Logic / Unit 6 Logic 274 short lesson, about 20 seconds
Overlapping Quantifiers
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The idea
With stacked quantifiers, order changes meaning: (x)(∃y)Lxy — everyone loves someone — versus (∃y)(x)Lxy — someone is loved by everyone.
In practice
The first is romantic comedy; the second is a celebrity.
Where people slip
Mixed-order quantifier swaps are invalid inferences and irresistible temptations. This distinction alone justifies the notation.
Your place on the trail
Every lesson rests on earlier ones and opens later ones. Tap any to jump.
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