The fallacies of composition and division are concerned with the relationship between the whole and the parts. If you attribute a certain quality to a part of something, it will not necessarily apply to the whole, and if you attribute a certain quality to the whole, it will not necessarily apply to the parts.
For example, supposing you are building a house. Each of the bricks weighs 2kgs. However, the house as a whole obviously does not weigh 2 kgs. You could pick up the bricks and throw them, but you couldn’t do that to the house, and so on. That is the fallacy of composition. For the fallacy of division you just need to turn this round. The house as a whole makes a good shelter from the rain – but that doesn’t mean that an individual brick makes a good shelter from the rain.
This example may seem obvious and absurd, but there are other instances where fallacies of composition and division are less obvious. It can even apply to colours. You might think it obvious that a whole made up of parts will be the same colour as its parts: but if the parts are blue and yellow, they may blur into green from a distance. A house that is white on the outside may also be built of bricks that are black on every side except the one that shows on the outside of the house. You might think that your body is alive, but it contains dead cells as well as live ones: what is true of the whole is not necessarily true of all the parts.
The reverse of either of these two fallacies is also fallacious. I can no more assume that parts necessarily do not share the properties of the whole as I can assume that they do.
One interesting application of this fallacy is that it seems to offer a good refutation of those who take either kind of metaphysical position on the mind-body problem, whether they are reductionists who think that our minds must be entirely material, or essentialists who think that the mind must be irreducible and essentially different from the body (for example, if it is a non-physical soul). Reductive materialists seem to be subject to the fallacy of composition: just because the components of the mind can all be understood as material objects, does not necessarily mean that the mind as a whole can be understood in that way. On the other hand, essentialists who want to insist that the mind is special and different are subject to the negation of the fallacy of division: just because the mind has certain special characteristics, such as consciousness, does not necessarily imply that its parts do not share those characteristics.
These fallacies can be similarly employed to point out the kind of mistake made whenever metaphysical conclusions have been drawn about a higher level of explanation being essentially different from or reducible to a lower one (in philosophy this is called supervenience). For example, whether life is or is not essentially different from mere chemical compounds, or whether reasoned behaviour is or is not essentially different from instinctual behaviour. I think we just have to live with the vagueness of these divisions in our ways of understanding the world, but it is too easy to rush into assumptions about rigid divisions.
To identify these fallacies in practice, you need to identify what the whole is and what the parts are. There may be good reasons in experience for believing that the whole either does or does not have the same characteristics as the parts, but a fallacy is taking place if it is being assumed that they necessarily have the same characteristics without further evidence.
Exercise
Are the following examples of the fallacy of composition or of division (or not)?
1. “Should we not assume that just as the eye, hand, the foot, and in general each part of the body clearly has its own proper function, so man too has some function over and above the function of his parts?” Aristotle, Nicomachean Ethics
2. Manchester United are likely to lose this match. Two of their strikers and several midfield players have chronic injury problems, and are likely to put in a disappointing performance.
3. Communism in the Soviet Union was a failure. Universal state employment meant that nobody was motivated to make an effort in economic life, and it was the economy that destroyed the Soviet system in the end.
4. I’ve tried one strand of spaghetti and it’s cooked, so the whole pan must be ready.
Picture: Fractal (Romanesco) Broccoli: In Fractals the parts do have the same qualities as the whole!