The Brain, a User's Manual:
What Is Stoic Logic?
By Gabriel Blanchard
Now, as we enter the Stoa, let's pause to examine a hitch in—well, a hitch in logic is just what it isn't, though many people think it is. Come and have a look.
What Is “Stoic Logic”?
Last time, we left off on an expression of relief that there won’t be any wrenches thrown in the works as we come to this final stage of our introduction to logic. And there won’t! No hidden catch, just a straightforward isn’t-that-nice. Anyway, it is time to move from Aristotelian logic (which uses categorical statements defined by the square of opposition) to Stoic logic.
Aristotelian logic is, as you can probably guess, named for Aristotle. No—Stoic logic wasn’t named for Stoistotle. It is named for the Stoic school of philosophy, which was founded by Zeno of Citium (334-262 BC), a native of Cyprus who came to Athens after the death of Aristotle; Zeno and, eventually, his disciples studied, debated, and taught in the Stoa Poikilē1—for which their philosophy was named. Stoicism throve for five hundred years or so; for a time, it was practically synonymous with classical philosophy, and much of its moral system was incorporated into both Neo-Platonism and Christianity.
One of the Stoics’ concerns was to avoid being deceived, either on purpose or accidentally, so they continued Aristotle’s work on logic, expanding it into two further kinds of predication: conditionals, or “if-then” statements; and disjunctives, or “A or B” statements. Both are slightly more complicated than they appear, partly because there are usually some un-intuitive wrinkles in logic—but also for another reason, one that also applied to Aristotelian logic, though we didn’t address it in detail.
Observation and Deduction
Consider the following five statements:
Some cats are not orange.
You must either adore playing football or hate playing football.
All elementary schools are underground.
You can only boil water if you place it over a heat source.
If you read Tolstoy, you will stop liking Shakespeare.
You probably think some of these statements are true and some are false, no? Where did you get that opinion? Probably you formed it either from your own observations, or from secondhand reports of someone else’s. They were not deductions, but discoveries.
"Two dead men, both with blackened fingers. What do you deduce from that?"
"I deduce nothing: nihil sequitur geminis ex particularibus unquam [nothing ever follows from two specific facts]."
... I was upset. I had always believed logic was a universal weapon, and now I realized how its validity depended on the way it was employed.
Now consider these syllogisms:
All elementary schools are underground.
Springfield Elementary is not underground.
∴ (Despite its name,) Springfield Elementary is not an elementary school.
If you read Tolstoy, you will stop liking Shakespeare.
I have read The Death of Ivan Ilyich.
∴ I have stopped liking Shakespeare.
Now, common sense would call both of these conclusions false—but why? There is no logical fallacy in either syllogism. The key terms could have been more clearly defined, surely; for example, if “read Tolstoy” meant reading his complete works, then the (unstated) premise “A person who has read at least one work by Tolstoy has ‘read Tolstoy'” would have to be dropped, and there would be nothing inconsistent about having read Ivan Ilyich yet still enjoying Shakespeare. However, that is not the real point here.
The real key to the problem is this. Deductive logic (used correctly) does show us connections between ideas, connections that are necessarily reliable—but logic is only ever as solid as the premises you feed into logic. Given a statement “If A, then B,” and also given sound evidence that B is not true, we may infer that A is not true; but only as long as the statement “If A, then B” was true in the first place. The only thing logic guarantees is connections between statements; it does not guarantee the statements themselves. You have to get those from somewhere else.
This can become especially tricky when the individual components of a conditional statement are true, but not truly connected: e.g., “If all cats are mammals, then Paris is the capital of France.” That statement is obviously false—the taxonomy of cats and the organization of France have nothing to do with each other—even though all cats are mammals and Paris is the capital of France. This may seem to throw a wrench into the reliability of logic, but again, logic is not the problem here. The problem is the false premise, the claim that a relationship between two facts exists; that kind of claim isn’t logic, but something that we put into the “machine” of logic: what the machine puts out will only ever be as good as what we put in.
Now we are ready to tackle the ifs, onlys, thens, and ors of Stoic logic.
1The phrase στοά ποικίλη [stoa poikilē] or ποικίλη στοά means “Painted Portico”; this one was a covered colonnade decorated with paintings of mythological and historical battles.
Gabriel Blanchard, a proud uncle to seven nephews, has worked for CLT since 2019, where he serves as editor at large. He lives in Baltimore, MD.
Thank you for reading the CLT Journal. If you enjoyed this piece, you might enjoy our series on the women and men of our Author Bank: in addition to Shakespeare and Tolstoy, we have profiles of Hesiod, St. Jerome, Averroës, Rousseau, Kierkegaard, and dozens more. You might also enjoy our recently-concluded series on informal fallacies, the immediate predecessor and companion to The Brain Manual.
Published on 9th January, 2025. Page image of a selection from a reconstruction of a painting from the Stoa Poikilē, depicting the Battle of Marathon; at the top are (from left to right) Apollo, Zeus, Hera, Hellas personified, Poseidon, and Eros.