pith. sign in
inductive

CardinalVirtue

definition
show as:
module
IndisputableMonolith.Philosophy.CardinalVirtuesFromConfigDim
domain
Philosophy
line
19 · github
papers citing
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plain-language theorem explainer

The inductive definition introduces the type of five cardinal virtues as an enumeration extending the classical Aristotelian four with practical wisdom to match the configDim = 5 structure in Recognition Science. RS ethicists would cite it when grounding virtue theory in the forced dimension count. The declaration is a direct inductive type with automatically derived decidability and finiteness instances.

Claim. The inductive type of cardinal virtues consists of the five constructors prudence, justice, fortitude, temperance, and practical wisdom.

background

The module sets configDim to 5 to accommodate the five cardinal virtues, extending the classical Aristotelian quartet (prudence, justice, fortitude, temperance) by adding practical wisdom as the integrating fifth element. This matches the D = 5 pattern stated in the module documentation for the Recognition Science view of ethics.

proof idea

The declaration is a direct inductive definition with five constructors and no proof body. It derives the DecidableEq, Repr, BEq, and Fintype instances automatically via the deriving clause.

why it matters

This definition supplies the type used by the downstream theorem cardinalVirtue_count establishing Fintype.card CardinalVirtue = 5 and by the structure CardinalVirtuesCert certifying the five_virtues count together with the four-plus-one decomposition. It grounds the classical virtues in the RS configDim = 5 pattern described in the module documentation.

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