ScientificParadigmShift
plain-language theorem explainer
The inductive definition enumerates five canonical scientific paradigm shifts and embeds them into the Recognition Science model as upgrades in recognition capacity. Historians and sociologists of science would cite it when formalizing Kuhnian revolutions as J-threshold crossings within the RS framework. It is realized as a finite inductive type deriving decidable equality and finite cardinality.
Claim. The inductive type of scientific paradigm shifts consists of five constructors: Copernican, Newtonian, Einsteinian, quantum, and biological.
background
In the Recognition Science framework, normal science operates with J-cost below the phi threshold while paradigm shifts occur when J-cost exceeds this threshold, triggering a restructuring of the recognition framework. The module maps Kuhn's five canonical shifts (Copernican, Newtonian, Einsteinian, quantum, biological) to configuration dimension D = 5. The inductive type serves as the enumeration of these shifts, with normal science satisfying J < J(φ) and revolutions corresponding to framework upgrades.
proof idea
The declaration is a direct inductive definition introducing five constructors and deriving the instances DecidableEq, Repr, BEq, and Fintype.
why it matters
This definition supplies the base enumeration for the certification of the history of science in RS, feeding directly into the structure HistoryOfScienceCert asserting cardinality exactly 5 and the theorem scientificParadigmShiftCount proving the count by decision. It realizes the mapping of paradigm shifts to configDim D = 5, linking to the broader Recognition Science model where higher J-thresholds correspond to recognition framework upgrades.
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