Conceptual Spaces — an interactive 3D map of the mind

Aristotle mapped the mind 2,300 years before cognitive science.

Peter Gärdenfors' conceptual spaces framework models concepts as geometry: quality dimensions form domains, concepts are convex regions, typicality is distance from a prototype. This visualization places that framework in the middle of the Aristotelian-Thomistic cognitive hierarchy — formal reception through the senses below it, the immaterial intellect above it — showing how the classical psychology fills the two gaps the modern framework leaves open. It is the interactive companion to the paper Beyond and Below Cognitive Space: A Framework for Perfecting Conceptual Spaces by Michael Mangialardi.

The three layers

The eight stations

The story

  1. One architecture, three layers: Gärdenfors' conceptual spaces — a geometric theory of concepts — occupy the middle layer. Below sits Aristotelian sense perception; above, the intellect. The claim: the old psychology fills the two gaps the modern framework leaves open.
  2. It starts in things: Real things act on the sense organs, transmitting their sensible forms. This formal reception is what connects all the later geometry to reality — the gap below the framework, filled.
  3. Five senses, five geometries: Each sense receives only its proper object — color, sound, savor, odor, heat. Each object is a quality domain with its own shape: color a spindle of hue, saturation, and brightness; taste a tetrahedron of sweet, sour, salty, bitter.
  4. One world from five streams: The common sense binds the separate qualities into a single sensible gestalt — and perceives what no single sense can: shape, number, movement, magnitude.
  5. The image that stays: Imagination holds the gestalt as a phantasm — an image that persists after the thing is gone, ready to be worked on by the higher powers.
  6. Perceiving things as things: The cogitative power registers what a thing looks like (aspectual), what it does (actional), and what it means for me (affectional) — each percept building on the last, converging in one gestalt percept of the individual thing.
  7. The phantasm, organized geometrically: A conceptual space is that cogitative phantasm laid out as geometry: quality dimensions form domains, concepts are convex regions, the prototype sits at the core, and typicality is distance from it — robin near the center, penguin at the shell.
  8. Aristotle's tree, Gärdenfors' regions: The Porphyry tree divides genus into species by differentia — discrete cuts. The nested regions are the same classification made continuous: BIRD and MAMMAL sit side by side inside ANIMAL, separated by their differentiae.
  9. Experience accumulates: Memory retains gestalt percepts with their temporal index. It sits beside the flow rather than on the rise: repeated encounters gradually carve the regions of the space.
  10. Beyond typicality: necessity: The intellect abstracts the intelligible species — essence without matter. Its predicables and categories classify necessarily and universally, where the space below classifies by degree. The gap above the framework, filled.

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