Statistical syllogisms

A statistical syllogism (or proportional syllogism or direct inference) is a non-deductive syllogism. It argues, using inductive reasoning, from a generalization true for the most part to a particular case.

Statistical syllogisms may use qualifying words like "most", "frequently", "almost never", "rarely", etc., or may have a statistical generalization as one or both of their premises.

For example:

Premise 1 (the major premise) is a generalization, and the argument attempts to draw a conclusion from that generalization. In contrast to a deductive syllogism, the premises logically support or confirm the conclusion rather than strictly implying it: it is possible for the premises to be true and the conclusion false, but it is not likely.

General form:

In the abstract form above, F is called the "reference class" and G is the "attribute class" and I is the individual object. So, in the earlier example, "(things that are) taller than 26 inches" is the attribute class and "people" is the reference class.

Unlike many other forms of syllogism, a statistical syllogism is inductive, so when evaluating this kind of argument it is important to consider how strong or weak it is, along with the other rules of induction (as opposed to deduction). In the above example, if 99% of people are taller than 26 inches, then the probability of the conclusion being true is 99%.

Two dicto simpliciter fallacies can occur in statistical syllogisms. They are "accident" and "converse accident". Faulty generalization fallacies can also affect any argument premise that uses a generalization. A problem with applying the statistical syllogism in real cases is the reference class problem: given that a particular case I is a member of very many reference classes F, in which the proportion of attribute G may differ widely, how should one decide which class to use in applying the statistical syllogism?

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