Author Archives: Bob Hunter

7. Dante’s The Divine Comedy

At rare moments in a cultural tradition, great works are created which sum up all the strands of thought and imagination that have gone into the making of that tradition. Such a unifying work is usually the work of a poetic genius. In the case of Western Christendom, that moment comes in the early part of the 14th century; the work is The Divine Comedy, and the poet is Dante Alighieri. (Mortimer J. Adler and Seymour Cain, Religion and Theology, volume 4 of The Great Ideas Program, Encyclopedia Britannica, 1961, page 109)

Thus Mortimer J. Adler and Seymour Cain introduce their guide to Dante’s The Divine Comedy, which I’ve now reached in my rereading of selections from Great Books of the Western World guided by The Great Ideas Program. They conclude their introduction to The Divine Comedy with this claim regarding it, “The result is both a literary masterpiece and an unforgettable view of man’s spiritual nature and destiny” (Adler and Wolff, page 110).

Adler and Wolff go on to: (I) consider the purpose and subject of The Divine Comedy; (II) survey its first two sections, “Hell” and “Purgatory;” (III) introduce the assigned reading, “Paradise;” (IV) identify and explain the significance of the figures that Dante meets in his ascent through Paradise; and (V) discuss three questions which they ask on Dante and The Divine Comedy. Here I’ll sketch the life of Dante, note what Adler and Wolff say about the purpose and subject of The Divine Comedy, and pose the three questions asked by Adler and Wolff.

Dante
Dante was born in Florence, Italy, in 1265. He received a rich education in classical and religious subjects. His idealized love for a beautiful girl, Beatrice Portinari, provided much inspiration for his writings. However, although grief-stricken by her early death, shortly afterwards he married Gemma Donati and they had at least three children.
Dante was active in the political and military life of Florence. He became involved in a political dispute between two groups, the Guelphs and the Ghibellines. A group within the Guelphs that was hostile to Dante gained control of Florence about 1300 and banished Dante. He spent the last few years of his exile in Ravenna, where he died in 1321.
Dante began working on The Divine Comedy in about 1308 and completed it in 1321. It was his masterpiece, but his other works also “hold an important place in the history of Italian literature and make their essential contribution to the formation of a literary awareness and tradition, establishing new literary forms and new aims of thought” (The New Encyclopedia Britannica, 1974, volume 5, page 481).

The Purpose and Subject of The Divine Comedy
The original title of the work was The Comedy of Dante Alighieri, with “comedy” referring to its happy ending at the throne of God. “Divine” was added in the 16th century, expressing admiration for its high quality as well as indicating its sacred theme. Dante’s aim was to affect human character and action. In a letter to his patron he wrote: “The subject of the whole work, taken merely in its literal sense, is the state of souls after death, considered simply as a fact. But if the work is understood in its allegorical intention, the subject of it is man, according as, by his deserts and demerits in the use of his free will, he is justly open to rewards and punishments.” (Adler and Wolff, page 111)

Questions asked by Adler and Wolff:
1. Are we to take Dante’s story as an imaginative fiction or as an allegory of religious truth?
2. Who was Beatrice? What does she represent in the poem?
3. What are Dante’s theological views?

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6. Aquinas’ Summa Theologica

In my rereading of selections from Great Books of the Western World guided by The Great Ideas Program, I’ve come to Aquinas’ Summa Theologica. The only systematic theology in the original Great Books of the Western World (Encyclopedia |Britannica, 1952), it occupies two volumes (19 and 20) of the 54 books in the set even though parts of it are omitted. (The 1990 edition of the set also includes selections from Calvin’s Institutes of the Christian Religion.) It constitutes the sixth reading in the fourth volume of The Great Ideas Program, Religion and Theology, by Mortimer J. Adler and Seymour Cain (Encyclopedia Britannica, 1961).

Adler and Cain conclude their introduction to Aquinas’ Summa Theologica in The Great Ideas Program by observing that although it was questioned and even attacked as heretical in some of its doctrines in its day, “this synthesis of reason and revelation has become in modern times the accepted intellectual structure of the Roman Catholic Church” (Adler and Cain, Religion and Theology, page 86). They go on to consider: (I) its sources and form of exposition; (II) First Part, Question 1: The Nature and Extent of Sacred Doctrine; (III) Second Part, Part II, Treatise on Faith, Hope, and Charity, Question 1: Of Faith; (IV) Second Part, Part II, Treatise on Faith, Hope, and Charity, Question 2:Of the Act of Faith and Question 3: Of the Outward Act of Faith; and (V) six questions which they ask on the reading.

