Jin Yuelin’s Simplification of Venn Diagrams

Chinese logician and philosopher Jin Yuelin published in 1935 a textbook Logic (in Chinese) in which he proposed proving the distributive laws by a slightly non-standard version of Venn diagrams. In Jin Yuelin’s modification some segments of the circles are marked with dashed instead of continuous lines, namely those that following the meet and join operations encircle the regions outside of the meet regions, as well as those that encircle the regions inside of the join regions. Hence the validity of distribution of meets over joins in the first distributive law and joins over meets in the second is observed by the sameness of the diagrams with exactly the same dashed and continuous line segments. This slight modification removes the need for shading empty regions and liberates one from using the cross mark “x” or some other ‘non-visuals’ for existence while freeing shading for some other uses (as e.g. opined by Venn and Peirce) and reducing clutter. In addition to such implications to the theory of Venn diagrams, we expose this little-known detail from the history of Venn diagrams and assess the factors that contributed to its discovery, such as whether Jin Yuelin decided to apply the dashed line following his reading of Peirce’s broken-cut notations.