Limits and colimits showed us how possibility condenses or opens under relational pressure. But they also quietly exposed a deeper instability: the very space in which constraints operate is not fixed.
If categories are theories of possible instances, then the choice of category is already a cut. And if that cut itself varies, then possibility is not merely shaped within a space—it evolves through changes in the space of articulation itself.
This post turns to that instability directly.
The Inadequacy of a Fixed Space
Much philosophical and mathematical thinking proceeds as if the space of description were given:
-
objects inhabit a world,
-
relations structure that world,
-
and theory merely charts what is already there.
But Category Cuts has consistently refused this picture. Categories do not describe a pre-partitioned reality. They constitute the field of possible instantiations.
Once this is accepted, a new question arises:
What happens when the system of cuts itself becomes variable?
At that point, we are no longer dealing with first-order constraint. We are dealing with constraints on construal.
Categories of Categories
In category theory, this reflexive move appears as categories whose objects are themselves categories, and whose morphisms are functors.
These higher-order categories do not sit “above” first-order ones in a hierarchy of reality. They articulate meta-perspectives: perspectives on how perspectives operate.
Meta-Cuts and Reflexive Constraint
A higher-order cut does not introduce new objects. It introduces new conditions on what counts as a coherent cut at all.
Such constraints include:
-
what kinds of relations are admissible,
-
what counts as identity across perspectives,
-
where invariance must be preserved,
-
and where variation is structurally permitted.
These constraints are not optional. They silently govern every act of theorising, modelling, or meaning-making.
The Evolution of Possibility
Once higher-order constraints are in view, possibility itself becomes historical—not in the sense of a temporal sequence of events, but in the sense of changing conditions of actualisability.
New possibilities do not emerge merely because new instances occur. They emerge because:
-
new cuts become thinkable,
-
new relations become admissible,
-
new configurations of constraint stabilise.
Gödel Revisited, Without Representation
This is where the series quietly reconnects with the Gödel work.
Gödel’s result did not show that reality exceeds formal systems. It showed that no single system of articulation can exhaust the space of possible articulation.
In relational terms:
-
every category leaves some cuts unavailable,
-
every theory of possibility generates its own horizon of impossibility,
-
and reflexivity forces expansion, not completion.
Against Meta-Foundations
It is tempting to seek a final meta-category: a theory of all possible theories of possibility. That temptation must be resisted.
Any such structure would itself impose constraints—and therefore generate further horizons.
The lesson here is not infinite regress, but finite situatedness:
-
every cut is local,
-
every theory is perspectival,
-
every stabilisation is provisional.
Yet this is not relativism. Constraints are real. Failures of coherence are real. Impossibilities are real.
They are real relationally.
Meaning at the Reflexive Edge
At this reflexive level, meaning becomes especially fragile—and especially powerful.
Meaning does not reside in objects, nor even in relations alone. It arises where:
-
constraints are recognised,
-
limits are respected,
-
and new cuts are responsibly made.
Higher-order categories give us a way to speak about this without mystification: meaning emerges where the space of construal is itself reconfigured.
The Cut Remains
This series has moved:
-
from cuts before objects,
-
through perspectival translation,
-
into mutual constraint,
-
across condensation and emergence,
-
and finally into reflexive transformation.
At no point did we arrive at foundations.
That is not a failure.
No comments:
Post a Comment