Tuesday, December 9, 2025

Libertarianism via purposes ontology

This is an idea that I was thinking about in this X/Twitter conversation (see comments there for amendments; in particular, “permanent engagement” was implausible, and unnecessary for the desired conclusions).

Consider the possibility of founding libertarian private property theory on an ontology of “purposes”. The structure of a purpose is, “agent S intends to do P with objects O₁, O₂, O₃, ... Oₙ at time T.” Purposes can be stated, and can be demonstrated in action. At every time T, every agent demonstrates-in-action some purpose with his own body. An object that has had a purpose demonstrated-in-action with it becomes “engaged” in action. The foundation of private property is simply the attempt to avoid “action conflicts”, which are attempts to use an object for conflicting purposes. Hence, once a previously unengaged object has been engaged, it remains engaged with the same agent until explicitly disengaged; this is original acquisition. Contracts are formalized statements of purpose which, by convention, also demonstrate purpose in action. Attempt to formalize this.

Let’s build a skeletal formal theory around your “purposes” idea and show how private property drops out of it.

I’ll use fairly simple, typed first-order logic with time and events.

1. Ontology

We assume:

  • A nonempty set of agents: A
  • A nonempty set of objects: O
  • A linearly ordered set of times: T with order <
  • A set of purposes (plans, action-types): P

We also assume each agent has a distinguished body-object:

  • body : A → O
    (read: body(s) is the object that is s’s body)

We treat bodies as just special objects in O, but they’ll get special axioms.

2. Purposes and actions

Your slogan:

“Agent S intends to do P with objects O₁…Oₙ at time T.”

We formalize two main predicates:

  • Intend(s, p, X, t)
    = at time t, agent s intends to realize purpose p using finite set of objects X ⊆ O.

  • Act(s, p, X, t)
    = at time t, agent s actually demonstrates in action purpose p with the objects in X.

You wanted: at every time, each agent is demonstrating some purpose with their own body:

  • Axiom (Continuous bodily action)
    ∀s ∈ A ∀t ∈ T ∃p ∈ P ∃X ⊆ O
    body(s) ∈ X ∧ Act(s, p, X, t)

So every agent is always doing something with their body, even if it’s just “remain seated”, “observe”, etc.

We don’t reduce intention to action here. We only assume a weak connection:

  • Axiom (No action without relevant intention)
    Act(s, p, X, t) → Intend(s, p, X, t)

3. “Engagement” of objects in action

Now we introduce the key relation:

  • Engaged(s, o, t)
    = at time t, object o is engaged in the ongoing activity of agent s.

This is the “property carrier” in your story.

3.1. Self-engagement of bodies

We encode self-ownership as permanent engagement of each agent with their body:

  • Axiom (Self-ownership as permanent engagement)
    ∀s ∈ A ∀t ∈ T: Engaged(s, body(s), t)
    and
    ∀s≠s' ∀t: ¬Engaged(s', body(s), t)

So: each body is always and only engaged by its owner.

3.2. Original engagement (“homesteading”)

Your rule: when an agent first uses a previously unengaged object for some purpose, that object becomes engaged to that agent.

We need a notion of “previously unengaged” at a time immediately before t. To keep it simple, use:

  • Unengaged(o, t) := ¬∃s Engaged(s, o, t)

We also need a “just before t” operator. Instead of building full temporal logic, we can use a schematic “earlier than t” condition:

“Previously unengaged” = unengaged at all times earlier than t.

  • Unengaged_before(o, t) := ∀t' < t ¬∃s Engaged(s, o, t')

Then:

  • Axiom (Original engagement / acquisition)
    For all s, o, t, p, X:
    If Act(s, p, X, t) ∧ o ∈ X ∧ Unengaged_before(o, t),
    then Engaged(s, o, t).

Intuition: the first agent to actually do something with the object brings it under their engagement.

3.3. Persistence of engagement

Your principle: once engaged, the object stays engaged with that agent until explicitly disengaged.

We add a special kind of action for abandonment:

  • Predicate Abandon(s, o, t)
    = at time t, s demonstrates in action the purpose of disengaging object o from his activity (e.g. discarding it, publicly renouncing control).

We then define no abandonment between times:

  • NoAbandonBetween(s, o, t₁, t₂)
    := ¬∃t (t₁ ≤ t < t₂ ∧ Abandon(s, o, t))

And impose the persistence axiom:

  • Axiom (Persistence)
    ∀s, o, t₁, t₂:
    if t₁ ≤ t₂ and Engaged(s, o, t₁) and NoAbandonBetween(s, o, t₁, t₂)
    then Engaged(s, o, t₂).

Abandonment cancels engagement:

  • Axiom (Abandonment frees the object)
    Abandon(s, o, t) → ¬Engaged(s, o, t') for all t' ≥ t.

So: objects are “sticky” to their engager until a specific action breaks the link.

4. Action conflicts

Your idea: the purpose of property is to avoid action conflicts — simultaneous attempts to use an object for incompatible purposes.

We introduce a primitive relation on purposes:

  • Conflicts(p₁, p₂, o)
    = using object o for purpose p₁ is incompatible with using o for purpose p₂ at the same time.

Example: drinking from a cup vs. smashing it at the same moment.

Then define:

  • Definition (Action conflict on an object)

    Conflict(s₁, s₂, o, t)
    :⇔ ∃p₁, p₂, X₁, X₂ such that

    • Act(s₁, p₁, X₁, t)
    • Act(s₂, p₂, X₂, t)
    • o ∈ X₁ ∩ X₂
    • Conflicts(p₁, p₂, o)

So a conflict is literally two incompatible demonstrations of purpose using the same object at the same time.

