Staying Sane with Syllogisms



“The madman is not the man who who has lost his reason. The madman is the man who has lost everything but his reason.” —GK Chesterton 1874-1936


That classic workhorse of logic—the syllogism—is enough to make anyone question their sanity:

Potatoes have skin.

I have skin.

Therefore, I am a potato.

Just in case you were wondering, I am not a potato. Clearly, something went wrong with this syllogism, but what?

Several things. One problem: equivocation, or shifting the meaning of a key term in the middle of a discussion, a common fallacy. Above, the meaning of the word skin shifts from something like ‘vegetable peel’ to ‘largest human organ.’ We’re not talking about the same skins. The former use of skin is figurative while the latter use is more denotative. But that’s just a symptom of a larger problem: validity.

Syllogisms have three parts: two premises and a conclusion. The validity of the conclusion is effected by the logic of the premises. If a conclusion is valid, then it logically arises from the validity of the two premises (which also makes the conclusion true). An invalid conclusion, on the other hand, can be either true or false. For the conclusion to be true, both premises must be true. Example:

major premise:     All panthers are pink.

(we know this is false or invalid)

minor premise:     Donald Trump is a panther.

(we know this also is invalid)

conclusion:             Donald Trump is pink.

(Invalid! And not true! He’s orange.)

All three statements in the above syllogism are false, and the conclusion does not reflect our understanding of reality. Now, look at this example:

All ostriches are real estate developers.

Donald Trump is an ostrich.

Donald Trump is a real estate developer.

How did this happen? We have a true conclusion based on two false premises! This is one of the drawbacks of deduction: false (invalid) premises can lead to true (valid) conclusions. When the premises are true, then the conclusion also must be true. And so, when used with care, deductive logic guarantees ‘the right answer.’

All men are mortal.  (this is the general claim)

I am a man. (this is a specific example of the general statement)

Therefore, I am mortal. (this must be true if the preceeding two claims are true)

Valid/invalid refers to the rules of logic, and not a judgment about reality which is expressed instead with true/false. These words are not synonymous. An argument can reach a true conclusion that is based on invalid reasoning. Or it can reach a false conclusion that is (logically) valid. As we see in the examples, if there’s a problem with either of the premises, then there’s a problem with the conclusion—but even when both premises are valid there can be problems.

We used to tell students that deductive reasoning moves from the general to the specific, and this heuristic can be a help in distinguishing deductive from inductive arguments (which are said to move from the specific to the general). But there’s a bit more to it: how the person putting forward the claim views the claim—do they think it’s certain? or only probable?

In deductive reasoning, the arguer believes the truth of the premises leads inexorably to the truth of the conclusion. With inductive, the arguer is reasoning probabilistically. In other words, the arguer’s view about the subject matter has an influence on the sort of reasoning that gets used with that subject matter. If the arguer seems to regard the premises as true: deductive and certain. If there is some element of past behaviors or past observations being used to justify a prediction about ‘tomorrow,’ then it is inductive and only probable rather than certain.

In another post, we’ll look more closely at inductive reasoning. In the meantime, be aware of the need for rigor when using logic, be aware of the difficulties associated with choosing premises, and be aware of definitional issues like equivocation. Also know that logic is only a tool, and like any tool it can be misused or misapplied.

Here’s an old joke about reasoning:

An astronomer, a physicist, and a mathematician were vacationing in Scotland. Looking out the train window, the three of them observed a black sheep in the middle of a field.

“How interesting,” observed the astronomer. “All Scottish sheep are black!”

To this, the physicist responded: “No! Some Scottish sheep are black!”

The mathematician rolled his eyes heavenward in supplication and then proclaimed, “In Scotland, there exists at least one field containing at least one sheep at least one side of which is black.”

Author: Craig Butcher

Craig Butcher is an award-winning educator who has taught critical thinking skills for more than two decades. In addition, he has worked on Capitol Hill as a congressional staffer and has been a top-rated broadcaster.