Chapter 38
Ontological Isolation
A reader who has come through Part Part II has met this chapter’s content already, in the form of a scientist that could learn nothing about a specimen without spending a token on it. It is stated again here, and abstractly, for a reason worth giving plainly: the population argument that follows does not need a budget, and stating the isolation principle without one makes visible how little the argument actually assumes. What was there an economic predicament is here a structural theorem. Nothing below depends on the learner being mortal, or on tokens existing at all.
A computational system \(\GSLT\) is ontologically isolated if, for any term \(P \in \terms(\GSLT)\) and any entity \(X\) outside \(\terms(\GSLT)\), \(P\) can interact with \(X\) only via an encoding \(\lceil X \rceil \in \terms(\GSLT)\). No term can refer to, branch on, or be influenced by unencoded external entities.
This is not an assumption but a structural consequence of what it means to be a term in a GSLT. The rewrite rules operate on terms; they cannot pattern-match on entities that have no term representation. The JVM sensor example makes this vivid: a stream of hardware events arriving at a JVM instance has no effect on any Java program until those events are encoded as Java data structures. The encoding step is where the world outside enters; without it, the outside world is simply absent from the computation.
For the purposes of studying the epistemic limits of agents in \(\GSLT\), it is without loss of generality to assume that the agent’s world consists entirely of \(\terms(\GSLT)/{\bisim}\). The outside world can be forgotten.
Any influence of the outside world on an agent \(P\) must pass through an encoding. The encoding is itself a term. The effect of the outside world on \(P\) is therefore indistinguishable, from \(P\)’s perspective, from the effect of the encoding term acting on \(P\) from within \(\GSLT\).
Ontological isolation is what licenses the move to the category of GSLTs as the natural setting for studying AI. If AI’s value proposition is that useful aspects of intelligence are faithfully rendered as computations, and if computations are ontologically isolated, then the category of GSLTs captures everything that matters for the limits of AI — without needing to appeal to an external world.