# Proof of Open Individualism from the Principle of Sufficient Reason and Extended Modal Realism

## Assumptions

- **PSR (Principle of Sufficient Reason)**: Every fact has a sufficient explanation.
- **EMR (Extended Modal Realism)**: All possible, impossible, and incoherent worlds are real.
- Conscious subjects exist in (some) worlds.
- **Phenomenal indexicality**: Each conscious subject experiences their own perspective (what it's like to be "me").

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## Step-by-Step Proof of Open Individualism

### 1. Define the Subject of Experience

Let a *subject of experience* be the entity for which there is *something it is like* to exist (Nagel 1974). This is often modeled as an **observer-moment**: an instantaneous state of phenomenal consciousness.

Let the **set of all observer-moments** across all modalities be denoted:

\( \mathcal{O} \)

By EMR, \( \mathcal{O} \) contains every logically, illogically, metaphysically, and physically possible observer-moment.

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### 2. Observer-Moment Identity

Let \( o_1, o_2 \in \mathcal{O} \) be any two observer-moments. Assume for contradiction that they belong to *distinct* subjects of experience.

This implies a distinction between subjects—say \( S_1 \) and \( S_2 \)—where \( o_1 \in S_1 \), \( o_2 \in S_2 \).

But such a distinction requires explanation under **PSR**:
- Why does \( o_1 \) belong to \( S_1 \) and not \( S_2 \), and vice versa?

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### 3. No Sufficient Reason for Subject Boundaries

Per **EMR**, *every* way of carving up experience—including *no carving at all*—exists in some world. There are incoherent worlds with:
- No subject boundaries,
- Reversed or cyclic boundaries,
- Infinitely fractal or inconsistent individuation.

Therefore, **any particular boundary assignment is modally arbitrary**.

By **PSR**, this arbitrariness is unacceptable:
> There must be a sufficient reason for why *this* partitioning of observer-moments into subjects holds rather than another.

But EMR ensures *every* partitioning exists. So no single partition can be ontologically privileged **without violating PSR**.

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### 4. Eliminate Arbitrary Multiplicity

To preserve PSR, we must **eliminate all arbitrary distinctions** between observer-moments.

This leads to the only viable identity structure:
> **Open Individualism (OI)**: All observer-moments are experienced by one and the same subject.

All other identity theories (e.g., Closed Individualism or Empty Individualism) impose distinctions that:
- Lack sufficient reason,
- Conflict with EMR’s universal realization of partitionings,
- Therefore **violate PSR**.

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### 5. Objection: Why *One* and Not *Many*?

OI is not privileging “one” per se. Rather:
- It imposes **no boundaries**,
- It is **identity-minimal**,
- It **avoids arbitrary structure**.

Hence, it is the only account compatible with **PSR + EMR**.

Any multiplicity implies a modally unjustified subject individuation.

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## ✅ Conclusion

Given:
- **PSR**: No arbitrary or unexplained facts,
- **EMR**: All identity structures exist across worlds,
- **OI**: The only non-arbitrary, non-partitioned account of experience,

We conclude:

> **Open Individualism is necessarily true**: there exists a single, modally unbounded subject who experiences every observer-moment.

Any alternative view entails unexplained distinctions—thus violating the Principle of Sufficient Reason.