Stoic News

By Dave Kelly

Sunday, August 31, 2025

Vector Spaces of Sterling's Six General Commitments


Vector Spaces of Sterling's Six General Commitments


Overview

Each philosophical commitment can be represented as a vector in a multidimensional space where the axes represent fundamental philosophical dimensions. These vector spaces allow us to analyze relationships, tensions, and coherence between commitments.


## 1. Substance Dualism Vector Space


**Dimensional Axes:**

- **Ontological Independence** (x₁): Degree to which mind exists independently of physical substrate

- **Causal Efficacy** (x₂): Extent of mental causation over physical events

- **Phenomenal Distinctness** (x₃): Qualitative difference between mental and physical properties


**Vector Representation:** **v₁** = ⟨1, 0.8, 1⟩


The commitment to substance dualism occupies the high end of ontological independence and phenomenal distinctness, with strong but not absolute causal efficacy (allowing for some physical constraints).


## 2. Metaphysical Libertarian Free Will Vector Space


**Dimensional Axes:**

- **Causal Indeterminism** (y₁): Degree to which choices are undetermined by prior causes

- **Agent Causation** (y₂): Extent of genuine origination by the agent

- **Ultimate Responsibility** (y₃): Level of moral accountability possible


**Vector Representation:** **v₂** = ⟨1, 1, 1⟩


Libertarian free will maximizes all three dimensions, requiring complete indeterminism, full agent causation, and ultimate moral responsibility.


## 3. Ethical Intuitionism Vector Space


**Dimensional Axes:**

- **Epistemic Directness** (z₁): Immediacy of moral knowledge access

- **Rational Apprehension** (z₂): Role of reason in moral discovery

- **Moral Transparency** (z₃): Clarity of moral truth to properly functioning minds


**Vector Representation:** **v₃** = ⟨1, 0.9, 0.8⟩


High epistemic directness with strong rational component, though allowing for some opacity in complex moral situations.


## 4. Foundationalism Vector Space


**Dimensional Axes:**

- **Self-Evidence** (w₁): Degree to which basic beliefs require no further justification

- **Inferential Independence** (w₂): Extent to which foundations stand alone

- **Epistemic Priority** (w₃): Temporal and logical precedence of basic beliefs


**Vector Representation:** **v₄** = ⟨1, 0.9, 1⟩


Maximizes self-evidence and epistemic priority, with very high inferential independence (allowing minimal coherence constraints).


## 5. Correspondence Theory of Truth Vector Space


**Dimensional Axes:**

- **Realist Commitment** (u₁): Degree of mind-independent reality

- **Matching Relation** (u₂): Strength of correspondence between belief and fact

- **Objective Determinacy** (u₃): Extent to which truth conditions are mind-independent


**Vector Representation:** **v₅** = ⟨1, 1, 1⟩


Correspondence theory maximizes all dimensions, requiring strong realism, perfect matching relations, and complete objective determinacy.


## 6. Moral Realism Vector Space


**Dimensional Axes:**

- **Objective Existence** (t₁): Degree to which moral facts exist independently of attitudes

- **Truth Aptness** (t₂): Extent to which moral judgments can be literally true/false

- **Universal Validity** (t₃): Scope of moral facts across contexts and cultures


**Vector Representation:** **v₆** = ⟨1, 1, 0.9⟩


High objective existence and truth aptness, with strong but not absolute universal validity (allowing for some contextual variation in application).


## Composite Vector Space Analysis


### Joint Commitment Vector

When all six commitments are held simultaneously:

**V_Sterling** = α₁v₁ + α₂v₂ + α₃v₃ + α₄v₄ + α₅v₅ + α₆v₆


Where α₁...α₆ represent the relative weights of each commitment.


### Key Vector Relationships


**Orthogonal Commitments:**

- Foundationalism and Correspondence Theory are nearly orthogonal, addressing different epistemic levels

- Substance Dualism and Moral Realism operate in distinct ontological domains


**Parallel Commitments:**

- Libertarian Free Will and Substance Dualism both maximize agency dimensions

- Ethical Intuitionism and Foundationalism share high values on directness/self-evidence axes

- Correspondence Theory and Moral Realism both maximize objectivity dimensions


**Tension Vectors:**

- **T₁**: Substance Dualism's causal efficacy vs. Physical Determinism

- **T₂**: Libertarian Free Will's indeterminism vs. Rational Predictability

- **T₃**: Foundationalism's independence vs. Coherentist pressures


### Coherence Metric

The coherence of Sterling's system can be measured by:

**C = 1 - (||T₁|| + ||T₂|| + ||T₃||) / 3**


Where higher values indicate greater internal consistency.


## Philosophical Vector Operations


### Addition

Combining commitments: **v_i + v_j** represents synthesizing two philosophical positions


### Scalar Multiplication

Adjusting commitment strength: **αv_i** represents holding position i with confidence level α


### Dot Product

Measuring alignment: **v_i · v_j** quantifies compatibility between commitments i and j


### Cross Product

Identifying tensions: **v_i × v_j** reveals orthogonal conflicts requiring resolution


## Critical Vector Subspaces


1. **Realist Subspace**: Spanned by {Correspondence Theory, Moral Realism}

2. **Dualist Subspace**: Spanned by {Substance Dualism, Libertarian Free Will}

3. **Foundationalist Subspace**: Spanned by {Foundationalism, Ethical Intuitionism}


These subspaces represent coherent clusters within Sterling's overall philosophical framework, each with internal logical dependencies and mutual reinforcement patterns.

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