## The paradox of generalizations about generalizations

A generalization is a claim of the form:
(1) All A’s are B’s.
A generalization about generalizations is thus a claim of the form:
(2) All generalizations are B.
Some generalizations about generalizations are true. For example:
(3) All generalizations are generalizations.
and some generalizations about generalizations are false. For example:
(4) All generalizations are false.
In order to see that (4) is false, we could just note that (3) is a counterexample to (4). The following argument is a bit more interesting, however.
Proof: Assume that sentence (4) is true. Then, given what (4) says, all generalizations are false. But (4) is a generalization, so (4) must be false, making (4) both true and false. Contradiction. So (4) can’t be true, and hence must be false.
(4) has an interesting property, however. Although, as we have seen, not all generalizations are false, and hence (4) fails to be true, it is itself a false generalization, and hence is a supporting. . .

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