Division

Form:

The object O has the property P.
Therefore, all of the parts of O have the property P.
(Where the property P is one which does not distribute from a whole to its parts.)

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.

Counter-Example:

People are made out of atoms.
People are visible.
Therefore, atoms are visible.

Exposition:

Some properties are such that, if a whole object has the property, then all of its parts will, too—for example, invisibility. However, not all properties are like this—for instance, visibility. Let's call a property which distributes from a whole object to each of its parts a "dissective" property, using Nelson Goodman's term. If P is a dissective property, then the argument form above is validating, by definition of what such a property is. However, if P is not dissective, then the argument form is non-validating, and any argument of that form commits the fallacy of Division.

Sibling Fallacy: Composition

Source:

Thomas Mautner (Editor), A Dictionary of Philosophy (Blackwell, 1996).