[CG] Re: Logical Graphs • Interpretive Duality

Logical Graphs • Interpretive Duality 4 • https://inquiryintoinquiry.com/2023/11/08/logical-graphs-interpretive-duali… Re: Peirce's Law • https://inquiryintoinquiry.com/2023/10/18/peirces-law-a/ All, Last time we took up Peirce's law, ((p ⇒ q) ⇒ p) ⇒ p, and saw how it might be expressed in two different ways, under the entitative and existential interpretations, respectively. The next thing to do is see how our choice of interpretation bears on the patterns of proof we might find. To that purpose the following table shows a pair of proofs, one of each kind, in parallel array. Peirce's Law • Parallel Proofs • https://inquiryintoinquiry.files.wordpress.com/2023/11/peirces-law-e280a2-p… For convenience, the formal axioms and a few theorems of frequent use are linked below. Axiom I₁ • Condense/Protract • https://inquiryintoinquiry.files.wordpress.com/2023/09/logical-graph-axiom-… Axiom I₂ • Cancel/Elicit • https://inquiryintoinquiry.files.wordpress.com/2023/09/logical-graph-axiom-… Axiom J₁ • Delete/Insert • https://inquiryintoinquiry.files.wordpress.com/2023/09/logical-graph-axiom-… Axiom J₂ • Collect/Distribute • https://inquiryintoinquiry.files.wordpress.com/2023/09/logical-graph-axiom-… C₁ Double Negation Theorem • Reflect/Reflect • https://inquiryintoinquiry.files.wordpress.com/2021/02/double-negation-3.0.… C₂ Generation Theorem • Regenerate/Degenerate • https://inquiryintoinquiry.files.wordpress.com/2010/04/logicalgraphfigure27… C₃ Dominant Form Theorem • Quit/Quip • https://inquiryintoinquiry.files.wordpress.com/2010/04/logicalgraphfigure29… Resource — Logical Graphs • Formal Development • https://inquiryintoinquiry.com/2023/09/01/logical-graphs-formal-development… Regards, Jon cc: https://www.academia.edu/community/VrmWr5