Distributive Fallacy


The argument turns on a confusion between the collective sense of a class (i.e. the class taken as a whole) and the distributive sense of a class (i.e. each of the elements of the class taken separately).



This fallacy takes two forms:

Composition, which moves from the distributive sense to the collective sense, i.e. from parts to whole, and

Division, which moves from the collective sense to the distributive sense, i.e. from whole to parts.



We make statements about classes of objects in at least two distinct ways. Sometimes our statement is intended to say something about the members of the class considered separately, as individuals; other times our statement is intended to say something about the class itself, or the members of the class considered together. For example:

(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 is collective, not distributive.

There are actually various ways in which we can talk about a class in a collective sense:

a composite - a whole made up of interacting parts, e.g. organizations, institutions, machines, banana splits, etc.

a collective - a class made up of members, e.g. sets and groups.

a generalization - a statistic about a class derived from facts about the members, e.g. averages and medians.

The Distributive Fallacy mimics good reasoning when the difference between the distributive sense of the class and one of these collective senses is subtle enough to be overlooked.


Source: I find common references to "distributive fallacy" as the name for the error of confusing the collective and distributive senses of a class. Traditionally logicians treat Composition and Division as separate fallacies, although they acknowledge their obvious relation. I am not sure which logician may have first treated them as different variations of the same fallacy.


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