Here I’ll sketch Aquinas’ life, summarize the first section in Adler and Cain’s guide, pose the questions which they ask on the reading, and summarize briefly how they answered the questions.

Thomas Aquinas

Thomas was born in 1224/25 near Naples and entered the University of Naples in 1239. In 1244 he joined the Dominicans, who immediately assigned him to study theology in Paris. Opposed to his doing so, his family abducted him on his way to Paris. However finding that nothing could shake his determination, they released him the following year.

Arriving in Paris in 1245, Thomas began studying theology at the Dominican convent under Albertus Magnus, a champion of Aristotle. When Albertus was appointed to organize a Dominican house of studies at Cologne in 1248, he took Thomas with him. After four more years of study, Thomas received his bachelor’s degree in 1252 and returned to Paris to teach and to train to become a master in theology, which he became in 1256.

Although only a little more than thirty-one, Thomas was appointed to fill one of the two chairs allowed the Dominicans at the university. However, in 1259, after three years of theological teaching there, he returned to Italy, where he remained nine years, teaching and writing. Suddenly, in 1268, he was called back to Paris to combat both those who were opposed the use of Aristotle in theology and those who were presenting an Aristotelianism seemingly incompatible with Christianity.

In 1272 Thomas was recalled to Italy to reorganize all the theological courses of his order. He went to Naples, where he taught at the university and continued to write. However his writing career came suddenly to an end on December 6, 1273. While saying mass that morning a great change came over him, after which he stopped writing. Urged to complete Summa Theologica, which he had begun in 1267, he replied: “I can do no more; such things have been revealed to me that all I have written seems as straw, and I now await the end of my life” (quoted in Great Books of the Western World, volume 19, page vi).

The following year Thomas became ill on his way to attend the Council of Lyons, stopped at the Cistercian monastery of Fossanova, and died on March 7, 1274.

Summa Theologica

“The Summa Theologica is a systematic exposition of theological knowledge, compiled from all available sources with the master purpose, of course, of setting forth and defending Christian doctrine” (Adler and Cain, page 87). Theological knowledge includes knowledge about man and the world as related to God as well as knowledge about God. The sources of Summa Theologica include classical Greek (especially Aristotle) and medieval Jewish and Islamic philosophers as well as Christian thinkers.

Summa Theologica consists of three parts divided into treatises. (The Second Part is also divided into two parts.) Each treatise is divided into questions, which are divided into articles. The title of each article gives the question in affirmative form. It is followed by a general negative answer, introduced by “We proceed thus to the [number of the article] Article,” and a listing of specific negative points called “Objections.” Then Aquinas summarizes the opposite view, introducing the summary with “On the contrary.” The body of the article, introduced by “I answer that,” gives Aquinas’ judgment on the various views. Finally Aquinas replies to the numbered objections in order. According to Adler and Cain, this form was typical of the day.

Questions

Is the God of philosophical reason the same as the God of religious faith?
Adler and Cain give three possible answers‒the first affirming that “philosophy provides an objective norm for the religious view,” the second affirming that “religious faith gives the only true picture of God’s nature and attributes,” and the third affirming that “both the philosophical and religious views do justice to the divine reality” (Adler and Cain, page 102)‒and ask which view Aquinas takes. In Question I, Article 1, of the First Part Aquinas speaks favourably of both the philosophical doctrine and the divine revelation about God, suggesting that he takes the third position. However in the same article he affirms that “besides the philosophical sciences discovered by reason there should be a sacred science obtained through revelation” for “man’s salvation, which is in God” (Great Books of the Western World, volume 19, page 3), suggesting that he takes the second position.

Is a man free to refuse the gift of faith?
Adler and Cain suggest seeing Question VI, Article 1, of Part II of the Second Part. In it Aquinas says that two things are required for faith: that the things which are of faith be proposed to a person and that the person assent to the things which are proposed to him or her. He also says that for a person to believe his or her will needs to be prepared by God with grace. However he doesn’t specify whether or not a person can refuse the gift of faith.

