IndisputableMonolith.Philosophy.ModalOntologyStructure
This module defines the modal ontology of Recognition Science by classifying objects as necessary, possible, actual or impossible according to their status under J-cost minimization and defect. Philosophers and foundational physicists working in the RS framework would cite it to ground modal notions in the Law of Existence. It is a definition module whose content consists of predicates and short uniqueness theorems.
claim$x$ is RS-necessary iff it is the unique $J$-minimizer with defect zero; $x$ is RS-possible iff its $J$-cost is positive and finite; $x$ is RS-actual iff it achieves the global $J$-minimum; $x$ is RS-impossible iff its $J$-cost is non-positive.
background
The module imports LawOfExistence, whose core statement is that an object exists precisely when its defect vanishes, and OntologyPredicates, which treat existence and truth as outcomes of cost minimization under the unique $J$ function. It therefore translates these operational definitions into the classical modal quartet (necessary, possible, actual, impossible) by reference to the same $J$-cost and defect. The setting is the Recognition Science ontology in which all modal status is derivative from the single functional equation that defines $J$.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the modal predicates (RSNecessary and siblings) that embed the Law of Existence into a philosophical ontology. It thereby prepares the ground for any later derivation that must distinguish necessary from contingent structures inside the Recognition Science framework.
scope and limits
- Does not derive any physical constants or spatial dimensions.
- Does not prove the existence of concrete objects or particles.
- Does not address interpretations of quantum mechanics or measurement.
- Does not contain theorems about the forcing chain T0-T8.
depends on (2)
declarations in this module (21)
-
def
RSNecessary -
def
RSPossible -
def
RSActual -
def
RSImpossible -
theorem
necessity_is_unique_minimizer -
theorem
necessary_is_one -
theorem
possibility_is_positive_ratio -
theorem
possible_has_finite_cost -
theorem
possibility_is_not_singleton -
theorem
actuality_is_j_minimum -
theorem
actuality_is_unique -
theorem
impossible_is_non_positive -
theorem
possible_not_impossible -
theorem
s5_necessity_implies_actuality -
theorem
s5_actuality_implies_possibility -
theorem
s5_possible_accessible_to_necessary -
def
modalDistance -
theorem
modal_distance_nonneg -
theorem
modal_distance_zero_iff_actual -
theorem
actual_has_zero_modal_distance -
theorem
ph013_modal_certificate