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. Look up fallacy in Wiktionary, the free dictionary. ... Hasty generalization, is a logical fallacy of faulty generalization by reaching an inductive generalization based on insufficient evidence. ...

The fallacy of composition is the converse of the fallacy of division. A fallacy of division occurs when someone reasons logically that something that is true of a thing must also be true of its constituents. ...

Example

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

Application

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: Keynesian economics, or Keynesianism, is an economic theory based on the ideas of John Maynard Keynes, as put forward in his book The General Theory of Employment, Interest and Money, published in 1936 in response to the Great Depression of the 1930s. ... Circulation in macroeconomics Macroeconomics is a branch of economics that deals with the performance, structure, and behavior of a national economy as a whole. ... The paradox of thrift is a paradox of economics propounded by John Maynard Keynes. ... In common usage, saving generally means putting money aside, for example, by putting money in the bank or investing in a pension plan. ... In economics, consumption refers to the final use of goods and services to provide utility. ...

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.

Another example is the Tragedy of the Commons where an individual would benefit from his unlimited access to a finite resource but the collective unrestricted demand from the whole group would eventually doom the resource through over-exploitation. The Tragedy of the Commons is a type of social trap, often economic, that involves a conflict over resources between individual interests and the common good. ...