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In the last chapter, we used the reductio ad absurdum method to show that the hypotenuse of the unit square was not commensurable with its sides. I then demonstrated that whole systems are not commensurable with each other.
Needless to say, I could use reductio ad absurdum ad nauseum. (I could prattle on about paradox until you felt sick in the stomach).
There are many paradoxes that seem inherent in language. The most famous is the statement: "This sentence is false." If the sentence is false, then it is true, which means it is false, and on to absurdity. This type of paradox is called the reflexive paradox and will exist in any system that allows a self reference. Any attempt to create an all inclusive philosophy will inherently include the reflexive paradox, because an all inclusive philosophy must, by definition, include itself.
The reflexive paradox is real and has important implications for the way that we organize our lives and political systems. For example, a democracy could vote in a tyrant, thus ending the democracy. To create a stable democracy one must take an undemocratic stance of putting the form of government outside the control of the will of the people.
As the Greek culture evolved, it is likely that people found more and more paradoxes.
It appears that this system of arguing in paradoxes reached its height in the Eleatic School, then quickly reached its depths with the ramblings of the Sophists.
Elea refers to an area in Southern Italy that was settled by Ionian Greeks around 535BC. It is likely the Ionians fled an advance of the Persian Army.
The Eleatic School were harsh critics of the Pythagoreans and other descendants of Ionian cosmology including the atomists. The atomists believed that matter was composed of infinitely small particals called atoms.
Like the Ionian philosophers, the Eleatic school was interested in discussing the elemental substance. Ionians had put forward that it was water, air or fire. The Pythagoreans put forward the idea that it was pure number. The atomists claimed things were composed of minute things called atoms.
The school of Elea discussed things such as the difference between being and becoming. They found systems where the elemental substance came in to being absurd. NOTE, current cosmology states that the substance around us was present at the Big Bang.
The Pythagorean system of numbers ran into absurdities as well. To avoid jumping to a long exposition on this point, I presented in the last chapter an example where you rotate a grid at a 45 degree angle with its source. All of the points, except the center of rotation, would be incommensurable after the rotation.
Parmenides of the Eleatic School found that all attempts to explain the elemental substance as a multiplicity of things ran into absurdity. If multiplicity led to paradox, then the elemental substance was a mysterious thing called "The One."
Modern cosmology speculates that the universe began as a "singularity" during an event called "The Big Bang."
Zeno of Elea (circa 495BC – circa 430BC) was a follower of Parmenides. Zeno created a system of argumentation that made frequent use of paradox in an effort to discredit the arguments of the Atomists and other Ionian Schools. Aristotle referred to this system as dialectics.
I would like you to pay attention to the use of this term. The meaning the word changes with different usage. At its basic level, the word simply is a synonym for "dialog." It means conversation. Many philosophers use the term dialectics in a positive sense.
In Rich Theory, I rail against a bugabear called foundational dialectics.
We do not know the exact wording of the paradoxes of Zeno. Most of the paradoxes have been lost to time. The paradoxes we do know appeared in various attempts to refute the paradoxes.
I believe that the paradoxes of Zeno made some extremely profound observations about the fundamental nature of matter. For example, the paradoxes would discuss an arrow flying through the air and show that that the idea that the arrow was composed of indestructable atoms led to absurdities.
I believe that it was not until the invention of quantum mechanics that anyone had a good explanation of how an arrow flies through the air. Quantum Mechanics has its own peculiarities.
I have great respect for Zeno. I trace the origins of "foundational dialectics" to the popularization of Zeno's dialectics.
Neither Plato nor Aristotle showed much love for a group of philosophers known as "The Sophists." To this day, the term "sophistry" is used as an insult referencing intellectual pretention.
I have more sympathy for the Sophists. The Sophists were essentially travelling educators. They would travel from town to town to engage in disputations. Often Sophists let their rhetorical skills for hire. Much of the animosity toward Sophistry is due to their desire to be paid for their work.
Academics of the ancient world would have the same contempt for Sophists gettting paid for their work as they would for this work that is covered with ads! (This work is self funded; So, please, I beg you, visit my sponsors)
I believe that we owe a great deal of our culture to the Sophists. The Sophists weren't simply interested in the arguments, they were interested in the form of the arguments. While it is poltically correct to disparague Sophists, the Sophists did two great things. They popularized intellectual inquiry, and they forced a more detailed examination of the structure of language.
Now for the truly dark side of Sophistry.
The Sophists prided themselves on winning arguments. As they learned the dialectics of Zeno and other tricks of the great philosophers, they developed ways to destroy and humiliate their opponents.
As mentioned, there is an infinite number of paradoxes. You can win battles by falsifying information, changing definitions, the intentional use of fallacies, and more.
One of the best ways to reduce a opponent to absurity is to ridicule them. One of the most effective tools of ridicule is the parody. A good example of parody is Steven Colbert's portrayal of conservatives.
The Ancient Greeks were finding dead ends in their quest for a perfect Cosmology.
While there was a widespread desire for improved education, there was a rapid deterioration in the quality of discourse. In the case of ancient Greece, the country found a positive direction in the philosophies of Socrates and later Aristotle.
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