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 (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.
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In Keynesian macroeconomics, the "paradox of thrift" theory 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, Keynesian economists argue that it may cause a recession by reducing consumer demand. Other economic schools, such as the Austrian School, disagree.[2]
The modo hoc (or "just this") fallacy is the informal error of assessing meaning to an existent based on the constituent properties of its material makeup while omitting the matter's arrangement.[3] For instance, metaphysical naturalism states that while matter and motion are all that comprise man, it cannot be assumed that the characteristics inherent in the elements and physical reactions that make up man ultimately and solely define man's meaning; for, a cow which is alive and well and a cow which has been chopped up into meat are the same matter but it is obvious that the arrangement of that matter clarifies those different situational meanings.[4]
Some properties are such that, if every part of a whole has the property, then the whole will, too. In such instances, the fallacy of composition does not apply. For example, if all parts of a chair are green, then it is usually acceptable to infer that the chair is green.[upper-alpha 1] Similarly, if all parts of a table are wooden, it is acceptable to infer that the table is wooden. A property of all parts that can be ascribed to the whole is called an "expansive" property, according to Nelson Goodman.[1] For a property to be expansive, it must be absolute (as opposed to relative) and structure-independent (as opposed to structure dependent), according to Frans H. van Eemeren.[5]
The meanings of absolutes do not imply a comparison, whereas the meanings of relatives do. E.g., being green or wooden are absolutes, whereas fast or heavy or cheap are relatives. We know whether something is green or wooden without reference to other things, whereas we do not know whether something is fast or heavy or cheap without implicitly comparing it to other things. Relative properties are never expansive. E.g., it does not follow that if all parts of a chair are cheap, then the chair is cheap.
Absolute properties shared by all constituent parts of a whole are expansive only if they are independent of the nature of the whole's structure or arrangement. That is, if it does not matter whether the whole is a summation or integration, an unordered collection or a cohesive whole, then the property is said to be independent.[5] Consider the example, X is green. It does not matter whether X is a chair (an integration or coherent whole) or just a pile of twigs (a summation or unordered collection). Green is therefore an independent property. Now consider the example, X is rectangular. Rearrange a rectangular object—e.g., tear up the pages of a book—and it might not stay rectangular. Rectangularness is a structure dependent property and is therefore non-expansive.
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