[CG] Re: Differential Propositional Calculus

Differential Propositional Calculus • 31 • https://inquiryintoinquiry.com/2023/12/23/differential-propositional-calcul… Tacit Extensions — Re: Table of Differential Propositions • https://inquiryintoinquiry.files.wordpress.com/2023/12/differential-logic-e… Returning to the Table of Differential Propositions, let's examine how the general concept of a tacit extension applies to the differential extension of a one‑dimensional universe of discourse, where †X† = {A} and †Y† = E†X† = {A, dA}. Each proposition fₖ : X → B has a canonical expression eₖ in the set {0, (A), A, 1}. The tacit extension εfₖ : EX → B may then be expressed as a logical conjunction of two factors, fₖ = eₖ∙τ, where τ is a logical tautology using all the variables of †Y† − †X†. The following Table shows how the tacit extensions εfₖ of the propositions fₖ may be expressed in terms of the extended basis {A, dA}. Table. Tacit Extension of [A] to [A, dA] • https://inquiryintoinquiry.files.wordpress.com/2023/12/differential-logic-e… In its bearing on the singular propositions over a universe of discourse X the above analysis has an interesting interpretation. The tacit extension takes us from thinking about a particular state, like A or (A), to considering the collection of outcomes, the outgoing changes or singular dispositions, springing or stemming from that state. Resources — Differential Logic and Dynamic Systems • https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part… Differential Logic • Tacit Extensions • https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part… Regards, Jon cc: https://www.academia.edu/community/laNmp5