2.2 Logical Fallacies, Formal and Informal

Generally and crudely speaking, a logical fallacy is just a bad argument — bad in the logical sense of being incorrect—not bad in the sense of being ineffective or unpersuasive. Alas, many fallacies are quite effective in persuading people; that is why they’re so common. Often, they’re not used mistakenly, but intentionally—to fool people, to get them to believe things that maybe they shouldn’t. Our goal for the remainder of this unit is to develop skills and ability for recognizing bad arguments for what they are so as not to be persuaded by them.

There are both formal and informal logical fallacies.

• Formal fallacies occur in arguments that are bad because they have bad (invalid!) form.
• Informal fallacies occur in arguments that are bad because of their content, their context, and/or their mode of delivery.

2.2.1 Formal Fallacies – Quick Look

Our primary concern in this module will be with informal fallacies, but before we focus on those, let’s take a moment to recall our work in Module 1, subsection 1.3.1 where we looked at counterexamples as a way to prove invalidity of deductive argument forms.  We learned about proving an ordinary-language argument to be invalid by finding a counterexample.  This entails using the exact same form as the original ordinary-language argument, and coming up with another ordinary-language argument that is invalid – it has true premises and a false conclusion. We were demonstrating formal fallacies!  And you revealed further formal fallacies in the 1.3.1 Skills Practice.

Before we turn to informal fallacies, we will looks at two more formal fallacies – arguments with bad form.  Both of these examples of formal fallacies are committed so frequently in ordinary discourse that they have been been given names. And both of these examples happen to have a premise that is a conditional (if-then) proposition.  At this point in the course, a deep understanding of all the fine points and mechanics of conditional statements is not required. (We will do in-depth work with conditional statements in Module 4.)  For now, be aware of this:

• The ‘if’ portion of a hypothetical proposition is called the ‘antecedent.’
• The ‘then’ part of a hypothetical proposition is called the ‘consequent.’
• The schematic forms in the examples that follow will use ‘A’ to represent the antecedent and ‘C’ for the consequent.

Several of the valid conditional argument forms in the  supplemental list at the end of Module 1 – Some Common Deductive Argument Forms – have a conditional (hypothetical) statement as a premise. Our examples involve invalid forms of two of those argument types.

Example 1: Affirming the Consequent

Consider this fallacious deductive argument:

The fact that Ralph is not playing video games does not infer necessarily that he’s doing his homework. He could be doing innumerable other things besides homework. The conclusion might be true but it could be false. The argument is invalid, it has this invalid form:

Any argument with this invalid form is fallacious and is an instance of the formal fallacy called Affirming the Consequent. This fallacy is a recognized erroneous version of a valid argument form called ‘modus ponens ‘. Here is the valid form:

This is how the valid form works:

1. In the first premise, the ‘if” part (A) necessitates the ‘then” part (C).  (If A is the case, then by necessity C is the case too.)
2. The second premise then affirms that the ‘if’ part – A – is in fact the case.
3. The conclusion then claims that the ‘then’ part – C – is also the case.

In our fallacious version, the second premise affirms the ‘then’ part (consequent) instead of the ‘if’ part (the antecedent). That is the formal error! One way to prove the invalidity of the invalid form is to create a counterexample that produces true premises and a conclusion known to be false.  For example:

Example 2: Denying the Antecedent

And now, consider this deductive argument:

With just intuitive consideration of this argument, its logic is not convincing; there are other likely reasons that Andre is not riding his bike on Tuesday. This argument is invalid, it has this invalid form:

Any argument of this form is fallacious. This is an instance of the formal fallacy called Denying the Antecedent.  This fallacy is a recognized erroneous use of the valid argument form called modus tollens.  Here is the valid form:

With the valid form:

1. In the first premise, the ‘if” part (A) necessitates the ‘then” part (C).  (If A is the case, then by necessity C is the case too.)
2. The second premise then denies that the ‘then’ part C is the case.
3. And the conclusion logically follows that the ‘if’ part (A) is not the case either.

In our fallacious version, the second premise denies the ‘if’ part (antecedent) instead of the ‘then’ part (the consequent). That is the formal error! Again, invalidity can be proved with a counterexample that has true premises and a known false conclusion; our prior counterexample works here too: