The Greek philosopher Aristotle (384-322 B.C.) was the author of many works on logic, metaphysics, ethics, politics and natural science. Unfortunately, most of Aristotle's writings have been lost. Still, what has survived has a profound effect on Western thought. Aristotle was trained in Athens at Plato's Academy, where he first went as a 17-year-old boy. He stayed there for twenty years, eventually becoming Plato's most renowned student. Aristotle in turn became a teacher, his most famous student being Alexander the Great. Aristotle based his philosophy on logic and rational thinking, and devoted much of his energy to studying the facts and laws of the physical world. Where Plato defined philosophy in terms of ideas, Aristotle defined it in terms of actual existence.


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Descartes, Rene

René Descartes (1596-1650) was a Frenchman whose work in philosophy and mathematics was seminal to 17th century thought. Descartes's father was an intellectual who ensured that his son had a thorough education by sending him to a Jesuit school, where the young Descartes was taught literature, grammar, mathematics and science. He then went on to earn advanced degrees, studying law, philosophy, theology and medicine.

At the young age of 22, Descartes devised a system, called analytic geometry, in which he applied the techniques of algebra to the solution of geometric problems. This approach to geometry was so useful that, although it was not published for 19 years, Descartes's work revolutionized mathematics. Today, every high school student learns how to use algebraic equations to work with geometrical shapes, and how to use the Cartesian coordinate system (with its X- and Y-axes) to graph various lines and curves. All of this was invented by Descartes.

Although Descartes had a broad education, he was left with the feeling (all too uncommon, unfortunately) that he actually understood very little. In a quest for precision and certainty, he came to look upon mathematics as the only subject that satisfied him intellectually. As he grew older, Descartes began to devote much of his time to philosophy, using his mathematical training to explain the world in terms of rational thought, as opposed to faith. Descartes, however, lived in a time when anything that challenged the supremacy of faith (not to mention the supremacy of the Catholic Church), was extremely controversial. For example, in 1633, he chose to delay the publication of one of his books, "The World", in which he defended the view that the Sun, and not the Earth, was the center of the universe. He did this because, a year earlier, Galileo had been severely condemned by the Church for proposing the same idea.

Unlike most of his contemporaries, Descartes believed that metaphysical discourse should be based on mathematical reasoning, rather than on the subtleties of academic sophistry. As such, he rejected the tradition of scholasticism, the philosophy of Western Christendom in the Middle Ages that sought to use reason to justify conclusions that were based on faith. In doing so, Descartes supplied the bridge between the philosophy of his times and all that was to follow and, today, he is remembered as the father of modern philosophy.

Descartes's most important philosophical theories are contained in two of his books "Discourse on Method" (1637) and "Meditations" (1641), in which he abandons the then current authoritarian system of thought for a more logical approach. Starting with the idea of universal doubt, he asserts that the only thing that cannot be doubted is doubt itself. Therefore, the doubter -- in this case, Descartes himself -- must exist. He then uses this idea, one step at time, to prove that God must exist as a first cause. From there, he develops a proof that the physical world is real, showing it to be mechanistic and completely separate from the mind.

The most well-known of Descartes's thoughts is the famous assertion Cogito, ergo sum, which, loosely translated from the Latin, means "I think, therefore I am". In other words, "Because I know that I think and, hence, that I doubt, I therefore know that I exist which, in turn, causes me to exist." (What is less well known is that Descartes once had a younger brother. Unfortunately, one day, in the heat of a philosophical debate, the brother uttered the words, "I don't think--" upon which, he instantly vanished.)


Hegel, Georg Wilhelm Friedrich

The German philosopher Georg Wilhelm Friedrich Hegel (1770-1831) wrote widely about life, religion, art and ethics, and is considered to be one of the most influential thinkers of all time. Hegel taught that the purpose of philosophy is to find the truth. To do so, he abandoned the logical, one-step-at-a-time method developed by Aristotle, in favor of a process that we now call "dialectical thinking". Dialectical thinking uses a variety of logical arguments in order to examine and analyze all the important aspects of a particular topic. To apply Hegel's methods, we first state an idea (often referred to as a thesis) and develop a contradictory idea (an anti-thesis). Then, by logical argument, we resolve the two contradictory ideas into a single, coherent whole. In Hegelian terms, the resulting synthesis "sublates" (that is, preserves and overcomes) the contradictions of the various arguments in order to create a higher, more truthful realization. Hegel rejected the idea that knowledge is gained by separate steps of logical reasoning leading to a final conclusion. To Hegel, true knowledge is a process that comes only when the arguments and analyses regarding a specific topic are considered in totality.


