Universal affirmative

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A universal affirmative is a categorical statement taking the form: “Every A is B” where A and B are predicates. In the language of predicate logic, this can be expressed as: ∀x:A(x)⟹B(x).

Universal affirmatives can only be partially converted. “All of Alma Cogan is dead, but only some of the class of dead people are Alma Cogan.”

As Monty Python had it, given the premise, “all fish live underwater” and “all mackerel are fish", one cannot conclude that “if you buy kippers it will not rain", or that “trout live in trees", much less that “I do not love you any more.”

Do not confuse a universal affirmative with an average

The universal affirmative “all Xs are Ys” is a different thing from the statistical observation that “the average of all Xs is Y”, and the two should not be, but by those under the thrall of identity politics commonly are, confused. Not only are they not the same, one does not imply the other either.

Take the statistical observation “the average hep-cat likes the Rolling Stones”. This is clearly not good grounds for concluding that “all hep-cats like the Rolling Stones”, much less the specific assertion that “this hep-cat in particular likes the Rolling Stones.”

At this point we direct you to the parable of the squirrels

See also