The Stoics

As we stated before, the Megarians, and through Chrysippus, the Stoics, concentrated on the more ordinary kind of "dialectic" logic that Plato had dismissed as being "eristic" and not really the rigorous, geometric logic that philosophers were supposed to do. However, this sort of logic turns out to be crucial to our understanding of how logic and the way our natural language really works. But let's do a little history first.

A Little History First

The founder of the Megarian school was Euclides, who was a contemporary of Plato. One of his students was Stilpo, who taught Zeno, who formed the Stoic school of thought. The original school was active around the end of the fourth century BC (300 BC, for those who aren't used to counting backwards). The Stoics themselves were active for the next hundred years or so.

Zeno was most famous for his paradoxes. A paradox is something that is either logically true but intuitively false, or a statement that seems to defy the principles of logic. Zeno picked up a number of these from Euclides and his other students. In fact, the teachers of the school were so attached to their paradoxes that Didorus Cronus was alleged to have committed suicide because he could not immediately solve a logical puzzle proposed to him by Ptolmey. Of course this story is not at all true.

A lot of Peripatetic philosophers made fun of the Stoics and their paradoxes, because they seemed terminally pointless. Unfortunately, we don't know exactly what sort of argument these paradoxes were supposed to be a part of, which is a pity because at least one of them turned out to be crucial to modern logic.

The Paradoxes

There were seven main paradoxes of Eubulides, a student of Euclides, but the Kneales and other later scholars often reduce these to four, since some were variants of these four basic thoughts:
The Liar Paradox
A man stands up and says "I am a liar." Is he a liar or is he telling the truth?
The Hooded Man
You say you know your brother. But you do not know this hooded man here, who happens to be your brother. So you must not know your brother.
The Bald Man
Would you say that a man who had one hair was bald? Yes? How about two hairs? Yes? If we continue this, eventually, every man is bald.
The Horned Man
What you have not lost, you still have. You have not lost horns. Hence you still have horns.
The last three paradoxes are of more interest to linguists than to logicians. They have to do with our definitions of the words "know", "bald" and "have", respectively. But the first paradox is much more directly involved with logic, and will crop up again and again in various forms.

I want to know more about this liar paradox.

Take me back to the History of Logic homepage.

Jason Corley -- corleyj@cobweb.scarymonsters.net