Brook Hatch Computability and Cognition 2000 Synthesis Paper 
During Fall Quarter 2000 of Computability and Cognition we read the writings of several Western philosophers considered most influential in formulating our current view of reality. What are the foundations that each philosopher proposed for making judgments and how do these judgments relate to truth? What are the limits of human understanding? What can we know? It seems somewhat unfair for a serious discussion on this topic to be bereft of anything but philosophy, but so be it. We may generously stipulate that philosophers have some knowledge of biology, history, art, music, and not just a narrowly focused concentration on mathematics and the logic of formal systems. In order to explore the questions raised about understanding, it will be necessary to examine Plato’s discussions, Descartes’ foundationalism & rationalism, Hume’s empiricism, and Kant’s solution.
According to Plato, Socrates felt that knowledge is something that is remembered rather than discovered. In Meno, Meno argues that the things we know, we do not seek to understand; likewise, the things we do not know, we cannot know, so therefore have no way of seeking to understand them. Socrates counters that argument with a demonstration wherein he “teaches” a slave boy to figure out how to double a square using diagonal lines. This counter argument seems to support the idea of re-incarnation. Each soul having existed in a formless place, previous to this fleshly incarnation, possesses all knowledge, having been a part of all things. The teacher’s job is merely to remind the student of what he or she already knows. Socrates acts as a midwife to his pupils, helping them to bring forth the ideas with which they are pregnant.
In the time of Plato, the idea of reincarnation was accepted popularly. In this day and age, the majority of people in the industrialized Western hemisphere seem to cling to a Judeo-Christian heaven and hell mythos which obviates the idea of reincarnation. A modern analogy to Plato’s (Plato as Socrates) innate knowledge is the idea that we are conditioned by our culture from birth to hold a worldview. Ideas that fit easily inside our worldview “intuitively” feel right and are thus more easily understood than ideas foreign to our worldview. Mass marketing and peer social interaction formulate our sense of what is real and what is fantasy.
Perhaps we could say that the nature of reality is democratic. The more people believe in something, the truer it is. This is a modern refutation of Protagorean relativism - "what seems true to anyone is true for him to whom it seems so" (Plato, Theaetetus 170a). Protagoras taught that man is the measure of all things. Socrates points out the fatal flaw in this reasoning by saying that we cannot elevate Protagorean teaching above our own. Sophists earn money by teaching people that they shouldn’t be listening to them. This is an inherent paradox.
The analogy of Plato’s cave illuminates subjective reality. In this analogy, what each person observes in their lives is but shadow and substance less form. Only by breaking free of illusions, perhaps by scholarly study, is it possible to glimpse the truth, that thing which is imperfectly imitated by a puppet show in the cave. Plato defines what is real in a structure that claims that reality is based on the absolute (or fully extended) expressions of abstractions. In other words, perfection, infinite line extension, truth, virtue, justice, mathematical principles, numbers, all these things are more real than our interpretations of what our eyes see and what we experience generally.
Descartes wished to know for himself what could be called real. He proposed that there was an evil trickster god bent on deceiving him in every way. He therefore propositionally eliminated from his list of real all perceptions. Furthermore he reduced dreams, memories, and knowledge in general. What he had left were only his thoughts about whose existence he could not doubt. He could not doubt that he was thinking. Thus he came about with the phrase, “I think, therefore I am.” This is a convenient and perhaps useful assertion for one individual, but says nothing about anything outside of one’s mind. His attempt at proving the existence of God involved extrapolation. If he could imagine it, it had some kind of reality. He could imagine God, so therefore God exists. This way of thinking would seem to lead inevitably to megalomania and insane delusion. Perhaps it has.
Just as ineluctable is identity. Everybody thinks they are me. Identity is perhaps the most fundamental characteristic of a human being. We carry identification cards and introduce ourselves with semi-unique names. We have unique social security numbers assigned to us. Despite language and cultural barriers it is the one thing we have in common with every other human on the planet. Western civilization carries this idea further than some other cultures, notably high context cultures like the Japanese. Each individual is considered autonomous and responsible only for his or her own actions.
Hume tried to cut out the sophistry and instead focus on abstracts that could be described and proved in a rigorous fashion using the tools of logic. He asks us to judge whether a teaching contains any abstract reasoning concerning quantity or number. If it does not, does it then contain any experimental reasoning concerning matter of fact and existence? If none of these conditions are fulfilled then the teaching contains nothing but sophistry and illusion and in Hume’s opinion is worthless and should be destroyed. 
It is interesting to note an inherent contradiction in Hume’s vision of reality. By stating that there is such a thing as the inscrutable, even if it is to be shrugged of as of no account, he is saying that not all knowledge is rational. Examples of irrational knowledge are the set of all religious experiences including the witnessing of miracles, occult phenomena, yogic Samadhi, chi, religious ecstasy, voodoo, witchcraft, and unsupported belief in a supreme deity. In fact, all of modern science has its roots in irrational knowledge. Astronomy developed from Astrology, Psychology from Physiognomy (study of hands, and heads as a guide to personality); Numerology was the precursor of arithmetic and higher Mathematics. 
A fact is nothing but a judgment concerning cause and effect, a purely empirical judgment I might add. The degree of assurance that we have about a given “fact” is what makes it more or less a fact. Imagine walking on a concrete sidewalk. As you walk, your eyes are scanning the way ahead for obstacles. You step boldly, without the fear that a yawning chasm will suddenly gape beneath your next step. Having walked on concrete thousands of time, it is a fact in your mind that concrete sidewalks provide an absolutely stable footing. Wet concrete doesn’t differ in visual characteristics from its more stable form. If you were to step in wet concrete that abutted dry concrete, your first shocked thought would be to question the fact that concrete always provides a firm footing. Concrete sidewalks are one of many contrivances used by our civilization to make the universe more predictable.
The words of Kant introduce a matrix within which all ideas exist. There are empirical and a priori ideas. These are further subdivided into analytic and synthetic categories. There are of course no empirical analytic ideas. The most important a priori ideas are the human interpretations of reality we call space and time. These a priori analytic ideas are synthesized into geometry and arithmetic respectively. Kant was a sort of realist in that he believed that there exists an objective reality, he just didn’t think anyone really knew the nature of it entirely. 
Each philosopher built successively on a foundation laid by the previous philosophers. Plato approaches knowledge as something to be uncovered or awakened, rather than created or discovered. Descartes, treating thoughts as mere symbols, dismissed the whole of reality excepting the subjective self. Hume went in the opposite direction, treating as real those things we could measure and prove with math. It seems that Kant’s view of reality has endured up to now with its dualism in things we experience and things we know before experience.