Abelard also points out that subcontraries containing subject terms denoting nothing, such as 'a man who is a stone', are both false. Terence Parsons argues that ancient philosophers did not experience the problem of existential import as only the A and I forms had existential import. He goes on to cite medieval philosopher William of Moerbeke  And points to Boethius' translation of Aristotle's work as giving rise to the mistaken notion that the O form has existential import. In the 19th century, George Boole argued for requiring existential import on both terms in particular claims (I and O), but allowing all terms of universal claims (A and E) to lack existential import. This decision made Venn diagrams particularly easy to use for term logic. The square of opposition, under this Boolean set of assumptions, is often called the modern Square of opposition. In the modern square of opposition, A and O claims are contradictories, as are E and I, but all other forms of opposition cease to hold; there are no contraries, subcontraries, or subalterns. Thus, from a modern point of view, it often makes sense to talk about 'the' opposition of a claim, rather than insisting as older logicians did that a claim has several different opposites, which are in different kinds of opposition with the claim. Gottlob Frege's "Begriffsschrift" also presents a square of oppositions, organised in an almost identical manner to the classical square, showing the contradictories, subalternates and contraries between four formulae constructed from universal quantification, negation and implication. Algirdas Julien Greimas' semiotic square was derived from Aristotle's work. The traditional square of opposition is now often compared with squares based on inner- and outer-negation. The square of opposition has been extended to a logical hexagon which includes the relationships of six statements. It was discovered independently by both Augustin Sesmat and Robert Blanché. It has been proven that both the square and the hexagon, followed by a "logical cube", belong to a regular series of n-dimensional objects called "logical bi-simplexes of dimension n." The pattern also goes even beyond this. The logical square, also called square of opposition or square of Apuleius has its origin in the four marked sentences to be employed in syllogistic reasoning: Every man is bad, the universal affirmative and its negation Not every man is bad (or Some men are not bad), the particular negative on the one hand, Some men are bad, the particular affirmative and its negation No man is bad, the universal negative on the other.