The fallacy of Division is committed when a person infers that what is true of a whole or of a class must also be true of its constituents or its members and justification for that inference is not provided. It has the following forms:
This is fallacious because characteristics of a whole of of a group are not necessarily characteristics of its parts or of its members. For example, it is true that 4 is even, but that doesn't mean that 1 and 3, both part of 4, are even too. 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 athlets is a football player, a track runner, a swimmer, a tennis player, a swimmer, etc. It is a special case of identification since it confuses two different levels of abstractions (an individual and a category or a part and a whole).
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. 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 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."
"Americans use much more electricity than Africans do. So Bill, who lives in primitive cabin in Maine, uses more electricity than Nelson, who lives in a modern house in South Africa. "
"Men receive more higher education than women. Therefore Dr. Jane Smart has less higher education than Mr. Dick Jones."
"Minorities get paid less than 'whites' in America. Therefore, the black CEO of a multi-billion dollar company gets paid less than the white janitor who cleans his office."
Each brick is three inches high, thus, the brick wall is three inches high.
Because the brain is capable of consciousness, each neural cell in the brain must be capable of consciousness.
Show that the properties in question are the properties of the parts, and not of the whole. If necessary, describe the parts to show that they could not have the properties of the whole.