Logic before Logic

Before there was any formal investigation of what the rules of logic explicitly were, there was logic. Logic is a subject which many people do not often think about explicitly: like most arts, we "know it when we see it." Likewise, the use of language developed before the science of linguistics.

This raises a particular question: since the use of logic is necessary to the investigation of logic, is it possible that the entire affair (and through it, all of mathematics, philosophy and science) is "bootstrapping" of the highest order? Is logic nothing more than a self-fulfilling prophecy? The answer is simple: even if it were, it would be impossible for us to ever know. Logic is so fundamental to our way of thinking that it is, almost by definition, impossible for rational brains to function in any other way. In fact, as systems of logic have progressed, they have become more and more flexible and complex, more accurately modelling the way our everyday thoughts occur.

In order to save headaches, whenever I refer to "logic" in the following pages, assume I'm talking about the "study of logic", rather than the "act of being logical," which came first.

Early Texts

One of the first surviving documents truly having to do with logic is the fragment known as the "Dissoi Logoi". If current archaeogical analysis of it is correct, it was written around the end of the fifth or the beginning of the fourth century BC. It has to do with the nature of falsehood and contradiction, and is easily the first document to recognize the dichotomy between the linguistic component of a statement and the truth-value of the statement.

For instance, the statement "I am over six feet tall" is true when spoken by Arnold Schwarzenegger, but not true when spoken by Danny DeVito. There is, concludes the "Dissoi Logoi", a separation between whether or not that statement is true and the words of the statement. On the other hand, it states, there must be some relation between the two: if we translate the statement "Sacramento is the capital of California" into another language, even one with a completely different alphabet, the truth of the statement remains. In a very primitive way, the "Dissoi Logoi" addresses the "use/mention" issues central to modern logic.

Though the "Dissoi Logoi" may have been the first real document specifically regarding the proper use of logic, the Pythagorans predate it by around half a century, and deserve at least a mention as some of the first true and formal users of logic.

Pythagorus

The Pythagorans: Crazed Supercool Geometers

Coming soon...an interactive illustration of the difference between a logical proof and a demonstration!

Pythagorus: The Man. The Myth. The Breakfast Cereal.

Pythagorus was supposedly born in Samos in the first half of the sixth century BC. He founded a metaphysical order of philosophers in Croton, a Greek city in Southern Italy. Much of the information we have about Pythagorus and his followers is spurious for one reason or another, since the Pythagoreans were organized along the lines of a religious cult similar to the mystery cults that flourished around that time period. Secrecy and elitism were the rule, not the exception.

The Pythagorans are most well-known for their studies in geometry, (they demonstrated the aptly-named Pythagoran theorem, and demonstrated the uncomputability of the square root of two) but the Pythagoran philosophy contained a great deal more, including thoughts on ideas with long names like metempsychosis (their theory of the afterlife, if you care.) They were the first numerologists, believing that everything in the universe could not only be described and defined by numbers, but was in fact actually composed of numbers. When you put them next to the "Big Thinkers" like Plato, Aristotle and Socrates, they often get overlooked, but their influence is evident throughout the remainder of classical logic and philosophy in general.

Pythagoran Resources on the net

• Pythagorus has a mention on Spatz's Ultra Fab Philosophy Info, which isn't as cheesy as it sounds.
• For a look at a modern extension of the Pythagoran occult beliefs, check out The Pythagoran Tarot by John Opsopaus. WARNING: Not logical at all.
• For a look at a modern extension of Pythagoran mathematics, you can download a MIT paper on Pythagoran triples. It's in LaTex format.

• I want to talk some more about geometry. Tell me about Euclid.
• I'd rather get on with the actual history of logic. You know, what these pages are supposedly about? Tell me about Aristotle and the Stoics.