The fallacy of Division is committed when a person infers that what is true of a whole must also be true of its constituents and justification for that inference is not provided.
There are two main variants of the general fallacy of Division:
The first type of fallacy of Division is committed when 1) a person reasons that what is true of the whole must also be true of the parts and 2) the person fails to justify that inference with the required degree of evidence. More formally, the "reasoning" follows this sort of pattern:
The whole, X, has properties A, B, C, etc.
Therefore the parts of X have properties A, B, C, etc.
That this line of reasoning is fallacious is made clear by the following case: 4 is an even number. 1 and 3 are parts of 4. Therefore 1 and 3 are even.
It should be noted that it is not always fallacious to draw a conclusion about the parts of a whole based on the properties of the whole. As long as adequate evidence is provided in the argument, the the reasoning can be acceptable. For example, the human body is made out of matter and it is reasonable to infer from this that the parts that make up the human body are also made out of matter. This is because there is no reason to believe that the body is made up of non-material parts that somehow form matter when they get together.
The second version of the fallacy of division is committed when a person 1) draws a conclusion about the properties of individual members of a class or group based on the collective properties of the class or group and 2) there is not enough justification for the conclusion. More formally, the line of "reasoning" is as follows:
As a collective, Group or class X has properties A, B, C, etc.
Therefore the individual members of group or class X have properties A, B, C, etc.
That this sort of reasoning is fallacious can be easily shown by the following: It is true that athletes, taken as a group, are football players, track runners, swimmers, tennis players, long jumpers, pole vaulters and such. But it would be fallacious to infer that each individual athletes is a football player, a track runner, a swimmer, a tennis player, a swimmer, etc.
It should be noted that it is not always fallacious to draw a conclusion about an individual based on what is true of the class he/she/it belongs to. If the inference is backed by evidence, then the reasoning can be fine. For example, it is not fallacious to infer that Bill the Siamese cat is a mammal from the fact that all cats are mammals. In this case, what is true of the class is also true of each individual member.
The fallacy of division is the opposite of the Fallacy of Composition. It consists of assuming that a property of some thing must apply to its parts; or that a property of a collection of items is shared by each item.
Because the whole has a certain property, it is
argued that the parts have that property. The whole in question may be either
a whole object or a collection or set of individual members.
"The ball is blue, therefore the atoms that make it up are also blue.""A living cell is organic material, so the chemicals making up the cell must also be organic material." "Bill lives in a large building, so his apartment must be large." "Sodium chloride (table salt) may be safely eaten. Therefore its constituent elements, sodium and chloride, may be safely eaten."