Logical Graphs, Iconicity, Interpretation • 1

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 f_{i} 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.

\text{Boolean Functions and Logical Graphs on Two Variables}

Boolean Functions and Logical Graphs on Two Variables

Resources

cc: CyberneticsOntolog ForumStructural ModelingSystems Science
cc: FB | Logical GraphsLaws of FormPeirce List

This entry was posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Constraint Satisfaction Problems, Deduction, Diagrammatic Reasoning, Duality, Equational Inference, Graph Theory, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Model Theory, Painted Cacti, Peirce, Proof Theory, Propositional Calculus, Propositional Equation Reasoning Systems, Spencer Brown, Theorem Proving, Visualization and tagged , , , , , , , , , , , , , , , , , , , , , , , , , . Bookmark the permalink.

3 Responses to Logical Graphs, Iconicity, Interpretation • 1

  1. Pingback: Logical Graphs, Iconicity, Interpretation • 2 | Inquiry Into Inquiry

  2. Pingback: Survey of Animated Logical Graphs • 4 | Inquiry Into Inquiry

  3. Pingback: Logical Graphs, Iconicity, Interpretation • Discussion 1 | Inquiry Into Inquiry

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