[CG] Re: Functional Logic • Inquiry and Analogy

Functional Logic • Inquiry and Analogy • 16 • https://inquiryintoinquiry.com/2023/07/13/functional-logic-inquiry-and-anal… Extending the Existential Interpretation to Quantificational Logic • https://oeis.org/wiki/Functional_Logic_%E2%80%A2_Inquiry_and_Analogy#Ex_Qua… All, One of the resources we have for this investigation is a formal calculus based on C.S. Peirce's logical graphs. For now we'll adopt the “existential interpretation” of that calculus, fixing the meanings of logical constants and connectives at the core level of propositional logic. To build on that core we'll need to extend the existential interpretation to encompass the analysis of quantified propositions, or “quantifications”. That in turn will take developing two further capacities of our calculus. On the formal side we'll need to consider higher order functional types, continuing our earlier venture above. In terms of content we'll need to consider new species of “elemental” or “singular“ propositions. Let us return to the 2‑dimensional universe X• = [u, v]. A bridge between propositions and quantifications can be built by defining a foursome of measures or “qualifiers” ℓ_ij : (B × B → B) → B defined by the following equations. Display 1. Qualifiers ℓ_ij • https://inquiryintoinquiry.files.wordpress.com/2022/05/qualifiers-lij-2.0.p… A higher order proposition ℓ_ij : (B × B → B) → B tells us something about the proposition f : B × B → B, specifically, which elements in B × B are assigned a positive value by f. Taken together, the ℓ_ij operators give us a way to express many useful observations about the propositions in X• = [u, v]. Figure 16 summarizes the action of the ℓ_ij operators on the propositions of type f : B × B → B. Figure 16. Higher Order Universe of Discourse [ℓ_00, ℓ_01, ℓ_10, ℓ_11] ⊆ [[u, v]] • https://inquiryintoinquiry.files.wordpress.com/2022/05/venn-diagram-4-dimen… Regards, Jon