Interpretive Duality in Logical Graphs • 3 • https://inquiryintoinquiry.com/2024/04/24/interpretive-duality-in-logical-g… Re: Interpretive Duality in Logical Graphs • https://inquiryintoinquiry.com/2024/04/22/interpretive-duality-in-logical-g… • https://inquiryintoinquiry.com/2024/04/23/interpretive-duality-in-logical-g… All, For a sense of how the choice of interpretation bears on cases beyond the bare minimum complexity let us start with the familiar example of Peirce's law, commonly expressed in the following form. • ((p ⇒ q) ⇒ p) ⇒ p The following two formal equations show how Peirce's law may be expressed in terms of logical graphs, operating under the entitative and existential interpretations, respectively. Peirce's Law • Dual Graphs • https://inquiryintoinquiry.com/wp-content/uploads/2023/11/peirces-law-e280a… Resources — Peirce's Law • https://inquiryintoinquiry.com/2023/10/18/peirces-law-a/ Regards, Jon cc: https://www.academia.edu/community/lPxGaY

Interpretive Duality in Logical Graphs • 5 • https://inquiryintoinquiry.com/2024/04/26/interpretive-duality-in-logical-g… Re: Interpretive Duality in Logical Graphs • 1 • https://inquiryintoinquiry.com/2024/04/22/interpretive-duality-in-logical-g… All, Another way of looking at interpretive duality in logical graphs is given by the following Table, showing how logical graphs denote the sixteen boolean functions on two variables under entitative and existential interpretations, respectively. Logical Graphs • Entitative and Existential Interpretations • https://inquiryintoinquiry.com/wp-content/uploads/2020/11/logical-graphs-e2… Resources — Logic Syllabus • https://inquiryintoinquiry.com/logic-syllabus/ Logical Graphs • First Impressions • https://inquiryintoinquiry.com/2023/08/24/logical-graphs-first-impressions/ Logical Graphs • Formal Development • https://inquiryintoinquiry.com/2023/09/01/logical-graphs-formal-development… Regards, Jon cc: https://www.academia.edu/community/5k8BwN

Interpretive Duality in Logical Graphs • 7 • https://inquiryintoinquiry.com/2024/04/30/interpretive-duality-in-logical-g… Re: Interpretive Duality in Logical Graphs • 2 • https://inquiryintoinquiry.com/2024/04/23/interpretive-duality-in-logical-g… All, Dualities are symmetries of order two and symmetries bear on complexity by reducing its measure in proportion to their order. The inverse relationship between symmetry and the usual dissymmetries from dispersion and diversity to entropy and uncertainty is governed in cybernetics by the Law of Requisite Variety, the medium of which exchange C.S. Peirce invested in his formula: Information = Comprehension × Extension. The duality between entitative and existential interpretations of logical graphs is one example of a mathematical symmetry but it's not unusual to find symmetries within symmetries and it's always rewarding to find them where they exist. To that end let's take up our Table of Venn Diagrams and Logical Graphs on Two Variables and sort the rows to bring together diagrams and graphs having similar shapes. What defines their similarity is the action of a mathematical group whose operations transform the elements of each class among one another but intermingle no dissimilar elements. In the jargon of transformation groups those classes are called “orbits”. We find the sixteen rows partition into seven orbits, as shown below. Venn Diagrams and Logical Graphs on Two Variables • Orbit Order • https://inquiryintoinquiry.com/wp-content/uploads/2020/12/venn-diagrams-and… Resources — Information = Comprehension × Extension • https://oeis.org/wiki/Information_%3D_Comprehension_%C3%97_Extension Regards, Jon cc: https://www.academia.edu/community/LEZn7Y