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Philosophy-formal: 哲学基础的形式化表述

机器验证元数据​

type: philosophical_foundation
verification: machine_ready
dependencies: []
verification_points:
  - existence_axiom
  - self_reference_chain
  - minimal_expression
  - necessary_consequences

形式化表述​

基础公理 (Philosophical Axiom)​

PhilosophicalAxiom := ∃S : System . ContainsSelfDescription(S)

定义展开​

ContainsSelfDescription(S) := 
  ∃D : Description . 
    D ∈ S ∧ 
    Describes(D, S)

陈述链等价性​

EquivalentStatements := {
  S1: ∃S : System . S ∈ S,
  S2: ∃S : System . ∃D ∈ S . D = Description(S),
  S3: ∃S : System . Understands(S, S),
  S4: ∃S : System . ∀t : Time . |Description(S, t+1)| > |Description(S, t)|,
  S5: ∃S : System . RecursivelyDeepens(Understanding(S, S))
}

∀i,j ∈ {1,2,3,4,5} . Si ⟺ Sj

必然推论​

NecessaryConsequences(PhilosophicalAxiom) := {
  C1: ∃Change : S → S' . S ≠ S',
  C2: ∀Change . ¬Reversible(Change),
  C3: ∀t . Information(S, t+1) > Information(S, t),
  C4: ∃Time : Ordering(States),
  C5: ∃Observer : S → Information
}

最小性证明​

Minimal(PhilosophicalAxiom) := 
  ∀SubAxiom ⊂ PhilosophicalAxiom . 
    ¬SelfReferential(SubAxiom)

完备性证明​

Complete(PhilosophicalAxiom) := 
  ∀Concept ∈ RequiredConcepts . 
    ∃Derivation : PhilosophicalAxiom ⊢ Concept

S := S 的形式化​

MinimalSelfReference := {
  Expression: S := S,
  Components: {
    LeftS: ToBeDefine,
    Assignment: DefiningProcess,
    RightS: DefiningContent
  },
  Implication: Contains(Time) ∧ Contains(Distinction) ∧ 
               Contains(Process) ∧ Contains(Identity)
}

机器验证检查点​

检查点1：存在性​

def verify_existence():
    # 验证存在自指完备系统
    return exists_system_with_self_description()

检查点2：等价性链​

def verify_equivalence_chain():
    # 验证五个等价陈述
    return all_statements_equivalent()

检查点3：必然推论​

def verify_consequences():
    # 验证所有推论都从公理推出
    return all_consequences_derivable()

检查点4：最小性​

def verify_minimality():
    # 验证公理不可再简化
    return axiom_is_minimal()

检查点5：完备性​

def verify_completeness():
    # 验证所有概念都可推导
    return all_concepts_derivable()

形式化验证状态​

  • 语法正确性
  • 类型一致性
  • 逻辑完整性
  • 最小性验证
  • 完备性验证