A Fallacy of Division is the reasoning error that occurs when one arguments or assumes that if something is true for a whole then it must also be true for some or for all of its parts.
The opposite of this fallacy is called the Fallacy of Composition, which arises when one fallaciously attributes property of some part of something to the thing as a whole.
If a system as a whole has some property that none of its constituents has (or perhaps, it has it but not as a result of some constituent having that property), this is sometimes called an emergent property of the system.
The Fallacy of Division example:
The universe has existed for fifteen billion years.
The universe is made out of molecules.
Therefore, each of the molecules in the universe has existed for fifteen billion years.
Another example of Fallacy of Division:
People are made out of atoms.
People are visible.
Therefore, atoms are visible.
Yet another example:
The second grade in this school eats a lot of ice cream. Carlos is a second-grader in this school. Therefore, Carlos eats a lot of ice cream.
Both the fallacy of composition and the fallacy of division were addressed by Aristotle in Sophistical Refutations.
Ancient philosophers used doctrine homoeomeria, which postulated that particles forming a substance must themselves have the same properties of that substance for example:
liquid water consists of atoms
water is wet
therefore, atoms are wet
There was a lot of research and argumentis about that in ancient times. For example, in Mereology (from the Greek word “part”) is the theory of parthood relations: of the relations of part to whole and the relations of part to part within a whole. Sometimes fallacy of division is called mereological fallacy because of that.
In statistics, an ecological fallacy is a logical fallacy in the interpretation of statistical data where inferences about the nature of individuals are deduced from inference for the group to which those individuals belong.
Common statistical ecological fallacies are:
- confusion between ecological correlations and individual correlations
- confusion between the group average and the total average
- Simpson’s paradox
It can be because of lack of representation, or even when the group is representative, not exhaustive.
Different Criteria Definitions for Macro and Micro levels
The Fallacy of Division can occur because of the different meanings of the property applied to part vs. to a whole.
In the Holy Church, all priests must be Holy.
Holy Church is called like this not because all priests are full of Holyness. To people and Church itself, different definitions of this adjective are applied.