 Reading off this diagram requires more than reading off visual containment among circles (as in Euler diagrams) or shadings (as in Venn diagrams), but also requires extra conventions for reading combinations of the symbols ‘o,’ ‘x,’ and lines. Peirce’s new conventions increased the expressive power of single diagrams, but the arbitrariness of its conventions and more confusing representations (for example, the above diagram) sacrificed the visual clarity which Euler’s original system enjoys. At this point, Peirce himself confesses that ‘there is a great complexity in the expression that is essential to the meaning’ (Peirce  1933:  4.365). Thus, when Peirce’s revision was completed, most of Euler’s original ideas about visualization were lost, except that a geometrical object (the circle) is used to represent (possibly empty) sets.