[CG] Re: Differential Logic

Differential Logic • 11 • https://inquiryintoinquiry.com/2024/11/10/differential-logic-11-a/ Transforms Expanded over Ordinary and Differential Variables — As promised last time, in the next several posts we'll extend our scope to the full set of boolean functions on two variables and examine how the differential operators E and D act on that set. There being some advantage to singling out the enlargement or shift operator E in its own right, we'll begin by computing Ef for each of the functions f : B×B → B. Enlargement Map Expanded over Ordinary Variables — We first encountered the shift operator when we imagined ourselves being in a state described by the truth of a certain proposition and contemplated the value of that proposition in various other states, as determined by a collection of differential propositions describing the steps we might take to change our state. Restated in terms of our initial example, we imagined ourselves being in a state described by the truth of the proposition pq and contemplated the value of that proposition in various other states, as determined by the differential propositions dp and dq describing the steps we might take to change our state. Those thoughts led us from the boolean function of two variables f₈(p, q) = pq to the boolean function of four variables Ef₈(p, q, dp, dq) = (p , dp)(q , dq), as shown in the entry for f₈ in the first three columns of Table A3. Table A3. Ef Expanded over Ordinary Variables {p, q} • https://inquiryintoinquiry.files.wordpress.com/2020/04/ef-expanded-over-ord… Let's catch a breath here and discuss the full Table next time. 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/5AqoEK cc: https://www.researchgate.net/post/Differential_Logic_The_Logic_of_Change_an…