Distributive Fallacy

Composition, which moves from parts to whole, and

Division, which moves from whole to parts.

     a composite - a whole made up of parts. Organizations, institutions and machines are all examples.

     a collective - a class made up of members. Sets and groups are examples.

     a generalization - a statistic about a class derived from facts about the members. Averages and medians are examples.

       (a) Cows eat grass.

       (b) Cows are important to the economy of Wisconsin.

In sentence (a) the meaning of the sentence is distributed to the members of the class. Each cow, considered as an individual, eats grass. In sentence (b) the meaning of the sentence is not distributed. While it is true that cows (as a group) are important to Wisconsin's economy, any particular cow might die without causing the economy of Wisconsin to go into a slump. The meaning of the sentence has collective value.

Of course, if we were to offer an argument in which the two senses occurred together, the result would be fallacious:

                    Cows are important to the economy of Wisconsin.
                    Bossie is a cow.
                    Therefore, Bossie is important to the economy of Wisconsin.

We cannot identify either the major premiss or the minor premiss as false. Rather, the error occurs because of a shift from collective meaning (in the major premiss) to the distributive meaning (in the minor premiss, and from there to the conclusion). Hence the fallacy has the characteristic earmarks of a Fallacy of Ambiguity. Distributive fallacy can also shift in the opposite direction:

                    Rocky Road ice cream, ketchup and potato chips are foods that I like.
                    A Rocky Road-ketchup-potato chip sundae is composed of Rocky Road ice cream,
                                      ketchup and potato chips.
                    Therefore, a Rocky Road-ketchup-potato chip sundae is a food that I like.

Again, both premisses are true. However, in this case, the major premiss has distributive meaning while the minor premiss and the conclusion have collective meaning.

There is no guarantee that qualities manifested in the parts will be manifested in the whole, or that the qualities manifested in the whole will be manifested in the parts. However, there are some interesting examples in which the inference from parts to whole or whole to parts is perfectly sound. For example, "The legs of this desk are made of wood. So is the writing surface, the back, the shelves, and the sides. This is a wooden desk." Or, "The company recommends comprehensive auto insurance. Comprehensive auto insurance includes collision insurance, liability insurance and emergency towing. Therefore the company recommends that you have each of these kinds of insurance."

What should we make of these examples? I think the lesson to be learned is that the move from parts to whole or whole to parts alone is not what makes the Distributive Fallacy fallacious. Rather it is the move from parts to whole or whole to parts in a context in which we are discussing an "emergent" property, i.e. a property that is true of the whole because of some sort of collective interaction among the parts. Non-emergent properties are common enough that arguments moving from parts to whole or whole to parts can often be used soundly and effectively. Unfortunately, since the distinction between emergent and non-emergent properties is easy to overlook (and is perhaps hard to understand), it is possible for the Distributive Fallacy to be passed off as non-fallacious.