Universal affirmative: Difference between revisions
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{{g}}A [[universal affirmative]] is a categorical statement taking the form: “Every A is | {{g}}A [[universal affirmative]] is a categorical statement taking the form: “Every A is B” where A and B are [[predicate|predicates]]. In the language of predicate logic, this can be expressed as: ∀x:A(x)⟹B(x). | ||
[[Universal affirmative]]s can only be partially converted. “All of Alma Cogan is dead, but only some of the class of dead people are Alma Cogan.” | [[Universal affirmative]]s 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.” | 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.” | ||
Note: the [[universal affirmative]] “all Xs are Ys” is a different thing from the normative statement “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 normative statement “the average hep-cat likes the Rolling Stones”. This is clearly ''not'' good grounds for concluding that “''all'' hep-cats like the Rolling Stones” — in fact only the reverse would be true — much less the ''specific'' assertion that “''this'' hep-cat ''in particular'' ikes the Rolling Stones.” | |||
{{sa}} | {{sa}} | ||
*[[Correlation]] and [[causation]] | *[[Correlation]] and [[causation]] | ||
*[[cognitive dissonance]] | *[[cognitive dissonance]] | ||
*[[Big data]] | |||
Revision as of 15:58, 21 October 2020
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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.”
Note: the universal affirmative “all Xs are Ys” is a different thing from the normative statement “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 normative statement “the average hep-cat likes the Rolling Stones”. This is clearly not good grounds for concluding that “all hep-cats like the Rolling Stones” — in fact only the reverse would be true — much less the specific assertion that “this hep-cat in particular ikes the Rolling Stones.”