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.

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Proof That Closed and Empty Individualism Cannot Be True Even Locally (Given PSR and EMR)

Premises

P1. Principle of Sufficient Reason (PSR)

Every fact or distinction must have a sufficient reason; no brute facts are allowed.

P2. Extended Modal Realism (EMR)

All possible, impossible, and incoherent worlds exist. Nothing is excluded from existence.

P3. Global Open Individualism (GOI)

There is only one subject of experience, numerically identical across all possible and impossible worlds.

GOI follows necessarily from P1 and P2 (as shown in prior proof), because:

• PSR forbids arbitrary metaphysical distinctions.
• EMR includes all worlds, persons, and configurations.
• Therefore, only one subject can exist without invoking brute identity constraints.

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Definitions

• Closed Individualism (CI): Each person is a numerically distinct subject who persists across time.
• Empty Individualism (EI): Each momentary experience belongs to a separate subject that vanishes immediately.
• Local Metaphysical Validity: A theory is locally valid if it can be ontologically true within a single world.

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Goal

To prove:
CI and EI cannot be metaphysically valid even within a single world, given the truth of GOI.

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Proof

Step 1: GOI Posits a Global Subject

From P3, there is exactly one experiencer across all centers of consciousness in all worlds.

Step 2: CI and EI Require Ontological Subject Distinctions

• CI posits that each person is a numerically separate subject of experience.
• EI posits that each momentary experience is ontologically isolated.

Therefore, both CI and EI assert real metaphysical distinctions between subjects.

Step 3: Any Metaphysical Distinction Requires Sufficient Reason (From P1)

Under PSR, any metaphysical distinction (e.g., between subjects) must be justified with a sufficient reason.

Step 4: No Such Sufficient Reason Exists in EMR

In EMR (P2), all configurations of persons exist, and GOI (P3) treats them all as perspectival variations of the same subject.

Therefore, asserting "this subject is not that one" introduces a brute distinction — which violates PSR (P1).

Step 5: CI and EI Are Metaphysically Invalid in All Worlds

Since CI and EI depend on subject distinctions that cannot be justified under PSR + EMR, they are never metaphysically valid — not even within a single world.

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Conclusion

∴ Closed Individualism and Empty Individualism are logically incompatible with PSR + EMR + GOI.
They cannot be true, even locally in any individual world.