Kant, Immanuel

Eventually, we are all faced with big questions about life: How do we reconcile our strong wish-to-live with the knowledge that we will someday die? Does our life have meaning? Is there a God? Such questions lead us to metaphysics, the area of philosophy concerned with the basic nature of existence. The German philosopher Immanuel Kant (1724-1804) is one of the towering figures in the history of metaphysics because of his ideas on how we should think about such questions, as well as the influence he had on other philosophers, both contemporaries and descendents. To Kant, our perceptions are translated into understanding by the use of reason. He suggested there were two types of perceptions: physical sensation and our sense of moral duty. When we apply reason to sensation, we are able to understand the world around us -- the highest expression of which is the creation of science. When we apply reason to our moral duty, we understand morality and ethics. To Kant, reality exists only because we can, in one way or another, perceive it and think about it. However, our mind -- the tool with which we reason -- is limited by its basic structure. Therefore, we are, by our nature, limited in our understanding of the universe, which renders us unable to answer certain crucial, but tantalizingly elusive questions. During his lifetime (80 years), Kant never traveled more than fifty miles from home.



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Machiavelli, Niccolo

Niccolo Machiavelli (1469-1527) was a political philosopher during the Italian Renaissance. Machiavelli was a diplomat and a highly educated author who wrote on a wide variety of topics. However, he is chiefly remembered for his book "The Prince", a cornerstone of modern political philosophy.

Within "The Prince", Machiavelli offers detailed advice to rulers on how to maintain and to extend their power. His main thesis is that a "prince" (that is, a ruler) who wishes to retain absolute control of his territory must use, not only wisdom and skill, but cunning and ruthlessness.

For example, in Chapter 17, Machiavelli asks the question, "Is it better for a prince to be feared or loved by his subjects?" He answers that it is better to be feared, because people are fickle, ungrateful and cowardly. "Men have less scruple in offending one who is beloved than one who is feared, for love is preserved by the link of obligation which, owing to the baseness of men, is broken at every opportunity for their advantage; but fear preserves you by a dread of punishment which never fails." However, although it is not necessary for a prince to be loved, he should not be hated.

Even today, "The Prince" is a powerful book that creates strong feelings in anyone who reads it. For instance, later in Chapter 17, Machiavelli explains that, although it may become necessary for a prince to kill someone, he should, on no account, take the property of one of his subjects. "Men more quickly forget the death of their father than the loss of their inheritance." Just take a moment to relate this type of thinking to modern politics, and you will see that some things never change.

It is easy to be cynical about Machiavelli's work, seeing it only as a textbook on expediency, an instruction book for ruthless leaders. (Indeed, we use the word Machiavellian to describe someone who is both clever and willing to abandon moral principles for political gain.) However, such judgments are a misinterpretation of Machiavelli's work.

Machiavelli finished "The Prince" in 1513 (although it was not published until 1532, five years after his death). Machiavelli was born in Florence at a time when Italy was embroiled in intense political conflict. There were four large city-states, Florence, Milan, Venice and Naples, as well as four major powers, the Papacy, France, Spain, and the Holy Roman Empire. In order to protect themselves, the city-states did their best to play the larger powers against one other. As a result, Italy was, for a long time, home to continual intrigue, blackmail and violence. When we view Machiavelli's work in this context, it makes sense that he would look for a leader who would be able to unify Italy and protect it from foreign intervention, even if it was (necessarily) a ruthless tyrant.

As I mentioned, "The Prince" is Machiavelli's most famous book. However, he also wrote upon a variety of topics: "On the Art of War" (1521) discusses military problems in relation to politics; "Discourses on the First 10 Books of Livy" (1531) offers a general theory of government; "History of Florence" (1532) is considered to be a literary masterpiece; finally, Machiavelli also wrote many poems and plays, including a ribald comedy "Mandragola"(1524).


