The duality between Entitative and Existential interpretations of logical graphs is a good example of a mathematical symmetry, in this case a symmetry of order two. Symmetries of this and higher orders give us conceptual handles on excess complexity in the manifold of sensuous impressions, making it well worth the effort to seek them out and grasp them where we find them.
Both Peirce and Spencer Brown understood the significance of the mathematical unity underlying the dual interpretation of logical graphs. Peirce began with the Entitative option and later switched to the Existential choice while Spencer Brown exercised the Entitative option in his Laws of Form.
In that vein, here’s a Rosetta Stone to give us a grounding in the relationship between boolean functions and our two readings of logical graphs.
cc: FB | Logical Graphs • Laws of Form • Mathstodon • Academia.edu
cc: Conceptual Graphs • Cybernetics • Structural Modeling • Systems Science
is clear enough on general principles, since 
holds for any proposition 
being false while its antecedent 
is true. If this is true, either its consequent, 
is true, when the whole formula would be true, or its antecedent 
is false. But in the last case the antecedent of 
that is 
is used in such a sense that 
means that from 
every proposition follows. With that understanding, the formula states the principle of excluded middle, that from the falsity of the denial of 
(Peirce, CP 3.384).
for implication. In one place he explains 
for less than or equal to; in another place he suggests that 
is an iconic way of representing a state of affairs where 
in every way that it can be, is 
Inquiry Into Inquiry 