Category Archives: C.S. Peirce

Differential Expansions of Propositions Panoptic View • Difference Maps In the previous post we computed what is variously described as the difference map, the difference proposition, or the local proposition of the proposition at the point where and In the … Continue reading →

Differential Expansions of Propositions Worm’s Eye View Let’s run through the initial example again, keeping an eye on the meanings of the formulas which develop along the way.  We begin with a proposition or a boolean function whose venn diagram … Continue reading →

Differential Expansions of Propositions Bird’s Eye View An efficient calculus for the realm of logic represented by boolean functions and elementary propositions makes it feasible to compute the finite differences and the differentials of those functions and propositions. For example, … Continue reading →

Cactus Language for Propositional Logic (cont.) Table 1 shows the cactus graphs, the corresponding cactus expressions, their logical meanings under the so‑called existential interpretation, and their translations into conventional notations for a sample of basic propositional forms. Table 1. Syntax … Continue reading →

Cactus Language for Propositional Logic The development of differential logic is facilitated by having a moderately efficient calculus in place at the level of boolean‑valued functions and elementary logical propositions.  One very efficient calculus on both conceptual and computational grounds … Continue reading →

Introduction Differential logic is the component of logic whose object is the description of variation — focusing on the aspects of change, difference, distribution, and diversity — in universes of discourse subject to logical description.  A definition that broad naturally … Continue reading →