How can sacred theology be a science if its origin is faith, and its aim salvation?
Adler and Cain note that Aquinas deals with this question in Question I, Articles 2 and 4, of the First Part. In Article 2 Aquinas compares sacred theology, which draws its first principles from divine revelation, with the sciences of perspective and music, which draw their principles from mathematics, and in Article 4 he decides that sacred theology primarily provides theoretical knowledge about God rather than practical knowledge about what people should do. However Adler and Cain claim that “the question is still an open one for us, since Aquinas’ answers are in terms of medieval notions of science and are inconclusive” (Adler and Cain, page 103).

How does a believer know that what he believes is divine revelation?
Adler and Cain observe, “The traditional answer is that he knows this through faith,” but continue, “But faith involves the gift of divine grace. How do we know that it is a genuine faith we have, and not mere conformity to what has been handed down to us?” (Adler and Cain, page 104). Aquinas claims that miracles and “the inward impulse of the Divine invitation” confirm the authority of Divine teaching but admits that the believer “has not…sufficient reason for scientific knowledge” (Great Books of the Western World, volume 20, page 399).

Is it legitimate for theology, as a scientific discipline, to use figurative expressions?
Adler and Cain note that Question I, Articles 9 and 10, of the First Part deals with the interpretation of scriptural symbols. In Article 9 Aquinas argues, “It is befitting Holy Writ to put forward divine and spiritual truths under the likenesses of material things” (Great Books of the Western World, volume 19, page 9). In Article 10 he considers different senses that a word may have in the Bible‒historical or literal, allegorical, tropological or moral, and anagogical.

Does “faith” mean anything besides intellectual assent to propositions?
In Question II, Article 1, of Part II of the Second Part Aquinas concludes that “to believe is to think with assent” (Great Books of the Western World, volume 20, page 391; on the previous page he defined “to believe” as “the inward act of faith”). However Adler and Cain distinguish between faith as intellectual assent to propositions and as personal trust in God.

6. Ptolemy’s The Almagest

The motions of the heavenly bodies have played a prominent role in the thoughts and lives of men since the earliest known times, The regularities of the stars in their courses have guided men in the planning and harvesting of food, in hunting and fishing, and other vital activities. The heavenly order and harmony has also played a role in religious life and in thought about the basic nature of the universe. This intense practical and spiritual interest in the heavens accounts for astronomy’s becoming the most highly developed natural science of the ancient world. The work of Ptolemy of Alexandria represents the peak of this development. ( Mortimer J. Adler and Peter Wolff, Foundations of Science and Mathematics, volume 3 of The Great Ideas Program, Encyclopedia Britannica, 1960, page 75)

Thus Mortimer J. Adler and Peter Wolff open their guide to Ptolemy’s The Almagest, which I’ve now reached in my rereading of selections from Great Books of the Western World guided by The Great Ideas Program. They go on to observe that although we no longer accept the picture of the world which Ptolemy drew–that the earth is the centre of the planetary system and that the heavens have perfect regular movement, we do accept many of his purposes and methods, pursuing astronomy as a science. They conclude their introduction to their guide to The Almagest thus: “In short, the heritage which Ptolemy has left us is that the entire physical universe must and can be explored by the mind of man” (Adler and Wolff, page 76).

In the guide itself, Adler and Wolff consider what is known about Ptolemy, summarize Chapters 1-8 of Book I of The Almagest, investigate Ptolemy’s purpose in The Almagest, examine the apparent irregularity in the motion of the sun, and discuss these questions:
– What do you think of the principle that all heavenly motions must be reduced to uniform circular motion?
– Is Ptolemy’s The Almagest a work of “celestial mechanics”?
– Are Ptolemy’s explanations of planetary motion true or false?
Here I’ll just sketch what is known about Ptolemy’s life and list the titles of the chapters of The Almagest assigned for reading in The Great Ideas Program.

Ptolemy
Ptolemy’s full name was Claudius Ptolemaeus. His birth and death dates aren’t known, but Adler and Wolff suggest that they were about 100 and 178 A.D. He worked in or near Alexandria in Egypt. Greek astronomy culminated in Ptolemy. His work drew heavily from his predecessors, especially Hipparchus (about 130 BC) but he had no successors. His fame rests chiefly on The Almagest (originally known as “The Mathematical Collection”), but he also composed many shorter astronomical and mathematical works. After The Almagest, his most important work is his Guide to Geography, which was for geography what The Almagest was for astronomy until well into the Renaissance. (The Renaissance was the great revival of art, literature, and learning in Europe in the 14th, 15th, and 16th centuries.)

