Fallacies of composition and division

The Fallacy of Composition arises when one infers that something is true of the whole from the fact that it is true of some part of the whole.  Conversely, the Fallacy of Division occurs when one infers that something true for the whole must also be true of all or some of its parts.  Both fallacies were described by Aristotle in Sophistical Refutations.

Fallacy of composition

The logical form of the Fallacy of Composition is:

     Premise 1: A is part of B

     Premise 2: A has property X

     Conclusion: Therefore, B has property X.

Two examples of this fallacy are:

• If someone stands up out of his seat at a baseball game, he can see better.  Therefore, if everyone stands up they can all see better.

• If a runner runs faster, she can win the race.  Therefore if all the runners run faster, they can all win the race.

Athletic competitions are examples of zero-sum games, wherein the winner wins by preventing all other competitors from winning.

Another example of this fallacy is:

Sodium (Na) and Chlorine (Cl) are both dangerous to humans. Therefore any combination of sodium and chlorine, such as common table salt (NaCl) will be dangerous to humans.

This fallacy is often confused with the fallacy of faulty generalisation, in which an unwarranted inference is made from a statement about a sample to a statement about the population from which it is drawn.

In economics, the Paradox of Thrift is a notable fallacy of composition that is central to Keynesian economics.  Division of labour is another economic example, in which overall productivity can greatly increase when individual workers specialize in doing different jobs.

In a Tragedy of the Commons, an individual can profit by consuming a larger share of a common, shared resource such as fish from the sea; but if too many individuals seek to consume more, they can destroy the resource.

In the Free Rider Problem, an individual can benefit by failing to pay when consuming a share of a public good; but if there are too many such ‘free riders’, eventually there will be no ‘ride’ for anyone.

Fallacy of division

The Fallacy of Division is the converse of the Fallacy of Composition.  The logical form of the Fallacy of Division is:

      Premise 1: A is part of B

      Premise 2: B has property X

      Conclusion: Therefore, A has property X.

An example the fallacy of division is:

A Boeing 747 can fly unaided across the ocean.

A Boeing 747 has jet engines.

Therefore, one of its jet engines can fly unaided across the ocean.

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