Fallacy Of Affirming The Consequent

Making correct decisions is a more subtle process than commonly thought. Instead of considering a truthful paradox or simple puzzle, today we consider what could be called and out and out fraud. That is, the subject, “Fallacy of Affirming the Consequent,” can be used to deliberately mislead people. It is often encountered in commercials on radio and TV and in political speeches. Sometimes the fallacy arises as a simple matter of not thinking clearly. Either way, this is a nasty little one.

This fallacy can be illuminated easily by reference to set theory and Boolean logic, but since I have already used an example from the new book The Philosophy Gym by Stephen Law, I will more or less follow his exposition. He starts with a straightforward correct syllogism.

1. If I am a man, then I am mortal.

2. I am a man.
3. Therefore I am mortal.

Statement #3, the conclusion, follows naturally from the two premises.

Now consider these similar two series of statements and decide if you think the conclusion is justified in either or both:

1. If John is happy, then John is playing football.

2. John is playing football.
3. Therefore John is happy.

1. If I am taller than Sue, then Sue is short.

2. Sue is short.
3. Therefore I am taller than Sue.

Many people who have not been trained to think logically see nothing wrong with either series, but they are both examples of faulty thinking. The second half of an “if… then” statement is called the “consequent.” Unlike the first example, the last two affirm the result or consequent and then infer that the “if” must be true. Yet John can be perfectly miserable playing football, and Sue could be short, but I could be shorter. The first example affirms the antecedent and draws the correct conclusion.

When we take a rather long seminar, chapter, or sermon and reduce it to a series of linked logical statements like this, even untrained people can spot the error. However it is not so easy when the affirmation of the consequent comes during a commercial for a new car.

1. If you are athletic, sexually attractive, and have a good personality, you want to buy a BMW.

2. You want to buy a BMW
3. Therefore you are…

Or consider the example Law gives in his book:

1. If God exists, then there is good in the world.

2. There is good in the world.
3. Therefore God exists.

Few people would be fooled by this argument when presented in such stark terms, but dress it up with a lot of quotes from your favorite Holy Text, add some anecdotes, and the logic becomes sufficiently obscured that this little bit of faulty reasoning can become the starting point for a suicide bomber’s final drive.

As an exercise, try to construct a faulty syllogism to show that if a tsunami kills 150,000 innocent people, then either God is evil or there is no God.

How does this relate to programming a computer to respond to the environment automatically by making decision based on sensor input? Simple, if the programmer does not understand the underlying object, the code developed can quite happily be made to accept the principle that affirming the consequent is acceptable.

Then we can get some nasty problems, because the results might be correct most of the time and so the programmer does some real world tests and the program seems to work just fine. After all, John is probably happy playing football most of the time. I might really be taller than Sue most of the time. Maybe the people who buy BMWs really are more desirable most of the time. Maybe there is a God. In fact, the more closely related the antecedent and consequent are, the more likely the program will give the correct answer in testing.

Of course there are several automated ways to check for the logical consistency of a series of statements, but I recommend against relying on them when you, the programmer, should have a good handle on simple logical inference. Readers wishing to pursue this further might either look for introductory logic books, set theory, or computer design books. All of these consider the same underlying logic, but often with radically different symbolism.