The Almagest
The Almagest contains 13 books (indicated below by Roman numerals), each with several chapters (indicated below by Arabic numerals).
I, 1. Preface
I, 2. On the Order of the Theorems
I, 3. That the Heavens Move Spherically
I, 4. That the Earth, Taken as a Whole, is Sensibly Spherical
I, 5. That the Earth is in the Middle of the Heavens
I, 6. That the Earth has the Ratio of a Point to the Heavens
I, 7. That the Earth Dies Not in any way Move Locally
I, 8. That There Are Two Different Prime Movements in the Heavens
(In I, 8, the two movements are the general daily motion from east to west and the slower movement of the planets, including the sun and moon, from west to east.)
II, 3. How, with the Same Things Given, the Height of the Pole is Given, and Conversely
II, 4. How One is to Calculated at What Places, When, and How Many Times, the Sun Comes to the Zenith
(In II, 3 and 4, Ptolemy explains the apparent irregularity in the motion of the sun. Adler and Wolff devote almost half of their guide to commenting on the two chapters.)

5. St. Augustine’s The Confessions

In this text St. Augustine, one of the greatest thinkers of the early Christian Church, gives us a profound and impressive example of Biblical interpretation. We witness a unique combination of personal piety and spiritual vision fused with literary and philosophical judgment. We see a man with an impassioned soul, wrestling for the truth, using all the highly developed faculties of his mind, and at the same time relying on divine grace to get at the supremely important meaning of Genesis. The words almost steam from the page in the heat of his ardor, but they bring us light and depth as well as heat.

Their speaker is no mere archaeological specimen in the history of thought. Augustine has had a remarkable, continuing influence on religious thought in the Western world from the 4th century to the present day. Texts like this one have earned him that perennial, vivifying influence.

(Mortimer J. Adler and Seymour Cain, Religion and Theology, volume 4 of The Great Ideas Program, Encyclopedia Britannica, 1961, pages 67-68)

In my rereading of selections from Great Books of the Western World guided by The Great Ideas Program, I’ve come again to St. Augustine’s The Confessions. Earlier I read and reported on its Books I-VIII; see
https://opentheism.wordpress.com/2017/09/15/8-st-augustines-the-confessions/. Its Book XI, Sections I-XIII, and Book XII constitute the fifth reading in the fourth volume of The Great Ideas Program, Religion and Theology by Mortimer J. Adler and Seymour Cain (Encyclopedia Britannica, 1961).

The quotation with which I opened this article comes from the introduction to Adler and Cain’s guide to the reading. They go on to consider: (I) some of the views held by Greek philosophers about the origin of the world; (II) how Augustine interprets“In the beginning God created” of Genesis 1:1; (III) how Augustine interprets “the heaven and the earth” of Genesis 1:1; (IV) Augustine’s admission that, although he holds to his interpretation of Genesis 1:1, other interpretations may be true; and (V) four questions which they ask on the reading.

Here I’ll just pose the questions which Adler and Cain ask on the reading and summarize briefly how they answer them.

Does Genesis say that the world was made out of nothing, or out of formlessness?
Adler and Cain consider both options.

If God is omnipotent and perfectly good, why did He create an imperfect world?
By “imperfect world” Adler and Cain mean a world that can fall away from perfection. They suggest different answers to the question by means of a series of questions.

Are graded levels of being necessary for an interpretation of Genesis?
After noting that Augustine held that all things were distant from (or close to) God, Adler and Cain discuss whether there may have been “qualitative distinctions in the various aspects of created being” (Adler and Cain, page 81).

Wherein is Augustine a Neoplatonist and wherein is he a Christian?
Adler and Cain summarize the Neoplatonic and Christian views of creation and ask a series of questions about the presence of each in Augustine’s view of creation.

5. Archimedes’s On Floating Bodies

In my rereading of selections from Great Books of the Western World guided by The Great Ideas Program, I’ve reached the fifth reading in the third volume of The Great Ideas Program, Foundations of Science and Mathematics by Mortimer J. Adler and Peter Wolff (Encyclopedia Britannica, 1960), Archimedes’s On Floating Bodies. I considered his On the Equilibrium of Planes in an earlier post. See it for some information about Archimedes.

