Distributive Fallacy - Division


The argument moves from a claim about the collective sense of a class (i.e. the class taken as a whole) to a claim about the distributive sense of a class (i.e. the parts taken separately).



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


"The set of mice is larger than the set of elephants. Hence, mice are larger than elephants."



There is no guarantee that 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 appears to be perfectly sound. For example, "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." It is not the move from whole to parts per se that makes Division a fallacy. Rather, it is the move from 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 interaction among the parts. Because the emergent property depends upon interaction, it cannot be found in the parts taken separately. In the example above, cows are important to the economy of Wisconsin precisely because there are so many of them. Bossie by herself is not enough cows to contribute significantly to the economy.

Unfortunately, the distinction between emergent and non-emergent properties is easy to overlook, and is perhaps hard to understand. The fallacy of Division mimics good reasoning, I believe, because it tries to pass off a context in which an emergent property is involved with a context in which a simple, non-emergent property is involved.


Source: Aristotle, Sophistical Refutations.


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