Fallacy of composition
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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. 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 so breakable.
This fallacy is often confused with the fallacy of hasty generalization, in which an unwarranted inference is made from a sample to the population from which it is drawn.
An application: In Keynesian macroeconomics, the "paradox of thrift" is an example of 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.
The fallacy of composition is the converse of the fallacy of division.