In their guide to On Floating Bodies, Adler and Wolff describe it as “a masterpiece of simplicity.” They continue:

All he asks us to grant him is a single postulate stating the characteristics of water and other fluids. The rest is a matter of geometric reasoning. This is all we need for the study of floating bodies, with Archimedes as our teacher.
The odd and wonderful thing about this is that you do not even need water or objects to put in it. It may be fun to verify some of the theoretical demonstrations in the washbowl or bathtub. But Archimedes gives the scientific essentials about floating bodies without experimentation. As you follow him along, you, too, may want to cry out “Eureka.”
( Mortimer J. Adler and Peter Wolff, Foundations of Science and Mathematics, volume 3 of The Great Ideas Program, Encyclopedia Britannica, 1960, pages 61-62)

“Eureka” refers to a story told about Archimedes. Hiero, the king of Syracuse (a Greek city on the island of Sicily), had ordered a new crown. The crown was to be made of pure gold, but the king suspected that the jeweller had mixed in some less costly silver. He asked Archimedes to determine whether the crown was made of pure gold or was a mix of gold and silver. The solution came to Archimedes while he was in the bathtub, and he was so excited that he jumped out of the tub and ran naked through the streets shouting “Eureka [I have found it]!”) Archimedes’s solution was based on equal weights of gold and silver having different volumes and thus that if a crown made of gold and silver were lowered into water it would displace more volume than a crown made of pure gold would.

The postulate which Archimedes asks us to grant him is:

Let it be supposed that a fluid is of such character that, its parts lying evenly and being continuous, that part which is thrust the less is driven along by that which is struck the more; and that each of its parts is thrust by the fluid which is above in a perpendicular direction if the fluid be sunk in anything and compressed by anything else. (Archimedes, On Floating Bodies, Great Books of the Western World [Encyclopedia Britannica, 1952], volume 11, page 538)

The postulate is followed by seven propositions. The first four are preliminary and are summarized thus by Adler and Wolff:

The cross-section of a sphere, through the center, is always a circle (Prop. 1), If a body equal in specific gravity with a certain fluid is submerged in that fluid, it will neither sink to the bottom nor stick out of the fluid, but will rest just below the surface (Prop. 3). A body lighter than the fluid in which it is submerged will partially submerge and partly project out of the fluid (Prop. 4). (Adler and Wolff, page 66).

The other propositions are:

Proposition 5. Any solid lighter than a fluid will, if placed in the fluid, be so far immersed that the weight of the solid will be equal to the weight of the fluid displaced.
Proposition 6. If a solid lighter than a fluid be forcibly immersed in it, the solid will be driven upwards by a force equal to the difference between its weight and the weight of the fluid displaced.
Proposition 7. A solid heavier than a fluid will, if placed in it, descend to the bottom of the fluid, and the solid will, when weighed in the fluid, be lighter than its true weight by the weight of the fluid displaced.
(Archimedes, pages 540-41)

Archimedes bases his proof for each of the propositions on a mathematical diagram, which he explains. I also found Adler and Wolff’s explanations of them (Adler and Wolff, pages 66-67) helpful.

Besides commenting on the propositions in On Floating Bodies, Adler and Wolff summarize Archimedes’s accomplishments in mathematics, recount two of the “fabulous” stories told about Archimedes, and discuss the following questions:
– How might the “crown problem” been solved?
– How would you measure the amount of weight a body loses by being immersed in water?
– What is the empirical evidence in which On Floating Bodies is based?

4. New Testament’s The Gospel According to St. Matthew

In my rereading of selections from Great Books of the Western World guided by The Great Ideas Program, I’ve reached The Bible’s The Gospel According to St. Matthew. It constitutes the fourth reading in the fourth volume of The Great Ideas Program, Religion and Theology by Mortimer J. Adler and Seymour Cain (Encyclopedia Britannica, 1961).

Adler and Cain introduce the reading by observing that the New Testament Gospels are not only historical documents and literary masterpieces but also an expression of the early Christian Church’s faith that God had directly revealed Himself in the life, teaching, and death of Jesus of Nazareth. They conclude their introduction thus:

The New Testament proclaims that God took on human form, suffered gross indignities, and died an ignominious death. In this humiliation and this death, as well as in the subsequent resurrection, lie the meaning and the glory of the Gospel story for the Christian faith. (Mortimer J. Adler and Seymour Cain, Religion and Theology, volume 4 of The Great Ideas Program, Encyclopedia Britannica, 1961, pages 49-50)

Adler and Cain go on to look at the land, people, religion, and politics of Palestine in Jesus’s time. Next they explain how the New Testament came into being and why they selected Matthew for their Gospel readings. Then they summarize the events recorded in Matthew, noting their significance in Jesus’s life and ministry. Finally they ask and discuss some questions about the Gospel. Here I’ll just pose the questions which they ask and summarize what they say in response to the questions.

