[CG] Differential Logic • Overview

Differential Logic • Overview • https://inquiryintoinquiry.com/2024/11/25/differential-logic-overview-a/ A reader once told me “venn diagrams are obsolete” and of course we all know how unwieldy they become as our universes of discourse expand beyond four or five dimensions. Indeed, one of the first lessons I learned when I set about implementing Peirce's graphs and Spencer Brown's forms on the computer is that 2‑dimensional representations of logic quickly become death traps on numerous conceptual and computational counts. Still, venn diagrams do us good service at the outset in visualizing the relationships among extensional, functional, and intensional aspects of logic. A facility with those connections is critical to the computational applications and statistical generalizations of propositional logic commonly used in mathematical and empirical practice. All things considered, then, it is useful to make as visible as possible the links between variant styles of imagery in logical representation — and that is what I hoped to do in the sketch of Differential Logic outlined below. Note. I'll give just the links to the main topic heads below. Please follow the link at the top of the page for the full outline. Introduction • https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_1#Introduction Cactus Language for Propositional Logic • https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_1#Cactus_Language_f… Differential Expansions of Propositions • https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_1#Differential_Expa… Propositional Forms on Two Variables • https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_2#Propositional_For… Transforms Expanded over Ordinary and Differential Variables • https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_2#Transforms_Expand… Field Picture • https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_3#Field_Picture Differential Fields • https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_3#Differential_Fiel… Propositions and Tacit Extensions • https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_3#Propositions_and_… Enlargement and Difference Maps • https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_3#Enlargement_and_D… Tangent and Remainder Maps • https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_3#Tangent_and_Remai… 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/546xOz cc: https://www.researchgate.net/post/Differential_Logic_Overview