are equivalent, the Planck constant also relates mass to frequency. By 2017, the Planck constant had been measured with sufficient accuracy in terms of the SI base units, that it was central to replacing the metal cylinder, called the International Prototype of the Kilogram (IPK), that had defined the kilogram since 1889. . . . For this new definition of the kilogram, the Planck constant, as defined by the ISO standard, was set to 6.626 070 150 × 10-34 J⋅s exactly. ' back

Platonism - Wikipedia, Platonism - Wikipedia, the free encyclopedia, ' In the 3rd century AD, Plotinus added additional mystical elements, establishing Neoplatonism, in which the summit of existence was the One or the Good, the source of all things; in virtue and meditation the soul had the power to elevate itself to attain union with the One. Many Platonic notions were adopted by the Christian church which understood Plato's Forms as God's thoughts (a position also known as divine conceptualism), while Neoplatonism became a major influence on Christian mysticism in the West through Saint Augustine, Doctor of the Catholic Church, who was heavily influenced by Plotinus' Enneads, and in turn were foundations for the whole of Western Christian thought. Many ideas of Plato were incorporated by the Roman Catholic Church.' back

Pope John Paul II (22 October 1996), Address to Plenary Session on 'The Origins and Early Evolution of Life', ' John Paul II refers to Pius XI’s hope that the Academy would become a Senatus scientificus. In relation to the origins of life and the universe the Pope asks: ‘How do the conclusions reached by the various scientific disciplines coincide with those contained in the message of Revelation? And if, at first sight, there are apparent contradictions, in what direction do we look for their solution?’ John Paul II surveys the Magisterium’s comments on the theory of evolution and adds that ‘to tell the truth, rather than the theory of evolution, we should speak of several theories of evolution’. Those theories of evolution which ‘consider the mind as emerging from the forces of living matter’ are ‘incompatible with the truth about man’. The human being, indeed, is ‘called to enter into eternal life’.' back

Pope Pius X, Lamentabili Sane: The Syllabus of Errors (Condemning the Errors of the Modernists) Sacred Congregation of the Holy Office, July 3, 1907, 'WITH TRULY LAMENTABLE RESULTS, our age, casting aside all restraint in its search for the ultimate causes of things, frequently pursues novelties so ardently that it rejects the legacy of the human race. Thus it falls into very serious errors, which are even more serious when they concern sacred authority, the interpretation of Sacred Scripture, and the principal mysteries of Faith. The fact that many Catholic writers also go beyond the limits determined by the Fathers and the Church herself is extremely regrettable. In the name of higher knowledge and historical research, (they say), they are looking for that progress of dogmas which is, in reality, nothing but the corruption of dogmas. ... ' back

Pope Pius XII (1950), Humani Generis, ' To our Venerable Brethren, Patriarchs, Primates, Archbishops, Bishops and other Local Ordinaries enjoying peace and communion with the Holy See concerning some false opinions threatening to undermine the foundations of Catholic doctrine.' back

Recovery of Aristotle - Wikipedia, Recovery of Aristotle - Wikipedia, the free encclopedia , ' The "Recovery of Aristotle" (or Rediscovery) refers to the copying or re-translating of most of Aristotle's books (of ancient Greece), from Greek or Arabic text into Latin, during the Middle Ages, of the Latin West. The Recovery of Aristotle spanned about 100 years, from the middle 12th century into the 13th century, and copied or translated over 42 books (see: Corpus Aristotelicum), including Arabic texts from Arabic authors, where the previous Latin versions had only two books in general circulation: Categories and On Interpretation (De Interpretatione).' back

Rolf Landauer (1999), Information is a Physical Entity, 'Abstract: This paper, associated with a broader conference talk on the fundamental physical limits of information handling, emphasizes the aspects still least appreciated. Information is not an abstract entity but exists only through a physical representation, thus tying it to all the restrictions and possibilities of our real physical universe. The mathematician's vision of an unlimited sequence of totally reliable operations is unlikely to be implementable in this real universe. Speculative remarks about the possible impact of that on the ultimate nature of the laws of physics are included.' back

Set theory - Wikipedia, Set theory - Wikipedia, the free encyclopedia, 'Set theory is the branch of mathematics that studies sets, which are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics. The language of set theory can be used in the definitions of nearly all mathematical objects. The modern study of set theory was initiated by Georg Cantor and Richard Dedekind in the 1870s. After the discovery of paradoxes in naive set theory, numerous axiom systems were proposed in the early twentieth century, of which the Zermelo–Fraenkel axioms, with the axiom of choice, are the best-known.' back

