Concept
Why does ∃ x Professor(x) ⇒ Human(x) produce a misleadingly true statement?
Stephen Davies, Ph.D. Version 2.2.2 Through Discrete Mathematics A Cool Brisk Walk / Chapter 1
"34. True or false: ∃ x Professor ( x ) ⇒ Human ( x ) . This is technically true, but for a stupid reason, and whoever wrote it almost certainly didn’t intend what they wrote. It says, “there’s at least one thing in the universe which either (a) isn’t a professor, or (b) if it is a professor, is also human.” Keep in mind: “ ∃ ” and “ ⇒ ” don’t really play well together. To drill this lesson home, realize that you could substitute almost any predicates for Professor () and Human () in that statement and it would still be true. (Try swapping out Professor () for Condiment () and Human () for As- trologicalSign (). Now try x =Euro- peanUnion and voila! the statement is true. The EU is not a condiment, nor is it an astrological sign, so both sides of the implication are false, and never forget: false ⇒ false = true .)"
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