Logic / Logic 274 · Atom · ~20 seconds
Overlapping Quantifiers
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State
With stacked quantifiers, order changes meaning: (x)(∃y)Lxy — everyone loves someone — versus (∃y)(x)Lxy — someone is loved by everyone.
Show
The first is romantic comedy; the second is a celebrity.
Watch for
Mixed-order quantifier swaps are invalid inferences and irresistible temptations. This distinction alone justifies the notation.