One of the foundational tools of the Gift of Set derived from, of all things, land use.
In trying to understand how to utilize their lands best, the Egyptians developed a set of methods for understanding divisions of space and their relationships. These methods would become the foundation of the ideas brought to Greece by Pythagoras. The Initiatory School he established passed down this method to us as geometry.
Egyptian geometry was primarily based on empirical observation and abstraction. If you had a triangular plot of land due to a river, and you could only measure two sides of the plot, they found that if you extended a square the length of one side and a square plot the length of the other and then added them up, it gave you a square the size you would get if you could plot a square off of the unmeasured side. As the Pythagorean Formula, the Greeks simplified this and abstracted it beyond land use. More importantly, the Greeks began to use known geometry to create proofs for unknown geometry, extending knowledge through using existing knowledge in new ways. The Greek use of proofs in geometry eventually extended toward creating proof methods for other activities.
From this legacy, one of the most potent instruments of reason developed: Logic.
Following the Peloponnesian War (431 to 404 BCE), with the defeat of Athens by Sparta, the need for proof took on new importance. Athens’s defeat had created severe issues related to ownership of property, repayment of debts, and settling interpersonal disputes. This was typically done by making speeches in the Agora of Athens, the center of the city and the heart of its lifestyle. Those speeches that worked best to settle disputes were arguments, and to help those seeking to craft arguments, a class of professional teachers of argumentation developed known as Sophists. This environment also produced one of the Sophists’ most essential critics and the father of European Philosophy, Socrates. Socrates, in turn, inspired his Athenian student Plato, who wrote accounts of Socrates’ ideas via dialogs, and Plato’s Macedonian student, Aristotle.
To Aristotle, we owe the most significant debt in the development of Logic. He was a keen observer of humans and nature, relying upon empirical methods in a way that neither Socrates nor Plato had. He focused this capacity for observation upon the practice of argument and whether arguments made were sound or if they were fallacious. His works in this area, especially Prior Analytics and On Interpretation, laid the foundation for what became known as “term logic.”
Of the various ideas developed by Aristotle, three fairly necessary tests for an argument have been the most influential. The first test is whether the terms maintain the same meaning throughout the argument. If it does, then it may be a sound argument. If the arguer suddenly changes the meaning midway through the argument, it is a flawed argument. The second test was whether the term was used in a contradictory way in the argument. The argument can be seen as sound if there is no contradiction. Finally, the terms of the argument must be clearly defined. Either the term exists for the sake of the argument, or it does not. There can be no middle ground within the argument.
With these pretty simple ideas, arguments can be evaluated. In the process, we can get closer and closer to good reasoning and perhaps an understanding of truth. The history of these ideas took a strange turn in the Medieval Period when the Catholic Scholastics rediscovered Aristotle’s Logic. The Scholastics derive from Aristotle’s Logic what has become known as the Laws of Thought. These are:
• The Law of Identity (For any Proposition A: A=A)
• The Law of Non-Contradiction (A cannot both A and Not A)
• The Law of the Excluded Middle (There is either A or Not A, nothing more)
These Laws simplify and focus Aristotle’s observations and inferences in pure term logic. Unfortunately, perhaps the Scholastics made a mistake that Aristotle did not. They turned these tools for testing the soundness of arguments into the Laws of Reality itself. As a result, the vast and wild field of Scholastic determinations about reality began, and a kind of intellectual fundamentalism overtook European thought for several centuries attributed to, but not evidenced in, Aristotle’s Legacy.
The true power of logic as a Tool of the Gift can be restored when it is returned to its proper footing: as a tool for evaluating arguments. As a starter text, A Rulebook for Arguments by Anthony Weston offer comprehensive advice. In addition to this, semi-regular use of logic puzzles can help hone your skills in applying logic to abstract and practical situations. Finally, learning to apply logical methods to test the soundness of your ideas is indispensable to keeping yourself from needlessly falling into delusion.
Setemheb 