Roger's Equations

Introduction

"Man is a being in search of meaning" - Plato

Socrates was a short, ugly, and generally annoying man who lived in Athens from 470 BC to 399 BC. He spent the first half of his life as a sculptor, which made sense since he was the son of a sculptor. Legend has it that he became a philosopher sometime after age 40 when the Oracle at Delphi indicated he was the wisest man in the world. The news of this surprised Socrates who, though educated in literature, music, and rhetoric, felt strongly that he wasn't very wise at all. It was only after he started interrogating the greatest thinkers of Athens that he came to realize that nobody really knew the things they supposed they did. This thus verified the oracle since he seemed to be the only person aware of the fact that nobody (including himself) seemed to truly know anything, which made him the wisest person in the world.

Socrates escaped execution a few times during his life. Finally, as an old man of roughly 70, he was found guilty of corrupting the youth of Athens and not believing in the gods of the state and was executed by being forced to drink poison (hemlock). When asked to flee by his followers, he responded that no true philosopher feared death and besides, where ever he ended up he would probably annoy them so much that it would lead to the same result (Crito).

It is popular to portray Socrates' trial and punishments as unjust, and there were a lot of politics at work in the trial and sentencing. Still, it is worth noting that twice previous to the trial there had been overthrows of Athens democratic government by students of Socrates (Alcibiades and later Critias). It's not surprising that his students would try to overthrow democracy since Socrates was a strong critic of it and said it made "Equals of everyone, including unequals".

What we know of Socrates today comes from his student Plato, the historian Xenophon, and the playwright Aristophanes. The first two exalt Socrates in Euthyphro, Phaedo, Sophist, and many other works; and the last satirized him in the play "Clouds" and briefly describes him as an instigator of sedition in "Birds." Socrates himself wrote nothing as far as we know. Thus the specific ideas of Socrates and those of Plato are hard to separate, since Socrates spoke but didn't write and Plato says he wrote only what Socrates spoke. Rather than worry about what was said by whom, lets combine the two and treat them as one person and examine their contributions to epistemology relevant to our discussions.

Theory of Forms - The Epistemology of Socrates as Expressed by Plato

The epistemology of Socrates (and Plato) is defined by the theory of Forms. The theory of forms essentially states that the objects of the world we perceive empirically (through our senses) are only imperfect aspects of more complete, idealized "Forms." The famous shadow on the walls of a cave story from The Republic does a good job of explaining this idea of "Forms;" here is the Wikipedia summary of the allegory:

In the dialogue, Socrates describes a group of people who have lived chained to the wall of a cave all of their lives, facing a blank wall. The people watch shadows projected on the wall by things passing in front of a fire behind them, and begin to ascribe forms to these shadows. According to Socrates, the shadows are as close as the prisoners get to viewing reality. He then explains how the philosopher is like a prisoner who is freed from the cave and comes to understand that the shadows on the wall do not make up reality at all, as he can perceive the true form of reality rather than the mere shadows seen by the prisoners.

The Forms are essentially abstract concepts that were more complete than the aspects of them that are perceived in the real world. Try thinking of it this way:

Imagine you were tasked with determining whether or not an object placed in front of you was a dog. Chances are you'd feel fairly confident that you'd recognize a dog if you saw one standing in front of you and the task wouldn't be too difficult.

Now imagine someone else is tasked with determining whether or not an object placed in front of them is a dog, except they have no idea what a dog is. You are allowed to explain to them what a dog is, but then must leave them to complete their task. Now the task is much more difficult.

We all think we know what a dog is, but when pressed to describe one to someone who has never seen one, it becomes difficult due to the variety of characteristics of dogs. This is a classic characteristic of the Socratic Dialogues. In these Dialogues, Socrates is constantly asking the person he's interacting with to define something and refine that definition. For Socrates, part of the problem was that people took for granted they knew what an object, virtue, emotion, etc. (dog) was, but when pressed to describe one would often fail miserably (since describing one is much harder than it sounds).

The fact that we recognized whether or not it was a dog standing in front of us was evidence to Socrates that we possessed an innate understanding that was deeper than the objects we came across in the real world. Socrates believed that there is a "Form" that was "dog" that we knew inherently so that when a dog was placed in front of us, we recognized it as such. This was also true for beauty, courage, table, fire, house, anger, etc. What we encountered in the real world were not these Forms themselves, but rather a shadow of these Forms (or if you like the book Flatland, a projection). Socrates felt that since the world we live in is filled only with shadows of the Forms, Forms themselves couldn't be fully appreciated (understood) by the senses. One must resort to rational thought (reasoning) to understand the Forms.

Socrates (and Plato) believed these idealized concepts (Forms) couldn't be learned, but rather had to be remembered. This is completely consistent with the theory of Forms, but may strike us in the modern world as strange. Basically Socrates reasoning was that all Earthly things are imperfect shadows of perfect Forms corresponding to those things. All varieties, shapes, and sizes of dogs were but imperfect shadows of the idealized Form "Dog." All varieties of courage were but imperfect shadows of the Form "Courage." Socrates thus believed that all of us were just imperfect shadows of the Forms of "Ourselves." The Forms of "Ourselves," being ideal and perfect, could perceive the Forms of all other things (Courage, Dogs, Beauty, etc.). Thus in order to understand the Forms of other things, we must somehow access that knowledge we forgot (lost) when we were projected from our perfect Form of "Ourselves" to that flawed shadow which inhabits the real world. Socrates believed rational thought (reasoning) allowed us to remember the things we forgot. Naturally, based on this way of looking at things, Socrates believed any outside stimulus was unimportant since when one used rational thought to discover Forms, one was remembering, not learning.

This link has an example of Socrates approach.

I have used the term "shadows" above in my explanation, but that is just a metaphor. A more accurate description of what Socrates believed would be Perfect Ideals (Forms) and that which exists in reality (Shadows). To summarize, Socrates believed there were perfect ideals (Forms) that corresponded to those imperfect or incomplete things that we come across in the real world (shadows). Socrates believed that we "ourselves" were no exception, and there existed an ideal version (Form) of "Ourselves" that knew the idealized versions (Forms) of everything else. Thus to understand the ideal version of everything else, we needed only remember that which we forgot when we were projected into the real world. This remembering was achieved with rational thought.

Consequences of the Theory of Forms to Epistemology

First and foremost, Socrates believed that absolute truths existed (Forms). He believed that empirical data were incomplete and distorted aspects of these absolute truths were thus irrelevant. The absolute truths (Forms) could only be learned through reasoning.

Socrates believed that Forms could have no self-contradiction. For example, if you say "all dogs are large" and then acknowledge "some dogs are small" then your original definition is wrong. Socrates consequently developed a method for disproving misconceptions through contradiction. The misconception is stated as a premise. Other short premises that are easily agreed upon are presented. Through a series of logical steps, a contradiction emerges that disproves the original misconception. This created a process of elimination by which one could move closer to the absolute truths (Forms) being examined.

"If particulars are to have meaning, there must be universals" - Plato

The next point is profound and it is hard to determine whether it came from Socrates or Plato. Basically it says "The whole of everything has a corresponding Form." What that means is that it is not enough that a definition be consistent with respect to a particular Form; it must be consistent with respect to all Forms since all Forms correspond to a single Form "the Universe." There can be no contradictions in general. A proof need only be proven incorrect once to be incorrect. This is a fundamental tenet of mathematics and science today.

In Part 3 we will see examine how Aristotle took the theory of forms and modified it in such a way as to create a foundation on which modern thinking was built. Link to Part 1.