  Boole noted in Chapter XV of LT that when a premise about \(X\) and \(Y\) is expressed as an equation involving \(x, y\) and \(v\), the symbol \(v\) expressed some, but only in the context in which it appeared in the premise. For example, All \(X\) is \(Y\) has the  expression \(x = vy\), which implies \(vx = vy\).  This could be interpreted as Some \(X\) is \(Y\).  A consequence of \(vx = vy\) is \(v(1-x) = v(1-y)\).  However it was not permitted to read this as Some not-\(X\) is not-\(Y\) since \(v\) did not appear with \(1-x\) or \(1-y\) in the premise.  