[CG] Re: Differential Propositional Calculus

Differential Propositional Calculus • 8 • https://inquiryintoinquiry.com/2023/11/23/differential-propositional-calcul… All, Formal Development (cont.) Before moving on, let's unpack some of the assumptions, conventions, and implications involved in the array of concepts and notations introduced above. A universe of discourse A• = [a_1, ..., a_n] qualified by the logical features a_1, ..., a_n is a set A plus the set of all functions from the space A to the boolean domain B = {0, 1}. There are 2ⁿ elements in A, often pictured as the cells of a venn diagram or the nodes of a hypercube. There are 2^(2ⁿ) possible functions from A to B, accordingly pictured as all the ways of painting the cells of a venn diagram or the nodes of a hypercube with a palette of two colors. A logical proposition about the elements of A is either true or false of each element in A, while a function f : A → B evaluates to 1 or 0 on each element of A. The analogy between logical propositions and boolean-valued functions is close enough to adopt the latter as models of the former and simply refer to the functions f : A → B as propositions about the elements of A. Resources — Logic Syllabus • https://inquiryintoinquiry.com/logic-syllabus/ Differential Logic and Dynamic Systems • https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part… Functional Conception of Propositional Calculus • https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part… Qualitative Logic and Quantitative Analogy • https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part… Formal Terms and Flexible Types • https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part… Regards, Jon cc: https://www.academia.edu/community/ldJmKV