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Surprise Quiz Paradox

Surprise Quiz Paradox. A teacher announces “Sometime next week, I am going to give a surprise quiz.” Using deductive reasoning, prove that the following statement is a logical truth. “Once a surprise quiz is announced you cannot give it.”

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Surprise Quiz Paradox

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  1. Surprise Quiz Paradox A teacher announces “Sometime next week, I am going to give a surprise quiz.” Using deductive reasoning, prove that the following statement is a logical truth. “Once a surprise quiz is announced you cannot give it.” Remember, the statement is not claiming that once a quiz is declared a surprise it no longer can be a surprise, it is making the claim that it is no longer possible to give the surprise quiz. Hint: Start with Friday

  2. Surprise Quiz Paradox • The quiz day cannot be Friday because if the quiz were not given on Monday, Tuesday, Wednesday or Thursday then a quiz on Friday would no longer be a surprise. • If a quiz on Friday were not longer possible, then the same rationale for ruling out the Friday quiz would no apply to Thursday. So now, the surprise quiz is not possible for Thursday either. • Apply the same rationale for Thursday to Wednesday and now Wednesday is ruled out. • Apply the same rationale for Wednesday to Tuesday and not Tuesday is ruled out. • Now that the quiz has been ruled out for Friday, Thursday, Wednesday, and Tuesday, the quiz can no longer be a surprise on Monday. Therefore, the surprise quiz cannot be given!

  3. Enthymeme • A syllogism with an implied or missing premise, one that is not explicitly stated. • Derived from the Greek phrase “in the mind” • Example: • “I live in Pittsburgh, so I am probably a Steelers fan.” Missing premise- Most people from Pittsburgh are Steelers fans

  4. Hypothetical Syllogism • A syllogism consisting of wholly or partly hypothetical propositions. They usually take the form of an “if-than” statement. • Informally called “reasoning in a chain” • Example: • If the Penguins win the Stanley Cup, I'll owe my dad some money.If I owe my dad some money, then I'll need to go to the bank.So, if the Penguins win the Stanley Cup, then I'll need to go to the bank.

  5. More on Hypothetical Syllogism • It is important to note that these are hypothetical or conditional statements and not necessarily asserting truth, but instead hypothetical relationships representing chains of cause and effect. • It is also important to note that hypothetical syllogisms only work forward from the antecedent (preceding occurrence, cause, or event) to the conditional (subject to, implying, or dependent upon a condition). They do not work in reverse.

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