AFFIRMATIVE AND NEGATIVE PROPOSITIONS

Intuitively there may be a difference between asserting that something is the case and ‘merely’ denying that something is the case. But there is no good logical or philosophical way of making the distinction. Modern logic allows that there is frequently an equivalence between positive-looking and negative-looking statements. Whether an assertion comes out positive or negative will depend on the way things are put and upon the menu of terms available: x is not married can be said as x is single; x is not guilty can be said as x is innocent, and so on. Not (p & not-q ) (negative?) is equivalent to p → q (positive?) and not-not-p (negative?) is equivalent to p (positive?).