Monday, September 22, 2008

Why stereotypes are treacherous, and other logical puzzles

Continuing my Logic for Theological Discussion thread, here are a couple of fallacies that are very common.

I had lunch with a pastor-friend recently, and he told me of a man in his congregation who has begun to doubt. Specifically, these doubts have focused on the man’s belief in a literal Hell-- the man doesn’t believe that there is literally a place that is Hell as the Scriptures describe.

As a consequence of this, the guy thinks he must abandon the rest of his beliefs in biblical truth as well-- in fact, he is beginning to wonder whether this doubt should compel him to abandon his faith altogether. His rationale is that, because he has serious doubts and even disbelief about one teaching of the Bible, he must abandon his belief in all of the teachings of the Bible.

This man is falling into the trap of the Fallacy of Composition. This fallacy follows a basic and common pattern: what is true of the parts that compose a thing must also be true of the whole thing. The tricky part of this fallacy is that the line of thinking is sometimes true-- but we are inclined to believe that it is true all of the time, because it is true some of the time (which is, itself, a Fallacy of Composition).

So, we reason: every blade of grass in my yard is green (true), therefore my lawn is green (also true). If that is true, then it must also be the case that: taking one pill from the bottle of prescription drugs is not poisonous, therefore, taking all of the pills at the same time would also not be poisonous. Or, every atom that makes up my body is invisible to the naked eye, therefore my body must be invisible to the naked eye.

As you can see from these examples, you cannot rely simply on the pattern of thought processes in the argument to determine whether an argument is sound or not. Therefore, this young man’s fallacy goes like this: I doubt one particular teaching of the Bible, therefore I must doubt all of the teachings of the Bible.

A closely related fallacy to Composition is the Fallacy of Division. It is the converse of the Fallacy of Composition, and follows this line of thought: what is true of the whole of a thing is also true of the parts of that thing.

Once again, because it is sometimes true, we often assume it to be always true. But that is not the case. Consider: An airplane can fly through the air for miles and miles; therefore, this hunk of metal I took off of an airplane can fly through the air for miles and miles. Or, I am able to see my desk without help from magnification, so I ought to be able to see the atoms that compose my desk without magnification.

Clearly, as you see, it doesn’t always hold up. Here’s what is interesting: these fallacies are based on the same kinds of conclusions, or inferences, as stereotypes. In other words, based on what we believe to be true of a whole group, we infer an opinion about the members of that group (Division); OR, based on our observations of members of a group, we infer a general principle about that group (Composition). Sometimes these inferences are true and sound, while at other times they are not. This is what makes stereotypes so dangerous.

So we might reason thusly: Everyone I know who has installed Microsoft Vista thinks it is awful; therefore, Vista must be a bomb. (Fallacy of Composition or not? It depends on how you measure it. On the one hand,
several hundred million copies of Vista have sold, making it an inherent financial success. On the other hand, as of August, Windows XP -- the six year old predecessor to Vista-- was still outselling Vista, and the numbers of people who have switched to the Apple Mac platform have increased substantially.)

Or this: Presbyterian churches are stuffy and dull; so this Sunday’s worship at Hickory Withe Presbyterian Church will probably be stuffy and dull, too. (Fallacy of Division? I hope not. Although it is true that some Presbyterian churches-- and some other churches, as well-- are stuffy and dull, this may be an unfair stereotype. It also may be an inference made out of ignorance: someone who is uninterested in worshiping God might find ANY church worship service dull, and even stuffy.)

So what do we do about the fallacies of Composition and Division? It all comes down to a simple question:

What is the justification for making that inference?

In other words, why do I feel safe in drawing the conclusion I have? What are the unstated factors in the argument? Is there a point of data-- or more than one-- that connects the part and the whole? If so, does that data hold up as good reason to draw the inference I have?

In the Microsoft example, there are points of data that might support the conclusion, but you still might question whether the starting point is the best one.

With the young man who doubts the Bible, the connecting points that are unstated are likely based on someone teaching the guy that he had to believe the whole Bible to be a Christian. While the Bible is the Word of God, and we cannot know the truth about salvation apart from it, attaching a required belief onto the saving grace of the gospel makes it into works salvation. While I want every believer-- and every unbeliever too-- to hear and receive Scripture as God’s Word, I cannot deny others their doubts. In short, one can be a Christian and not believe that everything written in Scripture is true.

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