Marx, Karl

The German philosopher Karl Marx (1818-1883) was one of the most influential political writers in history. Indeed, in the last half of the twentieth century, almost half the people in the world lived in countries governed by principles based on Marx's work.

To understand the scope and importance of Marx, we must look to his childhood and to the political situation of his time. Marx grew up in a learned family that prized education. In fact, he came from a long line of rabbis on both sides of the family. In 1835, at the age of 17, Marx went to the University of Bonn to study law. However, Marx's father felt his son should go to a more serious school so, a year later, Marx was sent to the University of Berlin where he studied for four years.

Even as a young man, Marx had a thoughtful, philosophical bent. When he was 17 years old, he wrote a letter to his father, in which he pondered the choices that a young person must make when choosing a profession:

"...But the chief guide which must direct us in the choice of a profession is the welfare of mankind and our own perfection. It should not be thought that these two interests could be in conflict, that one would have to destroy the other; on the contrary, Man's nature is so constituted that he can attain his own perfection only by working for the perfection, for the good, of his fellow men. If he works only for himself, he may perhaps become a famous man of learning, a great sage, an excellent poet, but he can never be a perfect, truly great man."

I have quoted from this letter at such length to show you that Marx was much more than a political philosopher. As he grew older, he developed into a highly educated economist, a historian, a social scientist and, eventually, a revolutionary.

In October 1842, not long after finishing his formal education, Marx began to edit a 4-month old liberal newspaper, "Rheinische Zeitung", in the Prussian city of Cologne. (At the time, Prussia was an independent kingdom, the largest and most important of the Germanic states.)

Up to now, Marx had looked at the study of the law only as an academic pursuit. However, "Rheinische Zeitung" was an outlet for the region's middle class and intellectuals, people who were strongly opposed to Prussian authoritarianism. As editor, Marx was obliged -- for the first time in his life -- to confront legal and political issues from a practical viewpoint. This led him to turn his attention to economics and, within a short time, he began to develop a progressive, anti-authoritarian philosophy.

In November of 1842, Marx met Friedrich Engels, a German writer who was visiting the newspaper on his way to England. Marx and Engels began to collaborate, the start of a fruitful and stimulating partnership that was to last the rest of their lives. Under Marx's guidance and Engels' influence, the newspaper became more and more radical. In March 1843, Marx was forced to resign and, two weeks later, the Prussian government closed down the paper.

Marx then traveled to Paris, where he became involved with working-class, socialist groups. At the end of 1844, he was expelled from Paris, and he and Engels went to Brussels, where they stayed for three years. During this interval, Marx devoted himself to an intensive study of history, developing a materialistic conception of the field. In doing so, he took a very important philosophical step.

At the time, European metaphysics was dominated by Hegel's philosophy of idealism, based on two ideas. First, that reality is a creation of the mind; second, that history can be explained as an eternal struggle between opposing spiritual forces, a concept known as the Hegelian dialectic.

For Marx, reality was material, not spiritual. He rejected Hegel's interpretation of history in favor of a more practical doctrine, which came to be known as Dialectical Materialism. According to Marx, all progress takes place because of a "struggle of opposites", a naturally occurring process that cannot be influenced by individuals. People make social decisions solely in response to their economic needs and, thus, over time, the characteristics of a society are determined by its economic structure. Within a particular culture, classes arise based on people's relationships to the means of production. (For example, there are owners, managers, workers, and so on.)

These ideas served as the basis of a complex political doctrine that came to be called Marxism. Briefly, Marxism holds that the history of society is best-understood as "the history of class struggle". In the same way that the old feudal nobility was replaced by the bourgeoisie (that is, the capitalist class), the bourgeoisie itself will, one day, be replaced by the proletariat (the working class). In a capitalist system, the bourgeoisie is able to flourish because it extracts surplus profit from the products produced by the proletariat. However, capitalism has inherent contradictions, fatal weaknesses that, over time, become more and more severe. Eventually, the proletariat will become so impoverished that they will revolt and take control of the means of production, resulting in a completely classless society. Once this happens, the oppressive, coercive capitalist state will be replaced by a society based on rational economic cooperation.

