Sorting Through Sophistries
What Is a Fallacy?

By Gabriel Blanchard

Fallacies come in all shapes and sizes—but if we want to get a handle on what they are, then first of all, what ... are they?

Logic: Almost the Basics

Aristotle’s guide to logic, the Organon, is really six different works* that were assembled into one later. Most are about understanding different sorts of statements people can make about the world, and how those statements can be fitted together into syllogisms. Even if you haven’t heard the term before, you have probably seen a good many syllogisms. For example:

All men are mortal.
Socrates is a man.
Therefore, Socrates is mortal.


All cats have four legs.
My dog has four legs.
Therefore, my dog is a cat.

Put simply, a syllogism is an instance of reasoning from the incomplete but real information we have in a given circumstance, to implications we can draw from that information which may not have been obvious before. Facts we already know—the “raw material” of reasoning, so to speak—are what we use to set down premises; in both of the syllogisms above, the first two lines are premises. We need at least two premises to reach a new, recombined piece of information; such new information is our conclusion. The conclusions in the examples above are the third lines, marked with the symbol , meaning “therefore.”**

However, our gentle readers may have noticed that that second syllogism there is flawed. We draw a conclusion from the premises, but it is a false conclusion—or (depending how you prefer to put it), we can’t draw any conclusion from the premises in the second example.

This is because logic operates according to a strict set of rules, which are laid out in the Organon. Only syllogisms with certain arrangements of their terms are valid; of the examples above, only the first has what’s called a valid syllogistic form. Validity here means that if you insert true premises into the syllogistic form in question, it will produce a true conclusion no matter what. Now, exactly how much confidence you should place in the truth of your premises is another question! In fact, putting false premises into a valid syllogistic form nearly guarantees you a false conclusion. But putting true premises into it means the conclusion has to be true, as much as two and two have to make four.

Hang on, though. I thought this post was about fallacies? What have they got to do with all this?

Formal Fallacies Wear Rented Suits …

A fallacy is like a syllogism, in that it claims to be offering you further information about the world. The difference is that fallacies are—and admittedly, the name is something of a spoiler—false. Whether by accident or design, a fallacy does not succeed at the task it claims to be doing; and it can do this in either of two ways.

Thinkers may be classed as follows: those who, in the first place, think for themselves, and those who think directly for others. The former think for themselves in both senses ...; they are the true philosophers; they alone are in earnest. ... The others are the sophists; they wish to seem, and seek their happiness in what they hope to get from other people.

If it is fallacious due to a technical error in the syllogism’s construction, this is what’s called a formal fallacy. There are a lot of formal fallacies, because the parameters of validity are so strict; some formal fallacies are common enough, and sound temptingly convincing enough, to have names. (For instance, in the faulty second syllogism above, we have the fallacy of an undistributed middle term. It is a lot easier to spot in this slightly silly example than it typically is “in the wild.”) Formal fallacies are often mere mistakes, caused by inattention or inexperience. But the thing about them that’s important here is that, having established what they are, we’re not going to talk about them much in this series going forward.

… Informal Fallacies Prefer Legal Suits

However, the other kind—informal fallacies—we will be discussing, and they have an extra name: sophistries. They get this name from the Sophists,† a group of slick, iconoclastic rhetoricians who flocked to Athens in the fifth century BC. Why? To hawk their powers as teachers of eloquence! Learn their techniques—for just a small down payment, of course, or perhaps a small payment the size of a large payment—and you too could get anything you wanted out of litigation. (And if that sounded immoral or socially destructive? Well, purely by happenstance I’m sure, they also had lots of skepticism to offer you as a side dish, lots of questions to “just ask” about whether morality or society were really that important anyway.) These techniques were often informal fallacies, which unlike formal ones are frequently deliberate. Many involve slyly introducing something irrelevant, manipulating the audience through pathos or humor or anger, or unfairly discrediting your opponent’s character.

Now, it would be unfair on our part to say all of the Sophists were cynically immoral, either in how they treated their pupils or in the techniques they taught them. Some were sincerely interested in philosophy. But there were plenty who cared more about their wallets or their egos, than about whether it was bad to help others make bad ideas sound good; and it was against these Sophists that Socrates set himself.

Socrates’ technique of patient, step-by-step questioning was called elenchos [ἔλεγχος]. This word could be translated “cross-examination, critique, refutation”—but it could also mean “reproach, accusation.” Unluckily for him, wandering around embarrassing people is not top of the list in How to Make Friends and Influence People. His clever method of inquiry made him sound (to the inattentive and, in many cases, resentful objects of his campaign) very like the Sophists whom everybody was just deciding in 399 BC had lost them a war with Sparta, and with it, an empire; the hemlock, of course, is history.

Reasoned Revenge

Two generations passed. Plato founded his Academy in Socrates’ memory, and there taught Aristotle; he went on to compose the six parts of his Organon. The final work belonging to that collection dealt with how to identify and refute informal fallacies; and, presumably in honor of his master’s master, he titled this book the Sophistic Elenchi [Σοφιστικοὶ Ἔλεγχοι], or loosely:

The Reproach Against the Sophists.

*For anyone who’s curious, the six parts of the Organon are:
The Categories: what kinds of things exist and the qualities and relationships they can have.
On Interpretation: the ideas of propositions and judgment, along with the square of opposition.
The Prior and Posterior Analytics: how reasoning by syllogisms operates, and the standards of proof and forms of argument proper to other methods of reasoning.
The Topics: the broad outlines of how to construct a solid argument.
And lastly, the Sophistical Refutations, whose material we are covering now.
**Yes, this does mean the “therefores” in our conclusions were technically redundant, but we didn’t want to just spring the new symbol on you unawares. Get to know each other first.
†The term “Sophist” is related to the Greek word sophia [σοφία], which meant “cleverness, shrewdness; wisdom, intelligence.” If you imagine them referring to themselves as the Intellectuals, you’ll get something of the feel for how they come across (at least when Plato is depicting them).


Gabriel Blanchard is the editor at large for CLT. He has a degree in Classics, seven nephews, and (like Socrates) an inevitably mortal nature.

If you enjoyed this piece, and would like to learn more about the history of philosophy, take a look at our incomplete index of the subjects of Western thought—we feel sure you’ll find something you enjoy there, and suggestions for where you can read more about it!

Published on 11th January, 2024. Page image of La Mort de Socrate (“The Death of Socrates”) by Jacques-Louis David, 1787.

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