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Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

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Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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The following two sentences were devised by the logician Saul Kripke. While not intrinsically paradoxical, they could be paradoxical under certain circumstances. Describe such circumstances.

  1. Most of Nixon’s assertions about Watergate are false.

  • Everything Jones says about Watergate is true.
  • (Hint: Suppose Nixon says (ii) and the only utterance Jones makes about Watergate is (i).)

    To determine

    Most of Nixon’s assertions about Watergate are false.

    Everything Jones says about Watergate is true.

    Explanation

    Given information:

    To describe the circumstances for the above sentences to be paradoxical, assume the following:

    • Mr. N says statement (i) and Mr. J says statement (ii) about Watergate.
    • All other assertions of Mr. N are equally split between true and false. That ¡s, sentence (ii) is either true or false.

    Concept used:

    In general, in the implication, A B(if A then B), A stands for the antecedent, and, B stands for the consequent.

    Calculation:

    Consider the following two sentences:

    (i) Most of Mr. N assertions about Watergate are false.

    (ii) Everything Mr. J says about Watergate is true.

    Note that sentence (ii) is also an assertion about Watergate.

    To describe the circumstances for the above sentences to be paradoxical, assume the following:

    • Mr. N says statement (ii) and Mr. J says statement (i) about Watergate.
    • All other assertions of Mr. N are equally split between true and false. That is, sentence (i) is either true or false

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