Let:
    •    O(x, r) = x has rightful ownership of r
    •    H(x, r) = x homesteaded r
    •    T(x, y, r) = x transferred r to y voluntarily
    •    C(x, y, r) = x coerces y regarding r
    •    J(x) = x is just
    •    S(x, r) = x has  possession/control over resource r

    •    NAP = Initiatory coercion against rightful owners is unjust
    •    E = exchange
    •    M = monetary system
    •    I = institutional/legal-monetary framework
    •    A = act of argumentation
    •    P = performative presupposition

Axiom L1 (Self-ownership)
∀x : O(x, bodyₓ)

Axiom L2 (Homesteading)
∀x∀r : H(x, r) ∧ ¬∃y O(y, r) → O(x, r)

Axiom L3 (Transfer)
∀x∀y∀r : O(x, r) ∧ T(x, y, r) → O(y, r)

Axiom L4 (NAP)
∀x∀y∀r : O(y, r) ∧ C(x, y, r) → ¬J(x)

Axiom L5 (Just coercion)
∀x∀y∀r : O(x, r) ∧ S(y, r) ∧ ¬T(x, y, r) → C(x, y, r) is just

III. Ownership vs Possession

Premise 1
S(x, r) ≠ O(x, r)

Premise 2
Ownership is normative; possession is factual.

Conclusion 1
Control alone is insufficient for ownership.
(Formally: ∃x,r : S(x, r) ∧ ¬O(x, r))

⸻

IV. Taxation as Ownership Recovery (State Argument)

State Claim SC
    
The state originates money → Orig(state, M)
The state controls money → S(state, M)
Therefore, the state owns money → O(state, M)
Taxation = recovery of owned property → just coercion

Libertarian Rebuttal LR
    •    Reject (3): Origination + control ≠ homesteading
    •    Printing ≠ homesteading of exchanged value
    •    Therefore taxation ≠ recovery but seizure

Conclusion 2 (Libertarian)
Taxation = initiatory coercion → unjust
V. Coercion Clarification (User’s Corrective)

Premise 3 (Agreed)
Coercion is not unjust per se; only unjust when initiatory.

Premise 4
If O(x, r) then coercion to recover r is just.

Conclusion 3
The moral status of taxation depends entirely on prior ownership.

⸻

VI. Exchange and Intersubjective Value Argument

Premise 5
What is exchanged is not physical tokens alone but recognized value.

Premise 6
Recognized value presupposes enforceable property titles.

Premise 7
Enforceable titles presuppose an institutional framework I.

Premise 8
I is monopolized and coercively enforced by the state.

Conclusion 4
Exchange presupposes state-created institutional conditions.
VII. Libertarian Escape: “Institutions Are Not Ownable”

Libertarian Claim LC
    
Only scarce rivalrous resources are ownable.
Institutions, norms, relations are non-scarce.
Therefore, I cannot be homesteaded or owned.
Therefore, the state has no ownership claim over exchange.

⸻

VIII. Scarcity Reintroduction (Pressure Point)

Premise 9
Access to courts, settlement, legal recognition, final discharge is:
    •    rivalrous
    •    excludable
    •    territorially bounded

Premise 10
Scarce + excludable → property-relevant under libertarian theory.

Conclusion 5
At least parts of I meet libertarian criteria for ownability.

Contradiction 1
Libertarians treat all other scarce infrastructures as ownable
but deny this only for institutional infrastructure.
IX. Voluntariness and Monetary Choice

Libertarian Claim VC
    •    Use of state money is voluntary
    •    Alternatives (gold, foreign currency, crypto) exist

Premise 11
Taxes must be discharged in state currency.

Premise 12
Large-scale contracts, courts, accounting, wages are denominated in it.

Premise 13
Refusal imposes systematic penalties.

Conclusion 6
Participation is not meaningfully voluntary.

⸻

X. Performative Contradiction (Core Result)

Hoppean Premise HP
    
Argumentation presupposes control over scarce means.
Denying such control while arguing is a performative contradiction.

Extended Premise EP
    
Argumentation also presupposes:
•    Stable legal order
•    Monetary economy
•    Enforced suspension of violence
•    Institutional standing

Premise 14
These presuppositions are provided by I.

Premise 15
Libertarians deny I can be owned or legitimately funded.

Conclusion 7 (Performative Contradiction)

Libertarians:
    •    Presuppose I in the act of argumentation
    •    Deny its legitimacy in theory

Formally:

P(A → I)
¬Legitimate(I)
∴ Performative contradiction
XI. Exhaustive Trilemma

At least one must be false:
    
Argumentation ethics fully grounds libertarian property norms
Exchange and argumentation presuppose only privately owned resources
Institutional-monetary frameworks are non-ownable
Participation in them is voluntary

They cannot all be true simultaneously.

⸻

XII. Final Syllogism (Compressed)

Syllogism
    
All justified coercion depends on prior ownership
Ownership presupposes enforceable institutions
Enforceable institutions are coercively monopolized
Libertarians deny those institutions can be owned or funded
Yet libertarians presuppose them in argument and exchange

Therefore:
Libertarianism relies on conditions it cannot justify within its own first principles.