Open Questions

PKT is not just a machine learning proposal. It raises questions that sit at the boundary of philosophy, cognitive science, and AI. These questions do not have answers yet — they are part of what makes this work worth pursuing. In the Popperian spirit, they are conjectures awaiting refutation.

1. Is Knowledge a Universal Structure or an Emergent Property?

If the Knowledge Tensor $\mathcal{T}^$ converges to a stable state, does that state reflect something *universal about the world, or is it merely an artifact of the particular data, rules, and architecture used?

The universalist view: Knowledge has a structure that any sufficiently advanced intelligence would converge on. Mathematical truths are true regardless of who discovers them. The laws of physics are the same everywhere. A well-designed PKT system, given enough data and the right rules, would arrive at the same $\mathcal{T}^*$ regardless of its starting point.

The emergentist view: Knowledge is shaped by the knower. Different data, different rules, different architectures would produce different “knowledge.” What we call knowledge is just the stable output of a particular learning process — there is no Platonic $\mathcal{T}^*$ waiting to be discovered.

Why it matters for PKT: If knowledge is universal, then the choice of rule set $\mathcal{R}$ is a matter of getting it right — discovering the correct deductive constraints. If knowledge is emergent, then $\mathcal{R}$ is a design choice, and different choices produce different (but possibly equally valid) knowledge structures.

2. Does Knowledge Require Agency?

A rock does not know anything. A thermostat responds to temperature but does not “know” the room is cold. Where does knowledge begin?

Popper argued that knowledge requires active conjecture — an agent that proposes hypotheses and tests them. Passive systems that merely react to stimuli do not produce knowledge; they produce behavior. On this view, knowledge is inherently tied to agency: the capacity to ask questions, form expectations, and be surprised when they fail.

The PKT tension: The proposed framework has an inductive process (learning from data) and a deductive process (testing against rules), but it does not have an agent that decides which conjectures to make or which tests to apply. The rules $\mathcal{R}$ are externally provided. Is this sufficient for knowledge, or is it merely sophisticated information processing?

A possible resolution: Perhaps agency enters through the rule selection process. If the system could learn or discover its own deductive rules — not just apply given ones — it would move closer to genuine agency. This connects to the problem of meta-learning: learning what to learn.

3. Can a Collective of AIs Develop Knowledge Without Human Seeding?

Current AI systems are trained on human-generated data. Their “knowledge” is, at best, a compressed and reorganized version of human knowledge. But what if we removed the human seed?

Consider a swarm of PKT-like agents interacting with an environment (not a text corpus, but a simulated or physical world):

Would such a system develop knowledge in any meaningful sense? Or would it develop something alien — an organized information structure that serves the agents’ purposes but is unrecognizable as knowledge to a human observer?

This question is related to the problem of grounding: whether knowledge requires embodied experience, or whether it can arise from any sufficiently rich interaction with an environment.

4. Popper’s World 3

Popper proposed three “worlds” (Objective Knowledge, 1972):

A mathematical theorem, once proven, exists in World 3 whether or not anyone is currently thinking about it. The content of a library exists in World 3 even when the library is closed.

The AI question: When an AI system produces a novel proof, a new theory, or a solution to an unsolved problem, has it created a World 3 object? Or is the output merely a World 1 artifact (bits on a disk) that humans interpret as World 3?

If PKT produces a Knowledge Tensor $\mathcal{T}^$ that encodes genuine, logically consistent, empirically grounded knowledge — is $\mathcal{T}^$ a World 3 object? Popper might say yes, since World 3 objects are defined by their content, not their origin. But this is contested.

5. What Experiments Could Test These Questions?

Philosophy without empirics is speculation. Here are testable predictions and experiments that could advance (or falsify) PKT’s core claims:

Experiment 1: Consistency under falsification

Train two identical models on the same data but with different rule sets $\mathcal{R}_1$ and $\mathcal{R}_2$. Measure whether both converge to the same $\mathcal{T}^$ on the *shared subset of rules. If yes, this supports the universalist view. If not, knowledge is more episteme-dependent than expected.

Experiment 2: Hard vs. soft constraint comparison

Implement both a soft-constraint system (standard LTN-style) and a hard-falsification system (PKT-style) on the same task. Compare:

Prediction: Hard falsification should produce lower hallucination rates but at higher computational cost. The trade-off curve is the empirical contribution.

Experiment 3: Emergent rule discovery

Initialize a PKT system with a minimal rule set and allow it to propose new rules based on patterns in $\mathcal{T}$. Measure whether the discovered rules correspond to known logical principles (e.g., transitivity, symmetry). This would test whether deductive structure can emerge from inductive learning.

Experiment 4: Multi-agent knowledge development

Set up multiple PKT agents in a shared environment with no human-generated data. Measure whether the agents converge on shared knowledge structures and whether those structures are interpretable to humans.

Why These Questions Matter

Most machine learning papers ask: “Does this method improve on the benchmark?” PKT asks different questions — questions about the nature of what’s being learned, not just its accuracy. These questions make the work harder to evaluate by standard metrics, but they also make it more interesting.

The Framework page defines the machinery. This page asks whether the machinery, if built, would produce something we should call knowledge.

References

See also: Research Log — where these questions are tracked over time.