The fallacy of Division occurs when it is concluded that what is true of a whole must also be true of its constituents and this inference is not justified. There are two main variants of the general fallacy of Division:
The first is committed when it is concluded that what is true of the whole must also be true of the parts and this inference is not adequately supported. It has this pattern:
Premise 1: The whole, X, has properties A, B, C, etc.
Conclusion: Therefore, the parts of X have properties A, B,C, etc.
That this line of reasoning is fallacious is made clear by the following example: “4 is an even number. 1 and 3 are parts of 4. Therefore 1 and 3 are even.”
It is not always fallacious to draw a conclusion about the parts of a whole based on the properties of the whole. If adequate evidence is provided in the argument, the reasoning can be good. For example, the human body is made out of matter and a reasonable argument can be made that the component parts are also made of matter.
The second version is committed when a conclusion about the properties of individual members of a group is drawn based on the collective properties of the group and there is inadequate justification for the conclusion. This reasoning is as follows:
Premise 1: As a collective, group or class X has properties A, B, C, etc.
Conclusion: Therefore the individual members of group or class X have properties A, B, C, etc.
That this 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 athlete is a football player, a track runner, a swimmer, a tennis player, a swimmer, etc.
It is not always fallacious to draw a conclusion about an individual based on what is true of the class they belong 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.
Defense: Avoiding this fallacy is a matter of checking to see if adequate reasons have been given to justify the inference from the whole to the parts.
“The ball is blue, therefore the atoms that make it up are also blue.”
“A living cell is organic material, so the subatomic particles making up the cell must also be organic material.”
Parent: “Look how big that dorm is!”
Child: “It is pretty big.”
Parent: “You’re going to have a nice, big room. That explains why the cost of college housing is so high.”
“Sodium chloride (table salt) may be safely eaten. Therefore, its constituent elements, sodium, and chlorine, may be safely eaten.”
“Americans use much more electricity than Africans do. So, Bill, who lives in primitive cabin in the Maine wood, 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 education than Mr. Bill Buffoon. “
“Minorities get paid less than whites in America. Therefore, the black CEO of a billion-dollar company gets paid less than the white janitor who cleans his office.”