Transforms Expanded over Ordinary and Differential Variables

As promised in Episode 10, 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 and act on that set.  There being some advantage to singling out the enlargement or shift operator in its own right, we’ll begin by computing for each of the functions

Enlargement Map Expanded over Ordinary Variables

We first encountered the shift operator in Episode 4 when we imagined being in a state described by the proposition and contemplated the value of that proposition in various other states, as determined by the differential propositions and   Those thoughts led us from the boolean function of two variables to the boolean function of four variables as shown in the entry for in the first three columns of Table A3.  (Let’s catch a breath here and discuss what the rest of the Table shows next time.)

cc: Category Theory • Cybernetics • Ontolog • Structural Modeling • Systems Science
cc: FB | Differential Logic • Laws of Form • Peirce (1) (2) (3) (4)