[The book is available on Amazon and the O’Reilly digital platform.]
Related readings:
- Ontological Prisms for beginners
- Ontological Prisms & The Geometry of Knowledge
- Enterprise’s New Brains
- Knowledge Engineering with Ontological Prisms (KEOPS)
- KEOPS Kernel
- Engineering Workflows with Ontological Prisms
These are selected verbatim of conversations with Claude (Anthropic).
Epistemic dimensions
I said:
Knowledge is meant to be framed by epistemic dimension: extensional, intensional, or logical. Extensional dimension pertains to reality as it can be observed, intensional dimension to mental representations, logical dimension to symbolic representations.
Claude said:
This converges all three terms cleanly under dimension, which resolves the terminological asymmetry — but I want to flag that it doesn’t resolve the substantive issue underneath it. The category mismatch I raised two messages ago was provisionally explained by the modality/dimension split (intensional as a cross-cutting mode rather than a parallel slot). With that split gone, the mismatch returns in full force, now within a single uniform category:
| Dimension | Anchor type | Anchor |
|---|---|---|
| Extensional | Object | Reality as observed |
| Intensional | Locus | Mental representations |
| Logical | Medium | Symbolic representations |
All three are now officially the same kind of thing — dimensions — yet they’re individuated by three different criteria: what they’re about (reality), where they occur (the mind), and how they’re encoded (symbols). That’s a heterogeneous basis for a supposedly homogeneous triad. A fully uniform version would pick one anchor type and hold it across all three. For instance, anchored consistently on object of representation:
- Extensional dimension → represents facts
- Intensional dimension → represents concepts/meanings
- Logical dimension → represents symbols/notations
This drops “mental representations” as the defining feature of the intensional dimension and replaces it with concepts as an object-type parallel to facts and symbols — which is close to your very first formulation (“concepts driving observations and interpretations”), not the later psychological one. Alternatively, anchored consistently on locus:
- Extensional dimension → reality (the world)
- Intensional dimension → mind (the cognizer)
- Logical dimension → language/notation (the symbolic community)
This keeps “mental representations” but requires reframing extensional and logical dimensions away from “facts” and “symbols” as objects and toward “the world” and “the symbolic medium” as sites, which is a smaller change but still a real one — extensional dimension would then be about the world as a site of facts, not facts directly.
Either repair is workable, but they’re not interchangeable, and the current formulation sits between them — extensional and logical implicitly use the object/medium anchor, while intensional alone uses the locus anchor. This is the same fork I raised before the dimension/modality terms converged; convergence of terminology didn’t settle it.
So: should the triad be re-anchored uniformly on object (facts / concepts / symbols), uniformly on locus (world / mind / language), or is there a third anchor type you intend that subsumes both — in which case what is it?
What is represented ?
I said:
Knowledge is meant to be framed by epistemic dimension: extensional, intensional, or logical. Extensional dimension pertains to reality as it can be observed, intensional dimension to the concepts used to make sense of reality, logical dimension to the symbolic categories used to represent reality.
Claude said:
This version resolves the heterogeneity I flagged — but it does so by changing the kind of resolution, not by picking one of the two repairs I offered. It’s worth being precise about how.
What changed structurally. Compare the grammar of the three definitions:
- Extensional: reality — as it can be observed
- Intensional: concepts — used to make sense of reality
- Logical: symbolic categories — used to represent reality
Intensional and logical are now perfectly parallel: both are mediating apparatuses defined by a function applied to reality (“make sense of,” “represent”). Extensional is no longer parallel to them in form — it’s not a mediator of reality, it is reality (as observed) — but this asymmetry is no longer a flaw, because it’s now a necessary asymmetry rather than an arbitrary one. You cannot coherently define reality as “the thing used to represent reality” without circularity. Something in the triad has to serve as the fixed referent that the other two are mediations of. Extensional dimension is that fixed point by logical necessity, not by inconsistency.
So the triad is no longer flatly heterogeneous (object/locus/medium, as before) — it’s now hierarchically anchored: one referent dimension, and two mediating dimensions defined relative to it, distinguished by the type of mediation (conceptual vs. symbolic).
This is structurally a classical semiotic triangle. What you’ve arrived at maps closely onto the Ogden–Richards triangle (referent / thought-or-reference / symbol), Frege’s Bedeutung / Sinn / Zeichen, or Peirce’s object/interpretant/sign. Reality plays the referent role; the intensional dimension plays the sense/interpretant role; the logical dimension plays the sign/symbol role. This is a good thing for the framework’s pedigree — it means the triad now has a well-worked precedent rather than being an ad hoc threeway split, and you can borrow established results about how those triangles behave (e.g., the classic problem of Sinn without Bedeutung, or signs that fail to correspond to any referent) as diagnostic tools for your own framework.
But this resolution opens a new and sharper question, one the previous flatter version didn’t even expose: if intensional dimension is “concepts used to make sense of reality” and logical dimension is “symbolic categories used to represent reality,” what stops a symbolic category from being nothing more than the symbolic encoding of a concept? In the classical semiotic triangle, sign and sense are not independent — the sign typically gets its representational power by expressing the sense. If the same holds here, logical dimension would not be a third autonomous dimension at all, but a derivative projection of intensional dimension into symbolic form — a notational shadow of concepts, not an independent epistemic category alongside it.
For your triad to genuinely have three dimensions rather than two-plus-a-notation-layer, there has to be something a symbolic category can do or fail to do that is not reducible to the concept it encodes — for instance, a symbolic category might be agreed upon (recall your earlier “agreed-upon representations”) even where the underlying concept is contested, or a symbol might be manipulated formally (inference, composition) in ways that outrun what the concept alone licenses. That would be the autonomy condition for logical dimension.
So: is logical dimension’s independence grounded in something like formal manipulability (symbols can be combined and inferred over by rules that don’t track conceptual content) or in conventionality (symbols can be agreed upon independent of conceptual agreement) — or do you intend logical dimension to be explicitly derivative of intensional dimension, with the triad being asymmetric on purpose?