Why does Jesus put together the two commandments‒to love God and to love one’s neighbor? (Matthew 22:34-40)
Adler and Cain observe that some people stress one of the commandments over the other, ask a series of questions on the relationship between the two commandments, and suggest seeing I John 4:20-21 for one view of the double commandment.

Is Jesus’ commandment to leave one’s family destructive of human relations and hence contradictory to the law of love? (Matthew 10:34-39)
Adler and Cain observe that there are many possible interpretations of Jesus’s injunction, consider two of them, and suggest rereading the passage and Matthew 12:46-50 and venturing your own interpretation of them.

Was Jesus’ ethical teaching influenced by his expectation of the imminent advent of the Kingdom of God?
Adler and Cain observe that some thinkers, notably Albert Schweitzer, think so but that others think that Jesus’s ethical teaching is addressed to ordinary earthly existence.

What does the term “Son of Man” mean?
Adler and Cain observe that in Jesus’s native Aramaic “Son of Man” meant mankind but that in apocalyptic literature it signified the Messiah. They note that the phrase is common in Matthew and that in each case the reader will have to determine from the context what it means.

4. Nicomachus’s Introduction to Arithmetic

In my rereading of selections from Great Books of the Western World guided by The Great Ideas Program, I’ve reached the fourth reading in the third volume of The Great Ideas Program, Foundations of Science and Mathematics by Mortimer J. Adler and Peter Wolff (Encyclopedia Britannica, 1960), Nicomachus’s Introduction to Arithmetic.

Nicomachus of Gerasa (probably a Greek city in Palestine) flourished around the end of the first century. His Introduction to Arithmetic was the first work to treat arithmetic as a discipline independent from geometry. Setting out the elementary theory and properties of numbers, it was used as a textbook for a thousand years.

Adler and Wolff consider the first sixteen chapters in Book One of Introduction to Mathematics and divide their study of them into these sections:
I ‒ a comparison of the concerns of Nicomachus’s and today’s arithmetic.
II ‒ an explanation of Nicomachus’s classification of numbers.
III – a presentation and discussion of three questions on the reading.
Here I’ll summarize briefly I and II, present the three questions, and indicate how Adler and Wolff answer them.

Comparison of Nicomachus’s and Today’s Arithmetic
Today we expect an arithmetic textbook to show us how to perform arithmetical operations such as addition, subtraction, multiplication, division. However Introduction to Arithmetic studies numbers themselves and their properties, relations, and classification. Adler and Wolff attribute this to Nicomachus’s belonging to the school of Pythagorus, a group of mathematicians and philosophers who thought that the principles of mathematics were the principles of all things.

Classification of Numbers
Like Euclid Nicomachus classifies numbers as even, odd, even-times even, even-times odd, odd-times even, and odd-times odd numbers. For Nicomachus even-times even numbers are numbers that have only even factors; even-times odd numbers are even numbers that are the product of 2 and an odd number; odd-times even numbers are numbers that can be divided by 2 several times eventually arriving at an odd number; and odd-times odd numbers are numbers that are the product of two odd numbers. Nicomachus also talks about perfect numbers, which are considered below in the first question.

Questions
– What is a perfect number?
A perfect number is a number which is the sum of its factors. Examples are 6 and 28, 6 because it is the sum of 1, 2, and 3 (its factors) and 28 because it is the sum of 1, 2, 4, 7, 14 (its factors)..
– What is a prime number?
Nicomachus says that a prime number “is found whenever an odd number admits of no other factor save the one with the number itself as denominator, which is unity, for example, 3, 5, 7, …” (Nicomachus, Introduction to Arithmetic, Great Books of the Western World [Encyclopedia Britannica, 1952], volume 11, page 817). However we generally consider 2 to be a prime number too because it has no other factors but 1 and itself.
– Is the Pythagorean concern with numbers foolish and superstitious or is there some point to it?
Adler and Wolff answer, “Modern mathematicians are still concerned with numbers, and with the properties of them as primeness, evenness, perfectness, etc. All these properties are treated in the Theory of Numbers.” However they go on to concede that “perhaps the Pythagoreans went to extremes when they made number a cosmological principle and considered numbers as the elements or principles of things.” (Adler and Wolff, Foundations of Science and Mathematics, Encyclopedia Britannica, 1960, pages 58-59).