While living in Brussels, Marx and Engels joined a newly formed organization of German emigre workers. The organization was based in London and called the Communist League. At the end of 1847, Marx and Engels traveled to London for a Communist League conference, where they were commissioned to write a "succinct declaration" of the organization's principles.

The result, published in 1848, was "The Communist Manifesto", arguably the single most influential political statement in history. Within the Communist Manifesto, Marx applied the concepts of dialectical materialism, asserting that social reform -- "the triumph of the working class" -- was not only desirable, but inevitable.

In May, 1949, Marx was once again exiled. This time he moved to London, where he would live for the rest of his life. During this time, Marx did a great deal of writing and political organizing.

In the 1850s, he studied political economics and wrote weekly articles as a foreign correspondent for the New York Daily Tribune. In 1857, he produced an 800-page manuscript called "The Grundrisse" (Outlines), which was not published until 1941.

In the 1860s, he wrote three large volumes, "Theories of Surplus Value", in which he discussed theories of political economics. And in 1864, he and Engels helped found the International Workingmen's Association.

From 1867 to 1894, Marx created his greatest work, a three- volume treatise called "Das Kapital" ("Capital"), in which he used Dialectical Materialism to analyze and explain economic and social history. The first volume was published in 1876, and Marx worked on the other two for the rest of his life.

On March 14, 1883, Marx died. At his funeral, he was eulogized by Engels: "Fighting was his element. And he fought with a passion, a tenacity and a success such as few could rival... Though he may have had many opponents, he had hardly one personal enemy. His name will endure through the ages, and so also will his work." After Marx's death, Engels edited and published the second and third volumes of "Das Kapital".

Although it is true that many of Marx's predictions about the course of the revolutionary movement were wrong (at least, so far), there is no gainsaying that he was a true genius who left a firm, enduring mark on the world in which he lived. Even today, there are many who believe, as Engels did, that, "just as Darwin discovered the law of development of organic nature, so Marx discovered the law of development of human history." As Marx himself wrote in a letter (to Engels in 1868):

"It is absolutely impossible to transcend the laws of nature. What can change in historically different circumstances is only the form in which these laws expose themselves."


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Nietzsche, Friedrich

The German philosopher Friedrich Wilhelm Nietzsche (1844-1900) was one of two thinkers who laid the foundation of existentialism (the other one being Kierkegaard). When Nietzsche was young, he was heavily influenced by Schopenhauer (who was not a happy camper). Eventually, Nietzsche mellowed out and rejected Schopenhauer's depressive outlook on life. Still, Nietzsche did recognize that life was not uniformly good. All lives are difficult, he taught, and full of pain. What makes some lives fulfilled is the manner in which the pain has been met. Happiness is not easy to achieve and requires much effort. He warned against that which artificially removed the pain of life, in particular, alcohol and Christianity. Of all his work, which was considerable, Nietzsche's masterpiece is considered to be "Thus Spake Zarathustra".



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Pascal, Blaise

Blaise Pascal (1623-1662) was a French religious philosopher, who was also a highly accomplished mathematician, physicist and inventor.

When Pascal was three years old, his mother died, leaving him to be brought up exclusively in the care of his father, the mathematician Étienne Pascal. (Pascal family trivia: Étienne Pascal was the discoverer of a curve called the "Limaçon of Pascal".) The elder Pascal took his son's education so seriously that he decided to teach the boy completely by himself. For reasons of his own, the elder Pascal decided that his son would not be allowed to study mathematics until he was 15 years old, even going so far as to remove all mathematics books from the house. (As you will see later, the Pascal family was, in general, a few variables short of an equation.)

Young Pascal was very bright and, as you might expect, the fact that he was forbidden to study math only served to stimulate his curiosity. At the age of 12, he secretly began to study geometry by himself (parents take note!). Within a short time, Pascal contrived a proof that the sum of angles within a triangle is always equal to two right angles (that is, 180 degrees). When the young lad showed the proof to his father, the elder Pascal relented and gave his son a copy of the work of Euclid.

