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LLM generated Marx theories in formulas.

Marxist Theory Formalization

Marxist Theory Formalization

Primitive Sets and Functions

π’œ: Set of all agents (individuals)
π’ž: Set of all social classes
β„³: Set of all modes of production
β„›: Set of all economic resources
𝒯: Ordered set of time periods, 𝒯 ⊂ β„€⁺
m(t) ∈ β„³: Mode of production at time t
Class(a, c, t): Agent a ∈ π’œ belongs to class c ∈ π’ž at time t
Owns(c, r, t): Class c ∈ π’ž owns resource r ∈ β„› at time t

Economic Base and Superstructure

B(t): Economic base at time t
B(t) = (m(t), OWNERSHIP(t))
S(t): Superstructure at time t
S(t) = f(B(t))

Class Definitions

Bourgeoisie(c, t) := (m(t) = Capitalism) ∧ (∀r ∈ β„›mp, Owns(c, r, t))

Proletariat(c, t) := (m(t) = Capitalism) ∧ (∀a ∈ π’œ, Class(a, c, t) ⇒ ¬∃r ∈ β„›mp, Owns(a, r, t))

Labor Theory of Value and Exploitation

L(r, t) ∈ ℝ⁺: Socially necessary labor time
V(r, t) ∈ ℝ⁺: Value of resource r at time t
V(r, t) = L(r, t)

W(a, t) ∈ ℝ⁺: Wage paid to worker a
Lcreated(a, t) ∈ ℝ⁺: Value created by worker a
s(a, t) = Lcreated(a, t) - W(a, t)
St = ∑a ∈ π’œw s(a, t)

Capitalist Accumulation and Immiseration

K(c, t) ∈ ℝ⁺: Capital owned by class c at time t
∀t′ > t, K(cb, t′) > K(cb, t)

∀t′ > t, ∑a ∈ π’œcp W(a, t′) ≤ ∑a ∈ π’œcp W(a, t)

Class Consciousness and Revolution

CC(c, t) ∈ {0, 1}: Class consciousness
CC(cp, t) = F(B(t), St)

Crisis(t) ∈ {0, 1}: Economic crisis at time t
Rev(t) := (m(t) = Capitalism) ∧ CC(cp, t) = 1 ∧ Crisis(t) = 1

Rev(t) ⇒ (m(t+1) = Socialism) ∧ (S(t+1) = f(B(t+1))) ∧ (B(t+1) ⇒ cp)

(m(t) = Socialism) ∧ (ClassAntagonism(t) ≈ 0) ⇒ ∃Ξ”t > 0, m(t+Ξ”t) = Communism

Mathematical Proof of Logical Consistency

1. Capitalist Accumulation: limt→∞ K(cb, t) = ∞
2. Immiseration: limt→∞ St = ∞
3. Class Consciousness: ∃t1 ∈ 𝒯, ∀t ≥ t1, CC(cp, t) = 1
4. Economic Crises: ∃t2 ≥ t1, Crisis(t2) = 1
5. Revolution: Rev(t2) = 1
6. Transition to Socialism: m(t2 + 1) = Socialism
7. Transition to Communism: ∃t3 > t2 + 1, ClassAntagonism(t3) ≈ 0 ⇒ m(t3) = Communism
Note: This is a proof of logical consistency within the Marxist framework, not empirical verification.

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