A compositional error is to assume that the parts or members of a whole will have the same properties as the whole. This leads to erroneous conclusions because what is true of different parties is not necessarily true at all.
Cause
Inferences based on this type of reasoning are considered fallacious because the collective (the group as a whole) and the distributive (the members of a group) do not necessarily share the same properties. In other words, just because individuals possess certain characteristics does not in itself guarantee that the class or group (taken as a whole) also possesses those characteristics.
The composition error follows the general form:
Y is part of X.
There is property A.
So X also has property A.
The fallacy of composition can arise when we expect more (or less) from the whole than the individual parts can deliver. For example, the statement "All the players on the team are the best at their position, therefore it is the best team" is based on an erroneous assumption, because "the best team" is not necessarily an aggregation of the best players. Other factors play a role, such as the ability to work together.
It is important to note that it is not always wrong to infer that a whole has a certain property from the observation that all of its constituent elements have that property. The words “All the parts of this office are made of metal; so this desk is made of metal” is clearly not misleading.
The problem with compositional errors does not necessarily lie in the transition from the individual to the whole. Rather, it is the transition from parts to whole in a context where an "emergent property" is applied (i.e. a property that a collection or complex system has, but which the individual parts do not possess) .
Because the emergent property depends on the interaction between the parts, it cannot be found in the parts taken separately. For example, salinity is a property of salt, but that does not mean that it is also a property of sodium and chlorine, the two elements that make up salt. Not realizing that a property is emergent leads to the fallacy of composition.
How to avoid a composition error?
Recognizing the fallacy of composition depends on our knowledge of the world and our ability to understand the parts-whole relationship in a given context. In the brick house example above, it's easy to spot the mistake because we know that a pile of bricks weighs more than a single brick. In other cases, it may be less obvious, so you have to ask yourself questions following:
Is the characteristic transferred from parts to a whole an absolute property (e.g., green, square, sour) or relative (e.g., small, rich, talkative)? A house is green regardless of where it is located, while being rich involves an implicit comparison and depends on context.
What sort of set or group is the characteristic transferred into? If it is transferred into a homogeneous whole, then the argument is valid. For example, if a spoonful of soup is spicy, then we can safely conclude that the entire pot of soup is spicy.
Does the aggregation of individual parts give rise to emergent properties? The way the parts interact with each other often changes the character of the whole. In this case, inferring something about the whole from the individual parts is fallacious. For example, human consciousness is considered an emergent property of the brain. The sum of all neurons in the nervous system generates complex human emotions like joy or fear, none of which can be attributed to a single neuron.
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