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.