Finding Mind I: From Compressed Causal Graphs to a Future Metaphysics
“Finding Mind, Part I.” — Lucius Meredith (Apr 2026)
In brief: A critique of Kant’s Prolegomena through the lens of graph-structured lambda theories. The animating question is not what is the right formalism for compressed causal graphs? but what is it like to be an agent existentially motivated to work out its situation? From inside that agent’s standpoint, the framework becomes nearly inevitable: the agent must compress, into rule-form, in its own substrate, at a cost commensurate with reach. The structural commitments unfold from the existential one.
Key takeaways
- Compressed causal graphs take the form of graph-structured lambda theories (GSLTs): a grammar of states, an equational quotient marking symmetries, and rewrite rules as elementary causal steps. Lambda calculus, π-calculus, and rho calculus are all instances.
- Space, in this framework, is not pre-given. It emerges from term structure as splittings of term graphs — locations as Dedekind-style cuts between context and subterm. Time emerges as paths through this discrete tangent structure.
- The agent’s hypothesis-space is a fibration over Turing-complete GSLTs, indexed by Turing’s ordinal hierarchy of halting oracles. The agent does not know which point in the fibration it occupies; what it commits to is the form of GSLT-shape itself.
- Phenomena are term-level structures — the agent’s encounters under its categorial apparatus. Noumena are bisimulation equivalence classes — the substrate-independent invariants that semantic-category morphisms preserve.
- Hennessy–Milner adequacy means the agent’s modal logic positively characterizes the noumenal — an improvement over Kant’s negative-only access to things-in-themselves.
Key questions
- If the GSLT-shape commitment is constitutive for any predicting agent, what does it mean for an agent’s prior to be wrong — and how would the agent know?
- Kant insisted his table of categories was complete. The framework contests that closure. What is the right way to investigate the structural commitments built into the cognizing subject’s stance?
- If the transcendental subject is a viable point in a fibration rather than a singular entity, what does selection pressure on priors look like at population scale?
- Where does the framework’s account of the synthetic a priori succeed where Kant’s metaphysical deduction did not, and where does it inherit the same weaknesses in different form?
Why it matters for developers
The framework’s claim is that any computational agent committed to predicting its situation must adopt a GSLT-shaped representation. That has practical consequences for how we build and evaluate agentic systems: the same structural apparatus that supports compositional concurrency (rho calculus, π-calculus, OSLF-generated modal logics) also supports a principled account of what the agent’s hypotheses can mean, what counts as the agent persisting, and what counts as one agent’s situation being the same as another’s. Bisimulation as the noumenal invariant gives engineering a target that is substrate-independent without being abstract.