[CG] Re: Differential Propositional Calculus

Differential Propositional Calculus • 8 • https://inquiryintoinquiry.com/2024/12/07/differential-propositional-calcul… 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° = [a₁, …, aₙ] qualified by the logical features a₁, …, aₙ 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/ Survey of Differential Logic • https://inquiryintoinquiry.com/2024/02/25/survey-of-differential-logic-7 Regards, Jon cc: https://www.academia.edu/community/LxkZen cc: https://www.researchgate.net/post/Differential_Propositional_Calculus