Ontic vs epistemic

What exists is one question; what a context lets you say is another. Most quantum paradoxes are category errors between the two.

definition · a definition, no claim attached

In plain terms

Here is the problem. Quantum mechanics keeps two kinds of statement in one notation. "The atom is here" sounds like a fact about the world. "The atom has a 30 percent chance of being here" sounds like a fact about what you know. The wavefunction carries both voices at once, and a century of argument has been about which voice is fundamental.

The map-versus-territory distinction is old and boring until you enforce it. Ontic: belonging to the territory, true whether or not anyone looks. Epistemic: belonging to the map some agent or apparatus draws. The trouble starts when a map-fact is mistaken for a territory-fact -- when a change in the description is read as a change in the world.

Collapse is the canonical casualty. If the state is a map, its abrupt update on measurement is no stranger than a weather forecast changing when you open the curtains.

In CSD

CSD makes the split load-bearing and never lets it blur. The outcome regions a measurement context defines live on the projected state space, and they are epistemic: the apparatus fixes the partition, and the partition is a description. The measure that weights those regions is ontic: an invariant volume on the constraint surface itself, fixed by symmetry, indifferent to anyone's knowledge.

The Born rule is precisely the handshake: an epistemic region, weighed by an ontic volume. Measurement is the ontic selection -- the record, on the surface -- of which epistemic region the one real trajectory realises. Keeping the two levels distinct is not philosophical hygiene; it is the structure of the reconstruction.

Mathematically

The two-strata reading is written into the axiom ledger. The operational stratum speaks the effect-and-density language and carries the Gleason-type representation; the ontic stratum computes weights as ratios of the Liouville measure over the preparation region. The corpus proves the two strata meet: the same Born vector is reached by the operational route and by the volume route, through structurally distinct machinery.

Related
constraint surface, outcome region, psi epistemic, typicality volume, collapse

Source links are pinned to a commit, so they do not drift. The anchors above are checked mechanically against the Lean tree on every build. The mathematics is not, and cannot be: that is a human responsibility and it rests with the author.

Part of Constraint-Surface Dynamics · Formalised in csd-lean4.

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