IndisputableMonolith.Ethics.VirtueComposition
The VirtueComposition module defines algebraic operations for combining virtues and their effects within the Ethics domain of Recognition Science. It introduces compose along with specific instances for love and justice, then establishes that compositions preserve sigma and are associative. Researchers extending the Recognition framework to ethical modeling would cite these results when analyzing virtue interactions. The module consists of targeted definitions followed by direct proofs of the preservation and associativity properties.
claimThe module defines a composition operation $compose(v_1, v_2)$ on virtues such that $composed_virtues_preserve_sigma(compose(v_1, v_2))$ holds, the operation is associative, and the special case $love_composed_with_justice$ satisfies the corresponding effect equations, with auxiliary definitions for $loveEffect$ and $justiceEffect$.
background
In the Ethics domain the module models virtues as operators that induce changes tracked by a state quantity sigma. VirtueEffect captures the state modification produced by a single virtue while compose supplies the binary merging operation. The setting treats sigma as an invariant under composition, mirroring the preservation of key quantities in the broader Recognition framework though without direct appeal to the T0-T8 forcing chain or phi-ladder. The single import from Mathlib supplies the algebraic scaffolding required for the stated properties.
proof idea
The module first introduces the core definitions VirtueEffect, loveEffect, justiceEffect and the compose function. It then states the theorems composed_virtues_preserve_sigma, love_composed_with_justice and virtue_composition_associative. Each proof unfolds the relevant definitions and applies elementary properties supplied by the Mathlib import.
why it matters in Recognition Science
VirtueComposition supplies the compositional tools that enable higher-level ethical constructions inside the Recognition Science monolith. It fills the role of guaranteeing invariant preservation and associativity for virtue combinations, thereby supporting any subsequent development of ethical recognition models. No explicit parent theorem is listed among the current dependencies, yet the module closes the basic algebraic layer for virtue ethics.
scope and limits
- Does not derive virtues from the J-uniqueness or phi fixed-point constructions of the physics chain.
- Does not assign numerical values to effects or connect them to constants such as G or alpha.
- Does not treat conflicts between virtues or non-associative compositions.
- Does not include empirical validation or links to physical observations.