  The diagnosis of the paradoxes of implication as failures of respect for sufficiency leads naturally to an alternative path to their resolution, of a piece with Sylvan’s concerns about universality. On this view, the paradoxes of implication are symptoms of taking too few possibilities into account. One may think of classical material implication as taking only one situation into account, giving rise to theorems like ‘if \(p\) then \(q\), or if \(q\) then \(p\)’, since either \(p\) is true (in which case, \(p\) or \(\twiddle q\) is true, and so q materially implies \(p\)) or else \(p\) is false (in which case, \(\twiddle p\) or \(q\) is true, and so \(p\) materially implies \(q\)). This is immediately resolved upon consideration of two possibilities, \(w_0\) and \(w_1\),