1

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

Is the disjunction p v -p necessary?

1
  • -p is impossible means necessarily --p, i.e. necessarily p.
    – Era
    Commented Feb 29, 2016 at 19:05

1 Answer 1

1

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.

6
  • Thanks Era for the reply. Subsidiary question: if 'p' is neither necessary, nor impossible. Is p = p v p necessary?
    – user13738
    Commented Feb 29, 2016 at 20:24
  • @student Can you clarify exactly what you mean by p = p v p?
    – Era
    Commented Feb 29, 2016 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
    Commented Feb 29, 2016 at 21:30
  • @student not impossible means possible. p can be possible without being necessary.
    – Era
    Commented Feb 29, 2016 at 21:56
  • So, if p is either not necessary or possible, is p necessary?
    – user13738
    Commented Feb 29, 2016 at 22:32

You must log in to answer this question.