These related fallacies are very similar to the fallacies of Generalization, discussed in the chapter “Too Simple,” and also similar to False Analogy in my book, Biblical Logic: In Theory and Practice. Both fallacies—Composition and Division— concern the relationship of members of a group to the group as a whole.
The Fallacy of Composition refers to applying the characteristics of the members as individuals to the group as a whole. For example, a single stick may be easy to break. But to infer, based on this, that a bundle of sticks is also easy to break, is to commit the fallacy of composition. Even if you can break individually every stick in a bundle, you still may not— probably cannot—break the bundle as a whole together.1 Imputing the weakness of one stick to the group as a bunch commits the fallacy.
The Fallacy of Division commits the opposite error. This refers to applying the characteristics of the group as a whole to each individual member of the group. For an example of this, take the converse of the bundle of sticks. Because the bundle as a whole is tough to break does not necessitate that any individual stick in the bundle is tough to break by itself.
Awareness of this fallacy guards against the neglect of ancient wisdom, in fact, revealed wisdom. Both Scripture and ancient traditions remind us that when similar things come together as a group, they acquire properties and characteristics inaccessible by the individuals alone. The Preacher in Ecclesiastes writes,
Two are better than one because they have a good return for their labor. For if either of them falls, the one will lift up his companion. But woe to the one who falls when there is not another to lift him up. Furthermore, if two lie down together they keep warm, but how can one be warm alone? And if one can overpower him who is alone, two can resist him. A cord of three strands is not quickly torn apart (Eccl. 4:9–12).
This, of course, is not to say that individuals have no value, but only to point out that groups acquire qualitative differences from the individuals that compose them. The same is true in reverse: individuals may each have qualitative differences that do not transfer to the group. . . .
Families as Democracies?
Examples of these Fallacies do not appear publicly as frequently as others, but they do occur. A questioner challenged conservative columnist John Rosemond on the question of authoritative parenting. The question reads,
You yourself have repeatedly said that parents should raise their children such that they are familiar and equipped to deal with the real world. If the real world is democratic, then shouldn’t American families be democracies?2
The question commits the Fallacy of Division, assuming that since the nation is governed as a democracy (by the way, it is not: it is a representative republic), then the institutions (in this case family) that make up that nation should function democratically as well. Rosemond has no trouble countering the fallacy: “The idea that the USA would be a ‘better’ democracy if its families were little democracies is baseless.” Not only baseless, I must add, but logically unsound. Rosemond approaches the same criticism when he responds that “although the political process in the Unites States is reasonably democratic, our society is definitely not. Rather it is composed of institutions that are structured hierarchically. . . . Within them, persons of greater authority are found instructing, directing and dictating to persons of lesser authority.” He points out that this holds true even within the “democratic” government itself: you cannot ignore laws you do not like in the name of “democracy,” you must abide by the authoritarian principles of law. Nevertheless, from a logical point of view, we must reject the viewpoint that the democracy of the larger group (nation) must also apply to each member of that group (families). This view commits the fallacy, and thus does not reflect the truth.
Many find it easy to conflate these two fallacies, Composition and Division. Here are some suggestions you may find helpful to keep them separate in your mind. To compose a group assuming the characteristics of its members is to commit the Fallacy of Composition. Conversely, to assume that the characteristics of a group divide out to each member is to commit the Fallacy of Division. So, to move from individuals to a group is to compose, thus Composition. To move from the group to individuals is to divide, thus Division. Composing begins with individuals; dividing be- gins with groups. I believe this provides a helpful way of remembering. If, however, you still find the two confusing, it will be enough to remember them together: that you cannot assume either that attributes transfer from individuals to a group or from a group to its members.
There are many expressions of these fallacies in human behavior. The evils of racism, sexism, and other related prejudices express these two fallacies in social ways. The beliefs that “all blacks are X, therefore this black man must be X” or that “a black family I knew was X, therefore the black race is X,” and all similar claims fall into the categories of Composition or Division. Of course, few racists actually state their belief so clearly and categorically as this, but this is a valid logical representation of what occurs in practice. Stereotypes in general commit this fallacy (as well as False Analogy and Sweeping Generalization), because they create an abstract image that allegedly represents a group of people; the stereotype then allows others to classify individuals as members of that group, and then uncritically to apply aspects of that imaginary group to each alleged member of that group. This stretches the facts in the worst way: it not only deceives people, but misrepresents them, marginalizes, and oppresses them. When fallacious argumentation masks racism and other unfounded prejudices, then the moral and ethical implications of logic become obvious.
- This helpful example, and its following converse, is provided by Engel, With Good Reason, 114.(↩)
- Quoted in John Rosemond, “Should families be democracies? No way,” The Atlanta Journal-Constitution, January 13, 2002, M6.(↩)