theory/Proof_of_OI.md
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# 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").
---
## 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.
---
### 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**.
---
### 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 EMRs universal realization of partitionings,
- Therefore **violate PSR**.
---
### 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.