Core Vector Space: Explanation

 

Core Vector Space: Explanation

In this frameworkq, a core vector space is a structured conceptual field that defines the meaning, function, and boundaries of a philosophical commitment. It is not a mathematical vector space in the strict formal sense, but an analogical extension: a set of interrelated concepts that cohere around a central theoretical axis and jointly determine how that commitment operates within the system.

Each term in the vector space functions like a dimension. No single term is sufficient to define the commitment on its own. Instead, the commitment is constituted by the simultaneous activation of all of them. To understand substance dualism, for example, is not merely to assert “the mind is non-physical,” but to grasp a network: subjectivity, intentionality, irreducibility, mental causation, unity of consciousness, and so on. Remove enough of these dimensions, and the concept collapses into a weaker or different view, such as property dualism, functionalism, or physicalism.

The core vector space therefore serves three functions:

1. Conceptual Content (What the commitment is)

The vector space specifies the internal structure of a commitment. It tells you what must be present for the concept to exist in its intended form. For substance dualism, this includes the rational faculty as a distinct substance, the first-person perspective, and independence from the body. These are not optional features; they define the commitment’s identity.

2. Dependency Role (What the commitment does in the system)

Each vector space is positioned within a larger dependency structure. The terms are selected not just for descriptive richness, but for functional necessity. For instance, “locus of control” and “agency substrate” are included because substance dualism must ground Foundation One (control). Likewise, “epistemic access” connects dualism to intuitionism, and “mental causation” connects it to libertarian free will. The vector space encodes how the commitment supports the system’s foundations.

3. Discriminative Boundary (What the commitment is not)

A vector space also defines exclusion zones. By specifying neighboring but incompatible concepts, such as reductionism, identity theory, and eliminativism, it clarifies the boundaries of the view. These opposing positions occupy adjacent conceptual regions but lack key dimensions, such as irreducibility or ontological distinction. This gives the vector space sharp edges rather than vague overlap.

A useful way to think about this is geometrically: a commitment is a point in a high-dimensional conceptual space. Its coordinates are given by the presence and weighting of specific terms. Competing theories occupy nearby but distinct regions because they share some dimensions while lacking others. The more dimensions you include, the more precisely you locate the commitment.

This approach has a major advantage over traditional definition-by-essence. Instead of trying to reduce a concept to a single necessary and sufficient condition, it recognizes that philosophical positions are structurally complex. Their identity lies in a pattern of interdependence, not a single clause.

Finally, when all six commitments are expressed as vector spaces, their intersections reveal the deep structure of the system. Shared dimensions, like truth, agency, and access, form higher-level clusters. At that level, the entire framework can be seen as a unified semantic field centered on one core idea:

agent-originated, truth-tracking judgment within a structured reality.

That is the conceptual center toward which all vector spaces converge.