It will be seen that "all is " and "no is " do not really differ in form, except by the substitution of not- for , and that the same applies to "some is " and "some is not ." It should also be observed that the traditional rules of conversion are faulty, if we adopt the view, which is the only technically tolerable one, that such propositions as "all is " do not involve the "existence" of 's, i.e. do not require that there should be terms which are 's. The above definitions lead to the result that, if is always false, i.e. if there are no 's, then "all is " and "no is " will both be true, whatever [Pg 163] may be. For, according to the definition in the last chapter, " implies " means "not- or " which is always true if not- is always true. At the first moment, this result might lead the reader to desire different definitions, but a little practical experience soon shows that any different definitions would be inconvenient and would conceal the important ideas. The proposition " always implies , and is sometimes true" is essentially composite, and it would be very awkward to give this as the definition of "all is ," for then we should have no language left for " always implies ," which is needed a hundred times for once that the other is needed. But, with our definitions, "all is " does not imply "some is ," since the first allows the non-existence of and the second does not; thus conversion per accidens becomes invalid, and some moods of the syllogism are fallacious, e.g. Darapti: "All is , all is , therefore some is ," which fails if there is no .