If exegesis raised a hermeneutic problem, that is, a problem of interpretation, it is because every reading of a text always takes place within a community, a tradition, or a living current of thought, all of which display presuppositions and exigencies — regardless of how closely a reading may be tied to the quid, to “that in view of which” the text was written.

Paul Ricoeur • The Conflict of Interpretations

If a picture is worth a thousand words, here’s my 48,000 words worth on the recurring question of logical graphs, their iconicity, and their interpretation, at least as concerns Peirce’s alpha graphs interpreted for propositional logic.  A few more actual words, literally speaking, may be called for.  I’ll return to that anon.

Referring to the Table —

• Column 1 shows a conventional name and a venn diagram for each of the sixteen boolean functions on two variables.
• Column 2 shows the logical graph canonically representing the boolean function in Column 1 under the entitative interpretation.  This is the interpretation C.S. Peirce used in his earlier work on entitative graphs and the one Spencer Brown used in his book Laws of Form.
• Column 3 shows the logical graph canonically representing the boolean function in Column 1 under the existential interpretation.  This is the interpretation C.S. Peirce used in his later work on existential graphs.

Resources

• Logic Syllabus
• Logical Graphs
• Cactus Language
• Duality Indicating Unity
• Futures Of Logical Graphs
• Minimal Negation Operators
• Survey of Theme One Program
• Survey of Animated Logical Graphs
• Propositional Equation Reasoning Systems
• Applications • Constraint Satisfaction Problems

cc: Cybernetics • Ontolog Forum • Structural Modeling • Systems Science
cc: FB | Logical Graphs • Laws of Form • Peirce List