Logic and the Stoics I

Logic isn't a closed body of learning.

Some people still think of it as something Aristotle created, and that allows for no improvement, so that the study of logic remains the study of Aristotelian principles to this day and forever.

But that is not true. First, much of what is touted as central to Aristotle’s contribution was simply taken over from his mentor, Plato. Recall the discussion of the turning top in The Republic.

But more important, not only did Aristotle not start it, he didn't finish it either. Quite soon after Aristotle’s death, perhaps before it, people (notably those of the Stoic school) were making new contributions, taking different perspectives.

Conditional statements fascinated the Stoics, “If p, then q.” It turns out there are different ways of interpreting that simple-seeming rubric, and Stoics thrashed them out. Note that the "if/then" rubric is already different from Aristotle's categorical statements. "All men are mortal" and so forth. A Stoic syllogism runs: if p is the case, then q. And p is the case. So, q.

A mere syntactical difference from Aristotle's, you might say, pish-posh. Except that if you are alive in the 21st century you are unlikely to say "pish posh" very often. but set that aside. I have to say that the conditional format for logic was an important innovation. First, it helps make clear the reversibility of valid inferences.

Consider the scenario in which someone who dislikes spicy foods, who is eating something new for the first time, and who doesn’t know the ingredients, might try to infer something about them in this way: If this food were spicy I would be unhappy. Yet I am not unhappy. So this food is not spicy. That follows the format we described, in which p is a fact about immediate reaction/happiness of the diner and q is the spice level of the food.

This is known as the modus tollens, a Latin phrase meaning "the method of denying."

Such technical innovations in logic came with a lot of Stoic baggage, especially including the notion of destiny. I'll get to that in my next entry.

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