theory/Proof_of_OI.md

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.