Analytic philosophy refers to a school of philosophy that grew in England during the early part of the twentieth century, thanks to thinkers such as Bertrand Russell and G.E. Moore. Analytical philosophy is so-called because of its focus on logical clarification, an analysis of logic itself, and the positing of logical problems. Analytical philosophy, in contrast to so-called Continental philosophy, also rejects grand sweeping philosophical systems or theories and focuses on the small details of philosophical problems.

Charles Sanders Peirce is largely credited with developing and defining pragmatism in the late nineteenth century, and fittingly was a chemist. Pragmatists described thought not as mirroring reality, but as instead being used to fully predict and plan in problem solving. Peirce's ideas about pragmatism were picked up and built on by early-twentieth-century American thinkers like John Dewey and William James.

Epistemology, which is a specific form of philosophy, is devoted to the nature of thinking itself, or the theory of knowledge. As such, epistemology deals with questions regarding how people know what they know or acquire knowledge. The field is remarkably new in the history of philosophy, only being coined by the Scottish thinker James Frederick Ferrier in the nineteenth century.

Immanuel Kant was the inheritor of the great pedagogical program of German scholasticism, drawing on a number of thinkers such as Wilhelm Gottfried Leibniz (especially through the works of Christian Wolff) and many, many others. At a certain point in his career, however, Kant came to the conviction that the excesses of these so-called "rationalistic" philosophers could not provide an adequate grounding for the sciences and for the moral life.

Therefore, Kant undertook a change of perspective that led to the publication of his three best known works: The Critique of Pure Reason, The Critique of Practical Reason, and The Critique of Judgment. These three texts sought to explain just what could be known within the bounds of finite human reason—thus providing a critical perspective regarding what he took to be the excesses and emptiness of the philosophy that he had taught for many years.

The notion of "Cartesian Dualism" is named after the thinker René Descartes(1596-1650)—a man who is often seen to be one of the fathers of modern philosophy. In his Discourse on Method and his Meditations on First Philosophy, Descartes makes a number of famous arguments. One of the most well known ideas is that the soul is completely distinct from the body. He concludes this from the idea that thought is clearly distinct from the notion of "body." The latter is really more of a geometrical "stuff" than anything else. He claims that even if we didn't have a body, we could still have self-consciousness.

His arguments are more complicated than this, of course, and they are open to many critiques. Be that as it may, one of the hallmarks of his philosophy is this kind of "dualism." In general a "dualism" occurs when we explain something through two different, unique principles that are not reducible to each other. Thus, for him, the human person is reduced to these two principles: soul and body. It's up to the philosopher to try to puzzle out how they are related.

The philosophy of Plato is known for many things. One of his most famous doctrines is the so-called theory of "Forms" or "Ideas." This refers to the notion that everything in the world "participates" in some kind of universal and separate Idea. Thus, we can only call this or that tree a "tree" because those various individual trees participate in the universal notion of "treeness."

This position is often called "extreme realism" because it supposes that our ideas are so real that they actually exist. It is like there is a kind of "heaven" (loosely speaking) in which the Ideas exist. A radically contrary position is sometimes named "nominalism", which indicates that there are no universal Ideas that are really "out in reality." Instead, a strictly "nominalist" position would state that universal ideas like "tree" and "dog" only exist because we give name to individual things.

Throughout the writings of Plato, we are presented with an image of Socrates as a disputant, constantly arguing with a group of philosophers known as the "sophists." The word "sophist" actually comes from the same roots as "philosophy," though the meaning is interesting—and quite telling about what had so angered Socrates. "Philosophy" literally means "love of wisdom." A "sophist" is someone who appears to be wise—but in fact is not. This is quite the vexing issue for Socrates. There are people who have the appearance of wisdom but in fact are not. Thus, in many of the dialogues, he is presented as arguing against this kind of sophistry. It is also for this reason that he expresses concerns about people who make images and write poetry. Such people seem to be just like sophists—who make bad arguments appear like they are good ones.

The Middle Ages were a complex period of time—spanning many centuries and having many thinkers. There were some thinkers Peter Damian who had negative thoughts about theology, as well as Bernard of Clairvaux, who warred at length with the Peter Abelard, accusing the latter of heresy. Indeed, even the philosophically erudite Bonaventure of Bagnoregio had his reservations regarding the place of philosophy in the curriculum at the University of Paris.

However, many figures (indeed, including Bonaventure) supported the use of philosophy in teaching. Such figures include the "big names" as Augustine of Hippo, Thomas Aquinas, John Duns Scotus, and many, many others. Indeed, even in the monastery schools (that would be important for thinkers like Bernard), some philosophy was indisputably necessary for learning.

However, what was quite unique to the Middle Ages—whether in academic settings like Paris or in the humblest of monastic schools—was the overall structure of the disciplines. For a Medieval philosopher, philosophy was always a "stepping stone" to something else. Indeed, its most important role was to be an assistant to theological studies. Hence, it is most often known as the "handmaiden of theology." (Indeed, Peter Damian gave this name to it so as to insult it—as if to say, "It is only a handmaiden.) Philosophy studies were really just a gateway to medical, legal, and theological studies (whether academic theology or the biblical theology of the monasteries). Above all, though, if we wanted to characterize the outlook regarding philosophy during these centuries, the best phrase (at least among those provided here) would be, "Handmaiden of theology."

The notion of the "liberal arts" is notoriously slippery. In different ages, different things are said to be part of the liberal arts. As the curriculum of the medieval university solidified, however, the seven liberal arts took up a basic form that became normalized by the twelfth / thirteenth century. These were divided into the "trivium" and the "quadrivium"—or, the "three subjects" and the "four subjects." The trivium was devoted to topics needed for all other learning, so it focused on grammar, rhetoric, and logic. These introduced the quite young students to the tools needed for later studies. The quadrivium was made up of primarily mathematical courses, namely arithmetic, geometry, astronomy (like physics today), and music (a study of harmonies and proportions).