As a young man, Pascal was unusually insightful and productive. At the age of 16, for example, he presented a short paper containing several projective geometry theorems, including one dealing with what is sometimes called "Pascal's mystic hexagon". From the ages of 19 to 22, he invented the first-ever digital adding machine, called the Pascaline. However, it was not a commercial success; only 50 were ever made.

Pascal was a natural mathematician who was instrumental in advancing many areas of mathematics including conic sections, projective geometry, probability theory (corresponding by letter with Fermat), and combinations, creating the so-called Pascal's triangle (used to calculate binomial coefficients). However, the young Pascal was also a physicist. He contributed significantly to the study of hydraulics, both as a theoretician and as the inventor of the hydraulic press. Today, Pascal is honored by having his name used in two important ways: first, the international unit of pressure is called the "pascal" (1 pascal = 1 newton/square meter); second, a well-known programming language, developed in 1970, was named Pascal. As a philosopher, Pascal met with less success because he developed an obsession with religion that came to dominate his life and stunt his intellectual achievement.

When Pascal was 14, his father seriously injured his leg and was cared for by two members of a religious movement. The two caregivers had a profound effect on the young boy, turning him towards a strong religious belief. Years later, at the age of 31, Pascal was involved in an accident in which he came close to being killed. Although he was not injured, he was affected psychologically and, within a few weeks, after having what he interpreted as a religious experience, he abandoned mathematics and physics permanently, in order to devote himself exclusively to religion and theology.

Over the years, Pascal wrote many essays dealing with religious philosophy. His most influential work was "Pensées" (French for "Thoughts"), in which he discussed his beliefs and inferences regarding faith in God and human suffering. In his lifetime, Pascal was not able to finish "Pensées". However, eight years after his death, in 1670, Pascal's notes were published in book form and soon became a classic of religious literature. (So when you read the book, be aware that Pascal did not consider it a finished product.) Although it is difficult to find relevance to modern life in "Pensées", one does encounter many interesting ideas. For example, in Section XII, Pascal observes, "The Gospel only speaks of the virginity of the Virgin up to the time of the birth of Jesus Christ," an intriguing thought to say the least.

As a religious philosopher, Pascal is best remembered for an argument within Pensées (Section III) that is now referred to as Pascal's Wager. Put simply and informally, Pascal's Wager asserts that we should all choose to believe in God because, whether or not he actually exists, we have nothing to lose and everything to gain. Today, there are many well-developed refutations of Pascal's Wager, and only the most naive of debaters would advance it as a serious argument. (If you ever get into an argument with such a person, you might point out that an all-powerful, all-knowing Creator of the Universe would surely be able to distinguish between real faith and the synthetic faith that comes from hedging one's bets.) Regardless of its shortcomings, Pascal's Wager has earned a permanent place in history as one of the two most famous arguments in the philosophy of religion (the other being St. Anselm's Ontological Argument for God's existence).

Although Pascal was a brilliant, unusually productive young man, his career was, unfortunately, cut short by misfortune. In his late 30s, Pascal developed stomach cancer and, in 1662, at the age of 39, he died in terrible pain, after the cancer spread to his brain.


Russell, Bertrand

The English philosopher Bertrand Russell (1872-1970) was a multitalented scholar who, during a long career, contributed substantially to a variety of disciplines. In his 20s and 30s, Russell became an authority in mathematics and logic, analytic philosophy, and social philosophy. As he grew older, he expanded his outlook into the popular culture, becoming one of the most important liberal thinkers and political activists of the 20th Century.

Russell's success as a leader was not unexpected: he was born into one of England's most distinguished aristocratic families. In fact, his grandfather, Lord John Russell, twice served as Prime Minister under Queen Victoria. After the death of his parents, and later his grandfather, Russell was raised by his grandmother, who did her best to mold and to educate him as a future prime minister. However, in 1890, when he was 18, Russell went to Trinity College, Cambridge, and his life turned in a different direction.

At the university, Russell excelled at philosophy and mathematics, and, in 1908, at the age of 26, he was elected to a Fellowship of the Royal Society, an unusual and prestigious honor for one so young. On the strength of his achievements, Russell was appointed to a lectureship at Trinity College in 1910. During this time, Russell collaborated with the mathematician Alfred Whitehead to publish "Principia Mathematica", a 3-volume landmark of mathematical thinking and logic (1910-1912).

