Universal affirmative: Difference between revisions
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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.” | ||
===Do not confuse with a statistical observation=== | ===Do not confuse with a statistical observation=== | ||
The [[universal affirmative]] “all Xs are Ys” is a different thing from the statistical observation “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. | The [[universal affirmative]] “all Xs are Ys” is a different thing from the statistical observation “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.” | 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.” | ||
Revision as of 16:05, 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.”
Do not confuse with a statistical observation
The universal affirmative “all Xs are Ys” is a different thing from the statistical observation “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.”