5. The normative core: property as a conflict-avoidance rule

Now we turn the descriptive structure into a libertarian property norm.

We introduce:

  • Permitted(s, p, X, t) = it is morally/permissibly allowed for s to perform Act(s, p, X, t) at time t.

Property rule:

Once an object is engaged to an agent, others must not use it in ways that conflict with that agent’s potential purposes for it.

We don’t need to know exactly which purposes the owner has; you can take “potential purpose” as any purpose they might choose to demonstrate with it.

We encode it schematically as:

  • Axiom (Property norm)
    ∀s₁, s₂, o, t, p₂, X₂:
    if Engaged(s₁, o, t) ∧ s₁ ≠ s₂ ∧ o ∈ X₂,
    then:

    For every possible purpose p₁ agent s₁ might adopt for o,
    if Conflicts(p₁, p₂, o), then ¬Permitted(s₂, p₂, X₂, t).

In words: if o is engaged to s₁, no other agent s₂ is permitted to demonstrate any conflicting purpose with o.

Then you get, as a theorem, that if everyone respects the property norm, no action conflicts occur over engaged objects:

  • Theorem (No conflict among respectful agents)
    Suppose:
    (i) All agents only perform actions that are Permitted.
    (ii) Engagement is generated by the axioms above.
    Then for any s₁, s₂, o, t, if Engaged(s₁, o, t) and s₁ ≠ s₂, there is no Conflict(s₁, s₂, o, t).

So property is precisely the rule that assigns exclusive authority over engaged objects, to systematically prevent conflicting uses.

Self-ownership is a special case: your own body is always engaged to you, so others may not use it for conflicting purposes (assault, coercion, etc.).

6. Contracts as formalized purposes

You suggest:

Contracts are formalized statements of purpose which, by convention, also demonstrate purpose in action.

We can model a contract event e as a particular kind of action that:

  1. States future purposes.
  2. Counts as a present demonstration of purpose (by convention).

To keep it simple, define:

  • A set of contract events C ⊆ Events.

  • For each contract c ∈ C:

    • parties(c) ⊆ A
    • subject_objects(c) ⊆ O
    • terms(c) = a structured description of conditional future purposes and transfers.

We won’t fully formalize terms, but assume they specify:

  • A set of trigger conditions on future states (e.g. “payment of price X by time T₀”)
  • A set of target engagement changes (e.g. “if condition holds, Engaged(buyer, o, t') instead of Engaged(seller, o, t') for t' ≥ T₀”).

We say:

  • Contract(c, t) = contract c is validly concluded at time t.

By your convention:

  • Axiom (Contract as purpose-demonstration)
    If Contract(c, t) and s ∈ parties(c), then:
    ∃p, X such that

    • subject_objects(c) ⊆ X
    • Act(s, p, X, t)
    • and p encodes the intention to be bound by the terms of c.

So signing/agreeing to a contract is itself an action that displays a purpose regarding the objects.

6.1. Transfer of engagement via contracts

Now we need a rule that says: when the contract’s conditions are satisfied, the engagement relation is updated as specified.

Introduce:

  • ConditionsMet(c, t) = at time t, the conditions of contract c are satisfied.

Then a generic transfer clause can be written:

  • Suppose c specifies that when conditions hold, for each o ∈ subject_objects(c):

    • engagement moves from some s_old to some s_new.

We encode this as:

  • Axiom (Contractual transfer of engagement)
    For any contract c, subject object o, time t:

    If

    • Contract(c, t₀) for some t₀ < t,
    • ConditionsMet(c, t),
    • Engaged(s_old, o, t⁻) (just before t),
    • and the terms of c specify transfer of o from s_old to s_new,

    then:

    • Engaged(s_new, o, t)
    • ¬Engaged(s_old, o, t)

This models contracts as purpose-structured actions that, once their conditions are satisfied, reassign engagement.

Note how cleanly this fits your idea:

  • The contract is a statement of purpose (the parties’ joint plan).
  • By convention, that statement is also an action (they bind themselves now).
  • The property system then updates who is engaged with what when the plan’s conditions occur.

7. Putting it all together

We now have:

  1. Purposes and actions: agents continually demonstrate purposes in action, especially with their own bodies.
  2. Engagement: a dynamic relation between agents and objects, created by first use (Act on previously unengaged objects) and destroyed by abandonment or contract-based transfer.
  3. Conflict: simultaneous, purposive uses of an object that are incompatible (Conflicts).
  4. Property norm: a moral rule forbidding others from using an engaged object in conflicting ways.
  5. Original acquisition: the first successful action with an unengaged object makes it engaged to the acting agent.
  6. Contracts: coordinated action-events that articulate future purposes and, under conventional rules, govern future updates to the engagement relation.

Conceptually:

  • Property = a normative closure condition on the engagement relation, whose function is to eliminate action conflicts.

  • Libertarianism appears as the doctrine that:

    • engagement is first justified by original acquisition (purposeful first use),
    • it persists until abandonment or contractual transfer,
    • and others must not act in ways that create conflicts with the purposes of the engager.

If you’d like, next steps could be:

  • Add explicit deontic operators to prove “no-conflict theorems”.
  • Work out edge cases (shared purposes, co-ownership as a joint engagement relation, leasing as temporary partial engagement).
  • Compare this to standard Lockean/Hoppean formalizations to see where your “purpose ontology” changes or clarifies things.
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