Dividing fallacy occurs when someone assumes what is true of a whole object is true of its parts. This error can be avoided by careful consideration of each element. The fallacy of composition is when a single item is seen as representative of a larger group. Both errors can be challenged by certain statements and objects.
A dividing fallacy occurs when someone argues that what is true of an entire object must be true of its constituent parts, without ample evidence to support this idea. A simple example of this fallacy is a situation where someone argues that because the ocean as a whole is blue in color, each drop of water individually must also be blue in color. A divisive error occurs in this statement as water by itself is essentially colorless and the properties of water drops by mass and their collective reflectivity do not represent each drop by itself.
While fairly simple in nature, a split error can occur in one of two ways. One way this error can occur is when someone sees the properties of a whole thing and assumes that parts of it must have those properties as well. This is seen in the previous example of the ocean and individual water droplets. A division error can be avoided through more careful consideration of each element of an object and true statements such as “the ocean is reflective, therefore individual water droplets must be reflective” can be made.
The other way someone can make a dividing error is through the assumption that the actions or beliefs of an entire population must represent the actions or opinions of every person in the population. Someone may, for example, consider a country rich enough and assume that every person within that country must be rich as well. The reality of this type of situation, however, is much more complex than such an assumption would imply. This type of division error can be avoided through careful consideration of population samples before such claims are made.
In contrast to the fallacy of division is the fallacy of composition, in which a single item or individual is seen as representative of a much larger object or group. This mistake can be made by someone touching a drop of water and seeing it disperse, then assuming that the ocean would disperse in much the same way if hit from a great height. The mass of water together in a large body such as the ocean creates a surface area with a greater force than a single drop of water, and injuries often occur due to the application of this type of error. There are some statements and objects that can challenge both an error of division and composition, such as the argument that “bricks are solid, therefore the wall they make must be solid; and this wall is solid, therefore the bricks of which it is made must be solid.”
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