What scholars call the “foundation of Liberal Arts” – the Trivium – is taught in order that one may expand to other subjects, building upon the skills learned. These subjects have been varied over time, based on the philosopher teaching them but they are now generally accepted as mathematics, geometry, music, and astronomy – the Quadrivium. While these subjects were taught by ancient philosophers (Pythagoras, Plato, Aristotle, etc) they became “the Quadrivium” in the Middle Ages in Western Europe, after Boethius or Cassiodorus had a go at translation. (Encyclopedia Britannica has an excellent article on Mathematics in the Middle Ages, which discusses the Quadrivium briefly.)
Anicius Manlius Severinus Boethius (usually known simply as Boethius) (c. 480 – 525) was a 6th Century Roman Christian philosopher of the late Roman period. Flavius Magnus Aurelius Cassiodorus Senator (c. 485 – c. 585), commonly known as Cassiodorus, was a Roman statesman and writer, serving in the administration of Theoderic the Great, king of the Ostrogoths. The former, Boethius, did a great deal to translate most of the ancient philosophers from Greek to Latin. Many of his works on Aristotle were foundational learning in the Middle Ages. Cassiodorus made education his life’s passion, particularly the liberal arts, and worked diligently to ensure classical literature was at the heart of Medieval learning. Both men have been credited with coining the term “Quadrivium,” or “where four roads meet.” Adding to the mix of Medieval education “influencers” is Proclus Lycaeus, one of the last classical philosophers and an ardent translator of Plato. He is considered one of the founding “fathers” of neoplatonism and had a great influence on Medieval education as well. His translations of Plato are peppered with his own ideas of education and philosophy. One of his most interesting books, considered a major work, is “The Platonic Theology.”
For the serious student of the classics, all of these philosophers, in their original Greek or Latin (with English translations alongside the original) can be found in the Loeb Classical Library series. Many used book stores, especially near universities, carry these books and they can be had for about 10$ each. There are hundreds of books but all are quite good as original references (See NOTE below…) Back to the Quadrivium…
While many see the Trivium and Quadrivium as “separate,” I think this is a manufacture of our modern educational system. The Trivium are the basics for communicating thought, generating ideas, and conveying those thoughts clearly; yet, like Freemasonry, I don’t know that you would have jumped completely away from your foundations. Plato, in The Republic, does note that the quadrivium subjects, as identified above, should be taught separately. The Pythagorean school divided the subjects up between quantity (mathematics and harmonics, or otherwise known as music) and magnitude (geometry, cosmology or astronomy.) Personally, I find it difficult to talk about music without first having at least fundamental mathematics and exploring both together makes sense. I have not delved into the curriculum of the universities of the Middle Ages in Europe but if someone else has, it would be interesting to hear about it. 
What I find most fascinating about the art surrounding the Quadrivium (and the Trivium, for that matter) is that nearly all of the plates, pictures, or engravings represent the subject matter as female or feminine. Perhaps it has to do with the receptive qualities of studiousness, or the idea of fecundity or maybe gentleness; whatever the reason, many of the Medieval and Renaissance European depictions show all subjects with a feminine demeanor. Since nearly all scholars in the middle ages in Europe were men, perhaps it was simply a bleed-over of the Medieval ideal of women. I’m sure this is another subject for another time…
On an additional side note, I searched for representations of the Quadrivium and Trivium in Islamic art, also knowing full well that Islam is aniconistic. Islam really had begun to gain ground at the last part of the classical period in North Africa & Europe and as such did not really experience the same type of “downfall” or Dark Ages, that Europe did. The schools of Islam continued to develop the subjects of the quadrivium and trivium uninterrupted until Europe “caught up.” In fact, many of the mathematics, geometry, and astronomy texts of the latter Middle Ages were translated from Greek to Syriac Aramaic or from Arabic to Latin, and later taught in Latin universities in Europe. Suffice to say that Islam did have an impact of the learning of the West, probably much more than most people today are aware.
So, why would the Freemason study the Quadrivium? The answer, to me, is obvious. If the one of the primary studies we must take on is Geometry, we need to understand how number fits into this process. We need Mathematics to understand Geometry, and Music to understand relationship of numbers, working in harmony. Astronomy teaches us our place in universe, and allows us to expand our knowledge of our own earth toward the heavens. Geometry, or the study of the measurement of the earth, is far more than the squares and triangle theorems we all know…and love. It’s about how to apply these numbers to the world around us. As we will see in each of the subjects, they can be taken for their base modern “ideas” or we can expand and overlap them, apply them to the natural world, and thereby become better caretakers of not only the earth we live on but the beings who live on it with us. The idea of a Renaissance Man is one who is well-versed in these foundations and has ideas that expand the world around us. They make the world a better place to live in, now and for the future. The Freemason, to me, embodies this idea completely.
Next stop, the subjects of the Quadrivium. Thank you for joining me!
NOTE: For those interested in more of the Loeb Classical Library, but limited access to purchase these books, Harvard University Press has been working to put them online. The link is here: http://www.hup.harvard.edu/features/loeb/digital.html.
Individuals can subscribe for a yearly cost, with subsequent years being cheaper, and non-profits can also subscribe for a reduced cost. If you are a serious researcher and you would like primary sources, this library is an excellent resource.
usical craftsmanship, the movement ends with a sublime message:
The ‘reduction to the absurd’ technique is used throughout Greek philosophy, beginning with Presocratic philosophers. The earliest Greek example of a reductio argument is supposedly in fragments of a satirical poem attributed to Xenophanes of Colophon (c.570 – c.475 BC). Criticizing Homer’s attribution of human faults to the gods, he says that humans also believe that the gods’ bodies have human form. But if horses and oxen could draw, they would draw the gods with horse and oxen bodies. The gods can’t have both forms, so this is a contradiction. Therefore, the attribution of other human characteristics to the gods, such as human faults, is also false.
