Philosophy of Mathematics

We find the goal of classical mathematics explained in Plato's Republic. The goal of these studies is "to draw the soul towards Being."

Now, there is philosophical talk here, but in this introduction, we will explain exactly what Plato meant, how it relates to Christian thought and how it works out in the Classical Liberal Arts Classical Mathematics courses.

WHAT IS "BEING"?

If you've been around the Academy for any time, you know that our first principle is this:  the soul is superior to the body.  This does not mean that the body is evil and the soul is good, for both body and soul were created by God and were declared to be "good".  The superiority of the soul is concluded from the fact that the body is temporary and must perish, whereas the soul will live after the body--to eternity.  Moreover, virtue tends to belong to the actions of the soul, rather than the body.

We learn from this that, as human beings, our thoughts and cares are not to be limited to the needs and desires of the body or even of this world.  As our nature is eternal and spiritual, our minds are to look beyond what our body can perceive by the senses to those things which our souls can know through faith and/or reason. 

In Plato's philosophical language he refers to everything that pertains to the bodily life as of as the world of "becoming".  By this he means a world that is temporary and often deceiving.  It is a world, as Jesus says, "where moth and rust destroy, and thieves break in and steal"--a world of change and uncertainty.  The realm of the soul he speaks of is eternal and unchanging--and therefore "real".  When such principles are held, the goal of all learning is to know of the world of "being", which is only possible when the studies are conducted through the eye of the soul, i.e., reason.  This idea is wholly compatible with Christian principles.  After all, this is the idea expressed in fundamental passages of Scripture, such as Romans1:17, "the just man shall live by faith", or 2 Corinthians 5:7, "we walk by faith, not by sight.". This notion is not merely a teaching of the classical philosopher Plato, but an absolute truth held also in Christianity, and is essential to restoring true Christian education. 

Let's consider an example.  When the soul leaves the body at death it will have no eyes to see with, no ears to hear with, no mouth to taste with, no hands to feel with, no nose to smell with.  What then will it do?  It will reason.  This activity of the soul need not begin after death.  In fact, Wisdom teaches us that reason is to govern the bodily senses, that is, we are to begin living today as we will live after death.  This is the difference between the worlds of "becoming" and "being" and mathematics were historically known to lead us to this sort of study.

Note: For an interesting read, we recommend C.S. Lewis' book The Great Divorce which provides an imaginative presentation of these ideas.

THE PURSUIT OF "BEING"

Mathematics are an important part of the classical system because they are studies that "invite or excite intelligence".  The best studies for the cultivation of wisdom are those that the senses are not adequate judges of.  Plato gives the example of looking at three fingers.  The eyes are adequate judges of whether they are fingers or not, and this study does not invite thought.  However, when the question turns to size or number of the fingers and further still to defining size and number, the senses often fail to guide us and we are required to turn to intelligence for answers.  For example, if I hold my finger in front of a distant tree my eyes tell me that my finger is larger than the tree.  However, intelligence is excited to clarify this confusion.  This is beginning of the road to true knowledge and understanding of the universe, for the senses are deceiving in many other areas as well.

How different is this system from modern study which believes just the opposite, that the senses (scientific experimentation) are the ultimate judges of truth and reality.  This is the crux of the issue in education and culture and the reason why so much harm is done by modern mathematics and science programs.