Epistemology is the study of how we know what we think we know, and how certain we are of certainty. It is an idea that goes back to antiquity, with the ever loquacious Hellenes mapping out the territory.
Axiomic Ontology, and Sophism
However, the most fundamental and influential text on epistemology, was not philosophical, but the Elements of Geometry by Euclid. Euclid's hypnotic system came down to two essential points. The first is that he had only a very small number of operations, and essentially only one assertion: the fifth postulate asserts the nature of flatness, the second is that the entire structure has a swiftly flowing narrative. The story of the Pythagorean Theorum is told in 48 propositions.
Later writers would pick at this structure, calling the first proposition a hidden axiom, but what would scratch at them is the fifth postulate, to see if it could be derived from the other four. However, after two thousand years, European mathematics finally gave in, and found that there were other shapes than flat. The irony, of course, is that geometry is "measuring the earth" and its axioms were not out of a universal basic generative requirement. Or to put it simply, one can have geometries on a flat surface that use other than a straight edge and compass. It was the technology of that time, which allowed for circles and lines even over long distances, and not deep truth that dictated what Euclid was interested in.
The other hypnotic idea from antiquity was the assertion of divinity. This assertion: that the universe is so much greater than we can imagine being created by physical means that we can see, implies a super-natural power or powers, is one that clearly runs deep in human beings. The twin miracles that are used as the proof of this are consciousness, and existence. Because consciousness and existence seem of a different quality than everything else we know, they must be from some other source. This is the ontological argument. The universe is larger than us, therefore it was made by something larger than our understanding.
These two assertions both contended with, and cohabitated with each other. We are often reminded of Descartes "cognito, ergo sum" but less often of what follows: he uses the ontological argument for God. Being is greater than not being, therefore there is a greater being. Newton became another thinker that married axiomic structure, with deistic substructure. In the nature of his universe, that of a static distance and static time, is the assertion of an uncreated creator. This is because what is in space and moves through time, does not create space, nor time.
The codification of this system of epistemology, is Immanuel Kant, who derided the "scandal of reality," namely that reality was required as an assumption, and it could not be deduced from our perceptual existence. He then launched on a systematic means of organizing knowledge beginning from absolute skepticism. The results of this will be touched upon later.
Axiomic ontology then, is one great tree of epistemological thinking. It can be said to rest on two assertions: the reality of self as shown by the ability of self to contemplate the question, and the reality of a beyond self, and beyond understandable self, to create the reality that the self is embedded in. For the self to be, there must be a being greater than self, but like the self, because it too, must be able to contemplate existence to exist.
However, it is far from the only idea on epistemology.
The other great tree of epistemological thought to emerge from antiquity rests on two different assertions. On is the assertion of the reality of our senses. That is, the question that bedevils the axiomic-ontological thinker's time, is essentially ignored. We see and feel, and so, the pragmatic thinker asserts, it is so. If you don't believe in the reality of the world, jump off a tall cliff and get back to me. The pragmatic thinker then asserts that since there is a unity between our senses and reality, there is a unity between our logic and reality. We sense, the sensation makes sense, and therefore making sense of sense, is equal to reality. Plato derided the early form of this idea as "sophism."
This is not as unsophisticated an idea as it might appear, and it is a close cousin of the axiomic-ontological view. It's first part, that of the reality of self by an activity of self, is a cousin. The axiomic thinker, however, makes cognition the basic act, where as the sophist makes sensation the act. Note that Descartes did not assert that "I sense, therefore I am." But the sophist doesn't dispense with cognition. Instead, where as the axiomic-ontologist asserts that the thinker exists, because he or she thinks, the sophist asserts that reality exists, because we can make sense of it. We think, therefore it is.
In the sophists view, this connection between reality and thought is created by language. Language is the ordering of the world. Again, the bubbling Greeks gave us the first mapped out form of this idea, and it was deep within their culture. The word barbaroi from which we get "barbarians" comes from the Greek term for people who did not speak Greek. If you knew the Hellenic tongues, you thought like the Hellenes. It is also in their term logos from which we get the word "logic" and all of those "-ology" words. It meant to count initially, but also an accounting, and so, words themselves. This is a point that will be important later, and several times later: counting and words are close together.
So the sophist argues that we sense, therefore we are, and we can make sense, therefore the world is. One can make good money even today pimping this as an original idea.
The sophist, however, has a problem, and that is the problem of the authority of language. The authority of language is embedded in there system, what has a word, is real, what does not have a word, is, as yet unreal. What makes sense, is sense. There is no difference then, between well written, and well reasoned. However, from where comes language? And who is to say what it is?
I did a fast gloss on two very large schools of thought on epistemology:
The first is that thought proves the existence of the thinker, and the thinker organizes knowledge, but must connect to reality, and that connection requires a larger being to explain it. Plato, Aristotle, the Gospel of St. John, Thomas Aquinas, Descartes, Newton, Berkeley, Hegel, and Kant, are all, to one degree or another, of this school, as are most religions. Order proves self, and the existence of self and order proves the over-self. Every garden variety religionist is embedded in this view, and will get very angry if provoked, stomping their feet and re-asserting what is, in actually, a supposition. The differences are only how large a circular argument they need before they have forgotten where they came from. This does not, in itself, indict axiomic-ontology as a view, but, at least, it dispenses with many of the simple forms of it.
The second is that sensation proves self, rather than cognition, and that logic proves reality. Sophism too has many practioners, high and low: Pierce, Quinne, Derrida, Ayn Rand, Sir Francis Bacon, Heidegger are all sophists. The problems with sophism are many, first off, because it is almost always dishonest. The sophist almost always asserts either that sophism is universal, and inescapable, or in the other direction, that they are the first sophist in the history of the world. Ayn Rand and Heidegger both take this second gambit. If the axiomic-ontologist says that you must agree with what is obvious to him, because the vastness of the world overwhelms all understanding, the sophist argues that you can't understand anything, unless you agree with him or her.
Yes, I am dismissing both of these theories, over which billions of words have been spilt, simply because one can wake up today, go to a forum, start from the fundamental moves of either, and still have an argument. These arguments do not so much evolve, but, like a virus, mutate, to avoid whatever killed the last rendition of the virus by losing some essential feature. A longer book than this essay would be required, of course, to grind out every single blind alley, or to do so in enough cases as to make it overwhelmingly abundantly clear that the defects in both are inescapable, ineradicable, and endlessly duplicated.
The third road is to attempt to combine both, a project that has dragged many minds prone to madness into a downward spiral. The man who shot Representative Gabby Giffords was obsessed with the problem that if grammar came to have no fixed meaning, how could we know anything? The post-structuralists, sophists to a one, came to the answer that the game of language itself provided an authority. That is, it is true, if people can play it. These attempts too, fall short, because eventually one must assert that God is the language giver, or that language proves the existence of God. The old joke still applies: if God created man in his image, man is a gentleman, because he returned the favor.
The assertion of the language-game as the ultimate arbiter of truth, that is, if we can organize it, then it is all the truth we have, dates to early Wittgenstein, who then spends the second half of his career refuting it, and instead arguing that the narrow conception of the language-game is the root of confusion. This is derived from a similar logic to Gödel's influential incompleteness theorum, in that that which is expressible must be expressible in a finite number of rules, but any finite number of rules that is rich enough to describe what we experience must also be able to express that something is inexpressible, which is a logical contradiction.
The maze of epistemology that these two schools create means that many people dispense with the question. The hell with it, I don't understand understanding.
But until the 17th century, this was considered a stupid, low, idea. That things are the way they have seemed to be.