Logic is mental training: once the words and language have been developed, we can 
Figures of speech are the use of any of a variety of techniques to give an auxiliary meaning, idea, or feeling. An example of this is dysphemism. This is the use of a harsh, more offensive word instead of one considered less harsh. Dysphemism is often contrasted with Euphemism. Dysphemisms are generally used to shock or offend. 
ural world around him, the study of grammar, regardless of the age of the individual, is pivotal. Grammar is foundational to all problem-solving methods.
and without a Freemasonic connection. It’s up to you, the reader, to decide what you’d like to do with the information.
That trust involves risk means that we place a value on trust that is above much of our common interaction with people. Having trust in something or someone can create a dependency that may be “warranted” or not. We need to see value in something in order to actually grant trust. Ergo, that value can be lost if trust is broken. We gain much when we trust – opportunities for cooperative activity, meaningful relationships, knowledge, autonomy, self-respect, and overall moral maturity. Perhaps trust itself has no value – that is, we grant trust not because we will obtain something for ourselves (and the trustee) but “just because” we find the person to be upright. Should we trust them solely out of respect for their person? If trustworthiness is a virtue, and we seek to grow it in ourselves, then doesn’t it behoove us to show respect for another simply because we see they are trustworthy? Shouldn’t others afford us the same quarter? “Trust would be a sign of respect for others if it were an attitude of optimism about the trustee’s character: that is, if it assumed that virtue resided within this person’s character. Moreover, trust that has intrinsic value of this sort presumably must be justified. If optimism about the person’s character was inappropriate, then the respect would be misplaced and the intrinsic value would be lost.” 
be invited to dinner. As the cliche goes, “It’s not about you. It’s about me.” I feel as if I am in constant discovery of myself so to be authentic for me is to be present. As long as I am thoughtful and searching my feelings with honesty, that is as authentic as I can be. Like everyone else, I change my feelings and mind, as I learn more about myself and knowledge about the world. Am I still worthy of trust if my authenticity is fluid? I hope so.
maintenance of the site. No one is exempt from this expectation except the infirm or very senior or aged attendees. In general, this seems to work very well. People are cooperative, happy to help, and understand not only the value of “many hands make light work” but also Industry or work are good for us overall. People feel better when they are participating and joining in the creation of a harmonious and giving space. When twenty people clean up, it means more time spent for everyone in other activities. The group is happy and the environment is uplifting.
and their responses, showing how it impacts others, and providing a few possible ways to approach the issue. I try to approach it as a discussion rather than an admonishment – at least the first time. Maybe even the second time. Yet, I always have that fear of bringing something up to someone and having them be upset; indeed, this is the reason most of us don’t do it in the first place. We think we are one of three things: we are not responsible, we’re acting beyond our authority, or we’re going to upset people.
As Freemasons, our behavior away from our Lodge is equally as important as our time within the Lodge. We’re taught how to behave with one another, including the ability to address concerns with a fellow Brother directly and with virtue. Shouldn’t we afford the rest of our community the benefit of our lessons learned? That is part of helping humanity improve, I think. It doesn’t make it easy when the rest of the world doesn’t play by the same rules. It also doesn’t exempt us from facing the challenges and the hard work ahead. If we dislike entitlement so much, and we resent the people who fall into that mode of being, what are we doing to combat it? What are we doing to improve it, whether it is a head-to-head conversation or immersion in supporting an organization like Habitat for Humanity or mentoring for job-training programs? It behooves us to be the examples of working hard to show the meaning of real service, gratitude, and entitlement. 
United States, prior to the advent of Yellow Journalism about 1895, received their “news” from varied opinions. Newspapers, the main form of information, were clear in their support of one political party or the other; with names like the Carolina Federal Republican, Democratic Press, or the Impartial Register, you knew clearly which way the articles and opinions would be written. You knew the “slant” of the news. From the printing of the “Federalist Papers” in the later part of the 18th Century until the end of 19th Century, people of the U.S. read partial and partisan newspapers willingly and enthusiastically. All indications are that people read more than one; it was not uncommon for people to read many papers espousing what they believed and what they did not in order to round out their opinions on the matter. The Jeffersonian way of thinking held sway:
In this new electronic media era, we are learning again how to debate and how to be tolerant. We are learning to see more than one side, and to perhaps give leeway to “the other guy;” being able to see the whole picture gives us a 360-degree view. If we didn’t have the other person’s outlook, we only get half of the story. As human beings, we need to remember that our perspective is limited by our senses. In addition to our physical perception only being able to see what is in front of us, we register different words and not others, we see different colors than are “true.” 
might be presented for differing points of view and to stimulate the thought that there may be varying sides of a debate even outside of the presented topic. Those who have been on debate teams are aware of the need for a well-rounded view when it comes to debate; seeking beyond what we know and what we think we know is difficult. We need that jolt of a drastically different viewpoint to understand that wider view of the world, and to understand how others think and live. In order for that to happen, we need to be able to listen well and with tolerance. 
instances, on one undertaking at one place and at the same time, and they might or might not use machinery.” In other words, a factory is industry but building a skyscraper is also “industry.”
