A formal fallacy exists because of an error in the structure of the argument. In other words, the conclusion doesn’t follow from the premises. All formal fallacies are specific types of non sequiturs, or arguments in which the conclusions do not follow from the premises. Formal fallacies are identified by critically examining the structure of the argument exclusive of the individual statements. As you read through the following types of formal fallacies and examples, this definition will become more clear.

Bad Reasons Fallacy (Argumentum ad Logicam)

In this fallacy, the conclusion is assumed to be bad because the arguments are bad. In practice, a premise of the argument is bad and therefore the conclusion is bad or invalid. This fallacy is seen often in debate or argumentation. We summarize the fallacy as: He gave bad reasons for his argument; therefore, his argument is bad. Consider the following claim:

The new employee is too quiet and has no sense of style. We should fire him.

“Bow Tie” by ambimb. CC-BY-NC-SA.

The problem here should be obvious. To be a good employee does not require a certain look or the ability to put together interesting outfits. (Just look around your campus or workplace and you’ll probably see how true this is.) As such, the reasons for concluding the new faculty member should be fired are bad. We commit a fallacy if the conclusion to fire him is also bad or wrong. While the given reasons don’t necessarily support the conclusion, there may be others that do.

Bad reasoning as well as good reasoning is possible; and this fact is the foundation of the practical side of logic. – Charles Sanders Peirce

Masked Man Fallacy (Intentional Fallacy)

The masked man fallacy involves a substitution of parties. If the two things we substitute are identical, then the argument is valid:

Rosamond Smith wrote the book Nemesis.
Rosamond Smith is an alias for Joyce Carol Oates.

Joyce Carol Oates wrote the book Nemesis.

This argument is valid because Rosamond Smith is in fact an alias for Joyce Carol Oates, so there is no flaw in the structure of the argument.

Consider the following example:

Chris told police that a red-haired woman stole her car. Ginny is a red-haired woman. Therefore, Chris told police that Ginny stole her car.

“Callan” by Kristy Davies. CC-BY-NC.

The fallacy in this example occurs between the second premise and the conclusion. Looking at each premise individually, we can see that each is true. However, simply because each premise is true doesn’t mean the conclusion is necessarily true. Even if Ginny did steal Chris’s car, this fact doesn’t make the conclusion true. The existence of this fact cannot be presumed to change what Chris told the police.

Fallacy of Quantitative Logic

Fallacies of quantitative logic revolve around the grammatical structure of the proposition. The focus is on the use of some sort of quantifying word such as “all” or “some.” Consider this example:

All philosophers are wise.

We can show the flaw in this statement by simply finding a counter-example. And since the fact of being wise is abstract, how do we truly know if one is wise or not? Consider how the statement changes with the use of a different quantifier:

Some philosophers are wise.

This statement is stronger because it allows for the possibility there are counter-examples. However, the error arises from the fact that it is not a known quantity. We must infer from the statement that some philosophers are not wise.

Let’s look at another example:

All conservatives are Republicans.
Therefore, all Republicans are conservatives.

Without thinking too hard you can probably think of one counter-example. Let’s try one more:

Some doctors are not MDs. Therefore, some MDs are not doctors.

While the first premise is true (there are other types of doctors), the second is clearly not true.

“…oops?” by jasmeet. CC-BY-NC-ND.