Sines & Sakellarakis (1987), Lenses in Antiquity, ' A recent find in the Idaean Cave in Crete of two rock crystal lenses of unusually good quality led to this investigation of other lenses in antiquity. This led to an investigation of other lenses from antiquity. The evidence indicates that the use of lenses was widespread throughout the Middle East and the Mediterranean basin over several millennia. The quality of some of these lenses was sufficient to permit their use as magnifying glasses. . . . The fine detail of Roman gold-glass portrait medallions and the discovery of a lens in the house of an artist in Pompeii and another in the house of an artist in Tania are presented as evidence for the use of lenses for magnifying purposes. Methods of producing optical quality lenses by simple procedures are also presented. back

Synapse - Wikipedia, Synapse - Wikipedia, the free encyclopedia, 'In the nervous system, a synapse is a structure that permits a neuron (or nerve cell) to pass an electrical or chemical signal to another cell (neural or otherwise). Santiago Ramón y Cajal proposed that neurons are not continuous throughout the body, yet still communicate with each other, an idea known as the neuron doctrine The word "synapse" (from Greek synapsis "conjunction," from synaptein "to clasp," from syn- "together" and haptein "to fasten") was introduced in 1897 by English physiologist Michael Foster at the suggestion of English classical scholar Arthur Woollgar Verrall.' back

The Pontifical Academy of Sciences, History, ' The Pontifical Academy of Sciences has its roots in the Academy of the Lynxes (Accademia dei Lincei) which was founded in Rome in 1603 as the first exclusively scientific academy in the world. The Accademia dei Lincei achieved international recognition, and appointed Galileo Galilei as a member on 25 August 1610, but did not survive the death of its founder, Federico Cesi. In 1847 Pope Pius IX reestablished the Academy as the Pontifical Academy of the New Lynxes. Pope Pius XI renewed and reconstituted the Academy in 1936, and gave it its present name. Since 1936 the Pontifical Academy of Sciences has grown increasingly international in character. While continuing to further the work of the separate sciences, it stresses the growing importance of interdisciplinary cooperation. Today the Academy's activities range from a traditional interest in pure research to a concern with the ethical and environmental responsibility of the scientific community.' back

Thomas Aquinas, Commentary on Aristotle De Anima 430a10-430a25, ' § 731. The reason why Aristotle came to postulate an agent intellect was his rejection of Plato’s theory that the essences of sensible things existed apart from matter, in a state of actual intelligibility. For Plato there was clearly no need to posit an agent intellect. But Aristotle, who regarded the essences of sensible things as existing in matter with only a potential intelligibility, had to invoke some abstractive principle in the mind itself to render these essences actually intelligible. . . .. § 732. Next, at ‘And this etc.’, he states four qualities or conditions of the agent intellect: first, its separation from matter; second, its impassibility; third, its purity, by which he means that it is neither made up of bodily natures nor conjoined with a bodily organ. Now these three qualities are also found in the potential intellect; but the fourth is proper to the agent intellect, and consists in its being essentially in act; whereas, the potential intellect is essentially potential and comes to act only by receiving an intelligible object.' back

Universe - Wikipedia, Universe - Wikipedia, the free encyclopedia, 'The Universe is all of spacetime and everything that exists therein, including all planets, stars, galaxies, the contents of intergalactic space, the smallest subatomic particles, and all matter and energy. Similar terms include the cosmos, the world, reality, and nature. The observable universe is about 46 billion light years in radius. back

University of Arizona, The Role of Printing in Medieval and Reformation Europe, ' Fifteenth-century Europe experienced a technological revolution in the invention of the printing press with movable type that bears comparison with that of computers today. Although in the earlier era dissemination of such an invention and the realization of its effects took several generations, its transformation of the processes of communication was drastic. Johann Gensfleisch Gutenberg (1397-1468), a goldsmith by craft, tried to conceal his manufacture of movable type and a machine for printing with it. There were in his day no patents or copyrights to shield the inventor against pirating. The length of time needed to carve the type compelled him to borrow money on which to live, and this eventually catapulted him into bankruptcy. Before the banker Johann Fust confiscated his press and began to use it himself, Gutenberg managed to produce his famed 42-line Bible, dated approximately 1455, and several smaller works. The Germans generally acknowledged the discovery of printing as Gutenberg’s and the method as a turning point.' back

Zeno's paradoxes - Wikipedia, Zeno's paradoxes - Wikipedia, the free encyclopedia, 'Zeno's paradoxes are a set of problems generally thought to have been devised by Zeno of Elea to support Parmenides's doctrine that "all is one" and that, contrary to the evidence of our senses, the belief in plurality and change is mistaken, and in particular that motion is nothing but an illusion.' back