[CG] Re: Differential Propositional Calculus

Differential Propositional Calculus • 12 • https://inquiryintoinquiry.com/2023/11/27/differential-propositional-calcul… All, Special Classes of Propositions (concl.) Last and literally least in extent, we examine the family of singular propositions in a 3‑dimensional universe of discourse. In our model of propositions as mappings from a universe of discourse X to a set of two values, in other words, “indicator functions” of the form f : X → B, singular propositions are those singling out the minimal distinct regions of the universe, represented by single cells of the corresponding venn diagram. Singular Propositions — The singular propositions s : Bⁿ → B may be written as products: • https://inquiryintoinquiry.files.wordpress.com/2020/02/singular-proposition… In a universe of discourse based on three boolean variables, p, q, r, there are 2³ = 8 singular propositions. Their venn diagrams are shown in Figure 10. Figure 10. Singular Propositions on Three Variables • https://inquiryintoinquiry.files.wordpress.com/2020/03/venn-diagrams-e280a2… At the top is the venn diagram for the singular proposition of rank 3, corresponding to the boolean product pqr and identical with the positive proposition of rank 3. Next are the venn diagrams for the three singular propositions of rank 2, which may be expressed by the following three forms, respectively. • pr(q) • qr(p) • pq(r) Next are the three singular propositions of rank 1, which may be expressed by the following three forms, respectively. • q(p)(r) • p(q)(r) • r(p)(q) At the bottom is the singular proposition of rank 0, which may be expressed by the following form. • (p)(q)(r) Regards, Jon cc: https://www.academia.edu/community/L6WJ8l