Venn diagram with increasing numbers of sides. They are also two-dimensional representations of hypercubes. Henry John Stephen Smith devised similar "n"-set diagrams using sine curves with the series of equations Charles Lutwidge Dodgson (aka Lewis Carroll) devised a five-set diagram known as Carroll's square. Joaquin and Boyles, on the other hand, proposed supplemental rules for the standard Venn diagram in able to account for certain problem cases. For instance, regarding the issue of representing singular statements, they suggest to consider the Venn diagram circle as a representation of a set of things, and use first-order logic and set theory to treat categorical
Campbell Dodgson the War Office; his 1918 CBE was a recognition of this work (DNB, 1941-50 : 216). He was the editor, in the 1920s, of "The Print Collector’s Quarterly". He was also a contributor to the "Burlington Magazine" and to the Dictionary of National Biography. Dodgson married Frances Catherine Spooner, daughter of William Archibald Spooner (Warden of New College and the eponymous author of 'Spoonerisms'), in 1913 (DNB, 1941-50 : 216). Dodgson gave generously to the British Museum during his Keepership, but at the same time amassed a very large collection of over 5,000 prints which he bequeathed to the Museum.