I am trying to read Smullyan A Beginners Guide to Mathematical Logic and there is mentioned under ' Complementation ', page 11/12 that A'' is A itself - so why to bother to mark it with a double apostrophe at all( I hope I am right how this mark is called) if it could be just be written A without any '?

I suspect it is really a silly question - Sorry about that - but I am trying to understand what's the point of it? Any clarification really appreciated!


1 Answer 1


The point is presumably to demonstrate this very property of double negation: for classical logic, complementation involutes (i.e., for every a, a'' is logically equivalent to a).

Note that p and p'' are structurally distinct, even though truth-equivalent. An application of a rule that complementation involutes is "required" to reduce one to the other.

  • Perhaps I will understand it better when reading further - at the moment it is too difficult to understand.
    – Aili J.
    Dec 7, 2016 at 23:04

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