What You Can Know

In 2025, the physicists DeBrota and List published a remarkable analysis of quantum mechanics. They identified seven theses about physical reality — non-contextuality, determinism, completeness, localism, non-fragmentation, non-superdeterminism, and absoluteness of observed events — and proved that these seven are jointly inconsistent. You can hold any six, but not all seven. Each quantum interpretation amounts to choosing which thesis to sacrifice.

This is not a problem for quantum mechanics. The predictions are the same regardless of interpretation. No experiment distinguishes Copenhagen from Many-Worlds, Bohmian mechanics from QBism. What changes is what you’re permitted to believe — which changes what you’re able to ask, which changes what you can discover.

The heptalemma is the sharpest example of a broader pattern. What you can know about a system depends not on the system alone but on the framework you bring to it. The framework doesn’t change the physics. It changes what the physics means.

This is different from the observer constituting the observable. When a measurement apparatus couples to a quantum system, it creates a joint system with new properties — the measurement changes the system. But the heptalemma’s seven theses don’t change quantum mechanics. They don’t alter the wavefunction or the Born rule or the prediction for any experiment. They alter the space of permissible interpretations. The system stays the same. The knowledge shifts.

When is this distinction real? When the same underlying data produces qualitatively different answers under different epistemic frameworks — not just more or less precision, but categorically different conclusions. Knowable vs. unknowable. Decomposable vs. irreducible. Ordered vs. disordered. The framework is the lens, and different lenses don’t just magnify differently. They reveal different structures.

Start with the cleanest case. Goedel’s incompleteness theorems show that any sufficiently powerful formal system contains truths it cannot prove. But the unprovable truths depend on the system. Change the axioms and different statements become provable, others become unreachable. The integers don’t change. The formal system does — and with it, the set of truths accessible from within it. This is conditional epistemics in its purest form: the framework determines what can be known without altering what exists.

The pattern sharpens in information theory. Partial information decomposition attempts to separate the information that two sources provide about a target into shared, unique, and synergistic components. But Williams and Beer, and later Rauh and colleagues, proved that this decomposition faces structural impossibility. Two systems with identical pairwise statistics can have different synergy under different decomposition frameworks. What you can decompose depends on how you decompose it. The answer isn’t waiting in the data. It’s waiting in the framework.

Computation reveals the same structure through a different door. Differential privacy — the mathematical guarantee that no individual’s data significantly affects the output — creates qualitative learnability barriers. Without privacy constraints, certain language classes are identifiable in the limit. Add epsilon-differential privacy, and those same classes become provably unlearnable. The data hasn’t changed. The language class hasn’t changed. An epistemic constraint — what the learner is permitted to infer about individuals — has made the knowable unknowable. The constraint isn’t on the system. It’s on the knower.

In physical systems, the framing effect manifests through disorder. Channelization transitions in erosion — the point where uniform seepage gives way to channeled flow — exhibit different transition characters depending on whether the disorder is quenched (frozen in place) or annealed (evolving with the system). Same material, same erosion, same transition. But the distinction between quenched and annealed is not a property of the material. It’s a property of how you model the heterogeneity. The model’s assumption about timescale determines whether you predict a continuous transition or a discontinuous one.

Even perception is conditional. Recent work in music cognition frames rhythmic meter as an ordered phase — a spontaneous symmetry-breaking in the listener’s temporal expectations. The same sonic signal can support multiple metrical interpretations. What counts as rhythm depends on whether the listener’s perceptual framework privileges regularity or variation. The framework constitutes the meter it detects. Two listeners hearing the same performance may, in a precise statistical-mechanical sense, be hearing different rhythms.

The formal backbone comes from the Information Bottleneck. Kline and Palmer showed that the Gaussian IB maps exactly onto soft-cutoff non-perturbative renormalization group flow. This means: what emerges at coarse scales depends entirely on what the bottleneck is asked to retain. The relevant variable Y determines the RG trajectory. Different Y produces different effective physics at every scale — different coupling constants, different fixed points, different phase structure. The choice of Y is the epistemic framework. Change it and you don’t just see different details of the same physics. You get qualitatively different physics.

The counterexample is instructive. Classical measurement of macroscopic properties seems framework-independent. The temperature of water doesn’t depend on which thermometer you use — assuming both are calibrated. In this regime, epistemics are unconditional. All frameworks agree.

But this works only in the thermodynamic limit, for coarse-enough questions. Ask whether this transition is first or second order, whether this system is chaotic or integrable, whether these correlations are long-range or short-range — and frameworks diverge. The unconditional regime is the degenerate limit, the place where the epistemic framework’s choice doesn’t matter because the question is coarse enough to absorb any framework’s bias. The interesting physics lives where the framework starts to matter.

This essay is the sixth in a sequence that began with boundaries, moved through compression, observation, and interaction order, and culminated in a capstone claim: descriptions participate in the structure they describe. Conditional epistemics sits at the center. The boundary has structure because different frameworks produce different boundary descriptions. Compression creates because what emerges depends on what the framework retains. Observation constitutes because the measurement framework determines the joint system. Three is optimal because the minimum framework for detecting synergy requires three elements.

The five previous essays make structural claims. This one asks a prior question: what determines which structures you can find? The answer is the framework — and the framework is never neutral.

Return to the heptalemma. Seven theses, seven possible sacrifices, one quantum mechanics. The physics is the same under every interpretation. What changes is the topology of permissible belief — which questions are well-formed, which experiments are decisive, which puzzles are problems and which are features.

The framework isn’t the answer. It’s the set of possible answers. And that set is not given by the world. It’s given by the knower’s relationship to the world — a relationship that constrains, shapes, and sometimes constitutes what the world can mean.