Suppose the sentence p is possible, and -p is impossible.

Is the disjunction p v -p necessary?

  • -p is impossible means necessarily --p, i.e. necessarily p. – Era Feb 29 '16 at 19:05

Formal tautologies are always logically necessary. Standard FOL has p v -p as a formal tautology, hence it is necessary regardless of whether p is necessary or possible. This breaks down if you consider alternative logics that don't have the Law of Excluded Middle as a tautology.

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  • Thanks Era for the reply. Subsidiary question: if 'p' is neither necessary, nor impossible. Is p = p v p necessary? – user13738 Feb 29 '16 at 20:24
  • @student Can you clarify exactly what you mean by p = p v p? – Era Feb 29 '16 at 20:42
  • OK, let's say that, on one hand, p is not necessary, and, on the other hand, p is not impossible. Is p necessary too? – user13738 Feb 29 '16 at 21:30
  • @student not impossible means possible. p can be possible without being necessary. – Era Feb 29 '16 at 21:56
  • So, if p is either not necessary or possible, is p necessary? – user13738 Feb 29 '16 at 22:32

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