MGTutoring

Education is "the systematic training of the conceptual faculty [of the young] by means of supplying in essentials both its content and its method." (Dr. Leonard Peikoff)

The purpose of education is to prepare a child for adult life by training his conceptual faculty. The need for education arises from the fact that man's conceptual faculty is volitional and develops over years of training.

The subjects needed to accomplish the primary goal of education are history, science, mathematics, literature, and grammar/language. History, because it is the story of man and of human nature. Science, because it is the organized study of the external world and natural law. Mathematics, because it is the science of measurement, teaching the tools of science, basic logic, and providing clues to the essence of deduction, induction and the application of knowledge. Literature, because it is the form of art that uses concepts as its medium.

Writing, as a tool of thought, should be done daily in as many subjects as possible. Logic should be taught implicitly in the various subjects through similarity and difference, essentializing, determining cause and effect, analysis and synthesis, induction, and deduction.

The basic principles that need to be applied at all times in all subjects are:

1) context/integration -- all knowledge is interrelated;

 Aristotle and Plato: Detail from The School of Athens by Raphael

2) hierarchy -- all knowledge has structure (lower to more abstract levels) so subjects should be taught step-by-step (see below for more info on hierarchy);

3) reality -- knowledge is knowledge of an objective reality;

4) values -- all knowledge has a value component, a use in attaining the values needed for human life.

A proper education rests on the principles that (1) man is a rational animal (and an individual), (2) reason is man's means of survival and method of cognition, (3) reason is volitional, (4) sense perception is valid, automatic and is the base of all our knowledge, and (5) the external world is intelligible, lawful, and independent of consciousness.

The implications are that one needs to present bite-sized units of knowledge appropriate to the audience's context; the pieces need to be integrated into larger units and into the whole of a person’s knowledge; the purpose and value of what you are teaching needs to drive your presentation; and you need to keep your audience focused on success and their own efficacy, and keep alive (through praise, rewards, and good direction) the burning desire to achieve and move forward -- and to look at failures and weaknesses as things that are in the process of improvement.

A proper education, based on rational principles, will teach students to be self-reliant, independent, objective, purposeful, responsible and value-oriented adults.

 Athena: Greek Goddess of Wisdom and War, artist unknown

"It is absurd to hold that a man ought to be ashamed of being unable to defend himself with his limbs, but not of being unable to defend himself with speech and reason, when the use of rational speech is more distinctive of a human being than the use of his limbs."   -- Aristotle, the Rhetoric.

Lisa VanDamme, the founder and director of the VanDamme Academy in California, has an excellent lecture on the importance of hierarchy in eduction, which you can listen to here: Part 1, Part 2, and Part 3.

"Hierarchy" is the name of the fact that all human knowledge has structure: all knowledge is ordered in degrees of abstraction, starting from the first level of sense perception: what we see and touch. We start with very basic conceptual knowledge -- such as "mom," "dad," "rock," "dog," "chair," "house," "one," "two" -- and build from there. From "mom," "dad," some family members and some friends, we go on to learn the concepts "family," "friend," "city" and "town;" and then on to learn concepts and theories regarding whole societies and history. From our first numbers, we go on to learn arithmetic, then algebra and geometry, then calculus.

The fact that knowledge is hierarchical implies that we must learn the lower levels before we learn the higher levels. It would be absurd to teach calculus before algebra, critical reading before elementary reading, or quantum physics before Newtonian mechanics. Likewise, it is inappropriate to teach "atoms" before the basic chemical theory of gases, "energy" before the basic theories of machines and motion, or "rights" before any study of government.

In her lecture, Mrs. VanDamme discusses the nature of hierarchy, identifies ways hierarchy is "abused" in modern education (since "hierarchy" as a universal aspect of human knowledge is a more recent philosophic discovery, it is not known, and therefore not practiced, in modern education), and discusses ways it should be used in a proper, rational education, using anecdotes from her own school and her own experience.

Study of Euclid’s Elements had a tremendous influence on Galileo Galilei, Sir Isaac Newton, and Abraham Lincoln.

Lincoln’s study of geometry is mentioned at the National Park Service’s website, on the page devoted to the Lincoln Memorial. In discussing his early years, they say:

Lincoln's mother provided his early education. She was a rarity on the frontier in that she could read and shared the skill with him at an early age. The vast majority of his education was acquired by reading. He seldom was without a book and spent long hours studying Shakespeare, Byron, and even Euclid's geometry. Despite having little formal education he triumphed with determination. Lincoln ultimately developed a talent for expression that could have led to a very different career. His "Gettysburg Address" is considered one of the most succinct and eloquently written speeches delivered by an American politician.

But there is a great deal more detail on how mathematics, specifically Euclid’s Elements, sharpened Lincoln’s reasoning skills in “An ‘Old-Fashioned’ Nationalism: Lincoln, Jefferson, and the Classical Tradition” by Drew R. McCoy. Here is an excerpt of this very interesting article:

      As one historian of mathematics has observed, "no work, except the Bible, has been more widely used, edited, and studied, and probably no work has exercised a greater influence on scientific thinking."… Specifically, Euclid's geometry had become, by Jefferson's time, a testament to the power of human reason to deduce truth. On the basis of some formal definitions of terms and five postulates and five axioms whose truth was self-evident—such as, "things that are equal to the same thing are also equal to one another," or "the whole is greater than the part"—Euclidean geometry "deduced an elaborate system of propositions that seemed both to accurately describe physical reality and to compose a flawlessly logical system.” In this sense Euclid did more than teach the principles and methods of correct reasoning in geometry; he could inspire readers of his Elements to apply reason to philosophy, economics, political theory, art, and religion, and in so doing, to arrive at truths that were as valid as mathematical truth.
      …
      As mental exercise, Lincoln's long hours with Euclid doubtless made him a better "close reasoner," to use Herndon's term, and hence a more effective lawyer, which was surely his conscious purpose. But they also helped prepare him, in ways he could not have known, for the unexpected resumption of his political career after 1854. Lincoln had always been noted for his ability to reduce his thought on any given subject to the simplest and plainest terms possible; and during these critical years for the republic, his mastery of that skill allowed him to argue the case against both proslavery and popular sovereignty with something close to "Euclidean coherence." Throughout his protracted debate with Douglas between 1858 and 1860, Lincoln "appealed repeatedly to the nature of proof in Euclid" as the appropriate standard for evaluating the arguments of the two combatants. And in a larger sense, the distinctive qualities of Lincoln's mature political thought, including its content as well as its form and precision, appears to have owed a great deal to his immersion in Euclid.

      Lincoln's ability to whittle down a complex issue to one key principle, or central axiom, directly informed his political message during the second half of the 1850s, when we might say he took a vexingly complex issue, slavery, and whittled it down to a simple issue: the humanity of the slaves. Amid the acrimonious wrangling over the complex details of the politics of slavery in the territories, Lincoln's simple message became unmistakable: If the Negro is a man, then slavery is wrong, and must be disapproved of, and discouraged by all possible legal and constitutional means. In 1859, drawing an explicit connection between Euclid and the Declaration of Independence, Lincoln identified "the principles of Jefferson"—including, of course, the eighteenth-century Euclidean truth that "all men are created equal"—as "the definitions and axioms of free society."