IndisputableMonolith.Foundation.UniversalForcing.MetaphysicalRealization

   1import IndisputableMonolith.Foundation.UniversalForcing.BiologyRealization
   2
   3/-!
   4  MetaphysicalRealization.lean
   5
   6  Structural, theology-neutral formalization of the metaphysical question from
   7  the Universal Forcing paper: if all realizations have canonically equivalent
   8  forced arithmetic, then the "source of distinguishability" is represented
   9  mathematically by the universal generator class.
  10
  11  This module does not identify that source with any specific theological or
  12  philosophical doctrine. It only makes the structural question precise.
  13-/
  14
  15namespace IndisputableMonolith
  16namespace Foundation
  17namespace UniversalForcing
  18namespace MetaphysicalRealization
  19
  20open Invariance.Universal
  21
  22/-- A metaphysical ground is a structural principle assigning every
  23Law-of-Logic realization its forced arithmetic, with the guarantee that these
  24arithmetic objects are canonically the same. -/
  25structure MetaphysicalGround where
  26  sourceName : String
  27  identifies_arithmetic :
  28    ∀ R : LogicRealization, (arithmeticOf R).peano.carrier ≃ ArithmeticFromLogic.LogicNat
  29  invariant :
  30    ∀ R S : LogicRealization, (arithmeticOf R).peano.carrier ≃ (arithmeticOf S).peano.carrier
  31
  32/-- The universal forcing theorem supplies a canonical metaphysical-ground
  33structure in the neutral, structural sense. -/
  34noncomputable def universalGround : MetaphysicalGround where
  35  sourceName := "Universal generator of distinguishability"
  36  identifies_arithmetic := fun R => R.orbitEquivLogicNat
  37  invariant := fun R S => ArithmeticOf.equivOfInitial (arithmeticOf R) (arithmeticOf S)
  38
  39/-- The metaphysical-ground identification is unique up to the same canonical
  40arithmetic equivalence supplied by Universal Forcing. -/
  41noncomputable def metaphysical_ground_unique (R : LogicRealization) :
  42    (arithmeticOf R).peano.carrier ≃ ArithmeticFromLogic.LogicNat :=
  43  R.orbitEquivLogicNat
  44
  45end MetaphysicalRealization
  46end UniversalForcing
  47end Foundation
  48end IndisputableMonolith
  49