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Give a set of inconsistent sentence with only one member?

  1. May 25, 2006 #1
    Is it possible to give a set of inconsistent sentences with only one member?

    An inconsistent set of senteces requires that it is not possible for all members of that set to be true.
     
  2. jcsd
  3. May 25, 2006 #2

    Hurkyl

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    { false }.
     
  4. May 25, 2006 #3

    honestrosewater

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    In case that isn't clear enough, can the negation of a tautology ever be true? (Such a sentence is called a contradiction, if you want to look up a definition.)

    There is at least one complcation, depending on (i) whether sentences (by your definition) can be simple or complex and (ii) what logic you're working in. In propositional logic, all simple, or atomic, sentences are contingent, i.e., non-tautologous and non-contradictory. This isn't so in, e.g., predicate logic, where you do have atomic tautologies.
     
    Last edited: May 25, 2006
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