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A 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 (or even of every proper part). For example: "This fragment of metal cannot be broken with a hammer, therefore the machine of which it is a part cannot be broken with a hammer." This is clearly fallacious, because many machines can be broken into their constituent parts without any of those parts being breakable.

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

The fallacy of composition is the converse of the fallacy of division.

1. Atoms are not visible to the naked eye
2. Humans are made up of atoms
3. Therefore, humans are not visible to the naked eye

In Keynesian macroeconomics, the "paradox of thrift" illustrates this fallacy: increasing saving (or "thrift") is obviously good for an individual, since it provides for retirement or a "rainy day," but if everyone saves more, it may cause a recession by reducing consumer demand. So here is one explicit argument (selected from a number of possibilities arising from these facts) that commits the fallacy of composition:

The thrift of any member of a group is beneficial to that member.
Therefore, the thrift of the group as a whole is beneficial to that group as a whole.

Commodity exports and dependency theory may also be used to demonstrate the fallacy of composition. Increases in the export of a certain commodity from one country may be beneficial to that country. However, exports of that commodity by many countries may flood the market, and thus drive down price, proving detrimental to the ensemble of exporting countries.

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