09.14 - [Go around with names] [Collect notes on 1.3] [Hand...

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[Go around with names] [Collect notes on 1.3] [Hand out time sheets] Preparation for section 1.3: Quantifiers Last time we saw that the negation of the proposition “All good people like dogs” is “Some good people dislike dogs” i.e. “At least one good person dislikes dogs”. That is (It is false that) (for every good person X) X likes dogs (There exists a good person X such that) (it is false that) X likes dogs Another example: (It is false that) (some bad people like cats) (All bad people dislike cats) (No bad people like cats).
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So the negation of “Some bad people like cats” is “No bad people like cats”. That is, the negation of “The number of bad people who like cats is greater than zero” is “The number of bad people like cats is zero”. Note that the negation of “Some bad people like cats” is NOT “Some bad people dislike cats”, because both of these propositions might be true. So the correct way to negate is as follows: (It is false that) (there exists a bad person X) X likes cats (For all bad people X) (It is false that) X likes cats Propositions involving 2 quantifiers : The order in which the 2 quantifiers occurs matters! Joke: “Did you know that every day, someone in New York City gets stabbed?” “Poor guy! Why doesn’t he move?” This joke hinges on the ambiguity of quantifiers in ordinary
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language. The first speaker intended the possibly true assertion
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09.14 - [Go around with names] [Collect notes on 1.3] [Hand...

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