Impossible Horizons ended without an ending. That was not an omission; it was a consequence. If possibility is relational, perspectival, and recursively generative, then no horizon can finally close. Every limit generates further limits; every construal opens new construals. We found ourselves, deliberately, at the edge of infinite construal.
But standing at an infinite horizon raises a pressing question:
If possibility never closes, what holds it together at all?
This new series begins there.
Why Horizons Are Not Enough
Horizons tell us where possibility opens. They show us edges, paradoxes, and generative impossibilities. But horizons alone do not tell us how these openings are structured, related, or stabilised—however provisionally—across perspectives.
After Impossible Horizons, one temptation is to retreat:
-
back to phenomena,
-
back to examples,
-
back to “applications”.
Another temptation is worse: to treat infinite possibility as ineffable, poetic, or mysteriously self-sustaining.
Both temptations miss something crucial.
What we need now is not more horizons, but a way of articulating the structure of cuts themselves—without reintroducing substances, representations, or hidden foundations.
This is where Category Cuts begins.
Cuts, Not Objects
A cut is not:
-
a slice through an independently existing world,
-
a selection from a pre-given set of possibilities,
-
or a reduction of richness to simplicity.
A cut is a perspectival structuring of potential. It is the moment at which a theory of possible instances is taken as an instance—without exhausting that theory.
What matters, ontologically, is not what things are, but how cuts:
-
relate to other cuts,
-
compose,
-
fail to compose,
-
generate limits,
-
and give rise to new horizons.
This already tells us something decisive:
The primary ontology here is relational and structural, not object-based.
And that tells us what kind of formal language we should even consider.
Why Category Theory (and Why This One)
Even more importantly:
-
categories are defined by composability,
-
limits are structural, not prohibitive,
-
and meaning lives in patterns of transformation, not in intrinsic content.
This makes category theory uniquely suited—not as a mathematical authority, but as a structural vocabulary—for a relational ontology of possibility.
But let us be clear about what this series is not doing.
This is not:
-
importing mathematics to legitimise philosophy,
-
reducing ontology to formalism,
-
or treating categories as representations of reality.
Instead:
Category theory is treated here as a theory of cuts:a way of articulating how perspectives relate, transform, and constrain one another without appealing to foundations.
From Infinite Construal to Structural Constraint
That does not mean “anything goes”.
Category theory gives us tools to speak about:
-
when cuts compose and when they do not,
-
how constraints generate new possibilities,
-
why some horizons stabilise while others collapse,
-
and how different theories of meaning relate without reducing to one another.
In short, it allows us to ask:
What kinds of structures can infinite construal actually sustain?
What This Series Will Do
In Category Cuts, we will explore:
-
Categories as theories of possible instances
-
Functors as perspectival shifts between systems of meaning
-
Limits and colimits as the structural form of hovering potentials
-
Adjunctions as models of dialogic co-individuation
-
Failure of composition as ontologically informative, not pathological
None of this will assume:
-
representational realism,
-
observer-independent structures,
-
or a collapse of meaning into value or coordination.
Everything will be treated as perspectival, relational, and constrained—but never foundational.
No comments:
Post a Comment