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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