"Principia Mathematica" left the world with two enduring legacies. First, within the mathematical community, Russell and Whitehead convincingly showed that formal logic was crucial to the study of set theory and the foundations of mathematics. While doing so, they introduced notation that was superior to what was currently being used, which had the secondary effect of helping to popularize the use of logic within mathematics.

Second, Russell and Whitehead were able to demonstrate important connections between formal logic and mainstream philosophy. This was no mean accomplishment and, to this day, Russell is considered one of the most influential philosophers of the 20th Century. Indeed, he is considered to be one of the founders of analytic philosophy, the branch of philosophy that seeks to apply formal logic to problems in epistemology (the nature of knowledge) and metaphysics (the nature of reality).

As accomplished as Russell was as a mathematician and a philosopher, it was as a social critic and humanist that he became a public figure. In his lifetime, Russell wrote over 70 books, as well as thousands of essays and letters, addressing a large variety of topics. Much of his work was non-technical, related to political activism. (As a passionate pacifist, Russell believed that war was morally unacceptable and is never justified). In his lifetime, Russell was arrested a number of times for antiwar activities, the first time during World War I. In 1916, at the age of 34, Russell was convicted of antiwar activities, an ignominy that cost him his lectureship at Trinity College. Two years later, in 1918, he was convicted again and spent six months in prison, during which time, he wrote the book "Introduction to Mathematical Philosophy" (a non- technical exposition of the ideas in "Principia Mathematica").

In 1939, he was offered a teaching position at New York City College. However, because of his beliefs -- Russell was not only a pacifist, but an atheist and a proponent of sexual freedom -- Russell's academic appointment soon caused a public outcry. There was an inquiry and, in 1940, a local court nullified the contract, pronouncing Russell "morally unfit" to teach at the college.

Such contretemps were typical of Russell's life. He ran, unsuccessfully, for the British parliament in 1907, 1922 and 1923; he was married four times, the last time at age 80; and he was involved, time and again, in political activities which often put him at odds with the prevailing culture. In 1961, at the age of 89, he was once again imprisoned, this time for antinuclear protests. However, Russell was also the recipient of many honors. In 1949, he was awarded the Order of Merit by King George VI (a rare honor); and in 1950, he was awarded the Nobel Prize in Literature "in recognition of his varied and significant writings in which he champions humanitarian ideals and freedom of thought".

In 1967, Russell wrote his very last essay. In it, he briefly pondered the state of the world and his role in working toward peace. He then observed: "There is an artist imprisoned in each one of us. Let him loose to spread joy everywhere." Three years later, in 1970, Bertrand Arthur William Russell, the third Earl Russell, died in Penrhyndeudraeth, Wales, at the age of 97.


Socrates and Plato

The work of Greek philosophers Socrates and Plato is linked forever. Socrates (460-399 B.C.) was a renowned philosopher, dedicated to self-knowledge and rational thinking. He developed a style of teaching that involved asking someone one question after another, in order to lead that person to the truth. (In case you want to try it, you should know that a lot of people found this to be highly irritating.) Eventually, Socrates fell afoul of the authorities in Athens, where he lived, and was put to death. (They charged him with corrupting the minds of the Athenian youth, and with not worshipping the city's gods.) Socrates' most important pupil was Plato (427-347 B.C.), who founded a school, called the Academy (386 B.C.), where he taught and wrote for much of his life. (Plato's most important student was Aristotle.) It is from Plato that we know about Socrates, as Socrates himself did not leave any written records. Plato presented Socrates' ideas in the form of dramatic dialogues. The writings are charming, and have been consistently popular and influential. However, there is no real way to know which views were Socrates' and which were Plato's. Both men were interested in moral philosophy and regarded natural philosophy (science) as an inferior type of knowledge. They saw knowledge as being good in its own right, and not for any practical purpose. (Platonic trivia: In the dialogue "Timaeus", Plato invented a tale about a fictional land he called Atlantis. It is from this tale that the myth of Atlantis arose.)