SEMANTIC / SYSTEMS Logic & Linguistics (English) 0 / 14 read

Modality

The database must have rejected the write.

— No, nothing in the policy requires rejection there.

The reply is perfectly reasonable English and completely fails to engage. The first speaker was not describing a rule. They were reasoning: given the logs and what we know about the system, rejection is the only explanation still standing. The second speaker heard an obligation and produced evidence about obligations. Both used the same word, and the conversation is now two conversations.

One must is epistemic — necessity given what is known. The other is deontic — necessity given some set of rules. They are refuted by entirely different things. You defeat an epistemic must by producing another explanation the evidence permits. You defeat a deontic must by showing the rule does not exist, does not apply here, was overridden, or came from someone with no authority to issue it. Calling both of them “necessity” conceals the only thing that would settle the argument.

Force and background

Modality is talk about possibility and necessity relative to a set of alternatives, and every modal claim has two moving parts.

Force is how much of the alternative set the claim covers. Does it require merely that some acceptable alternative fits (may, might, can), or that all of them do (must, cannot)? That is the difference between possibility and necessity, and it is the part English marks clearly.

Background is which alternatives count as acceptable, and English marks it almost not at all. Acceptable according to the evidence? The regulations? The laws of physics? The current plan? A person’s abilities? “The door can open” may report a working mechanism. “You can open the door” may grant permission. “That can be the cause” records an epistemic possibility. Nothing in the word can distinguishes them; the background comes entirely from context, and when context is thin or contested, the sentence is not yet a claim.

Formal treatments make this precise — a set of relevant facts, plus an ordering that ranks the remaining possibilities by how well they satisfy the relevant rules or ideals. I will keep saying background for both parts, which is looser than the theory but exact enough for the question that actually unsticks modal disputes:

Given what, exactly?

“We cannot delay.” Delay is physically impossible? Contractually forbidden? Too expensive under the current budget? Incompatible with a goal somebody chose last quarter? Or simply unwelcome? Five readings, five different sets of alternatives, five different kinds of evidence that would refute the claim — and one sentence that hides which one you are being asked to accept.

The families of background

Epistemic backgrounds are made of evidence. “The key may be expired” says expiry is consistent with what we know. “The key must be expired” says every serious possibility left open by the evidence involves expiry. “The key cannot be expired” says expiry conflicts with it.

Epistemic must is strong and defeasible at the same time, which sounds contradictory and is not. “The lights are off, the car is gone, nobody answers — they must be out” is a responsible conclusion that could still be wrong, because the necessity is relative to an information state, not to the world. There is a well-known consequence worth noticing: “It must be raining” is in one sense weaker than the bare “It is raining,” because must advertises that you inferred it rather than looked. A speaker at the window does not say must.

When stakes are high, the information state should be stated. “Given the access logs and the clock synchronization, the request must have originated after 14:00” is an inference with its premises attached, and each premise can be audited. “It must have happened after 14:00” leaves the evidential background suppressed.

Deontic backgrounds are made of norms: law, policy, contract, promise, role, or somebody’s instruction. “The custodian must retain the record” is an obligation. “The custodian may destroy the duplicate” is a permission. “The custodian must not disclose the key” is a prohibition.

Every deontic claim has a source and a bearer, and English lets you omit both. Who made the rule, on what authority, on whom does it fall, and under what conditions? “We have to do this” is unfinished when the completion could equally be “the statute requires it,” “our director prefers it,” or “our current plan assumes it.” Those three sit at wildly different distances from being renegotiable, and the sentence flattens all three into the same shape.

Permission has scope as well as a bearer. “The Provider may terminate the agreement” gives the Provider an option. It does not predict termination, and it grants the Customer nothing. In legal drafting may is almost always normative; in ordinary prose it usually is not, and the two registers collide constantly.

Dynamic backgrounds are made of capacities — what an agent or object is able to do. “Rae can read Mandarin” is an acquired skill. “This material can bend without cracking” is a disposition under suitable conditions. “The service can process 10,000 requests per second” is a capacity under some load model that the sentence does not describe.

Ability claims survive by hiding their enabling conditions. Ten thousand requests per second on which hardware, with which request mix, at what latency bound, with what error rate? A person can perform the task with which tools, preparation, and help? Can asserts that success is available under some conditions. It never predicts that the event will occur.

Circumstantial backgrounds are made of the surrounding facts, independent of anyone’s permission or skill. “The convoy can leave before dawn” may mean the road, the fuel, and the schedule allow it. Watch how readily this collapses into its neighbors: “The patient cannot be moved” could be a medical fact, an equipment limit, or a court order, and the three call for three different responses from the person hearing it.

Goal-relative backgrounds — also called teleological — measure options against an objective. “To meet the deadline, we must cut scope or add capacity.” “You can reduce variance by increasing the sample.” This is the most fragile family, because the necessity evaporates if the goal changes or if the listed alternatives were never exhaustive. “We must launch Friday” typically unpacks as Friday is necessary given the revenue target, the current staffing assumption, and a refusal to reduce scope — and any of those three may be far more negotiable than the conclusion they support.

Four words, and what they cost

Can. “Can I leave?” conventionally asks permission, though its literal shape asks about ability, which is why answering “yes, you are physically capable” is either a joke or an act of obstruction. In specifications the vagueness stops being funny. “Administrators can revoke tokens” might describe an implemented capability, might grant authorization, or might report only that revocation happens somewhere in the system by some means. Those are three different builds. Write “the system provides administrators with a revocation control” when you mean capability, and “only administrators are authorized to revoke tokens” when you mean permission.

May alternates between epistemic possibility and deontic permission, with nothing but context to separate them. “The export may contain personal data” is a possibility. “The auditor may inspect the export” is a permission. Now negate the second: “The auditor may not inspect the export” is genuinely ambiguous between perhaps the auditor will not inspect it and the auditor is forbidden to inspect it. Legal prose defaults to prohibition, ordinary predictive prose to uncertainty, and a reader outside their home register has no way to tell. Might not and is prohibited from cost two words and remove the ambiguity entirely.

Must keeps its abstract necessity force and changes its background. “The process must be stuck; CPU use is zero” is evidence. “The process must be isolated under policy” is a rule. “To inspect its memory safely, we must isolate it” is means and end. The formal force remains stable even though pragmatic confidence can vary; what changes most sharply is what would count as a refutation. This is the opening exchange again, and the practical rule is symmetrical: an argument about policy cannot touch a diagnostic inference, and evidence of CPU activity cannot repeal a policy.

Should is the softest and the most often abused. It marks a defeasible norm (“you should disclose the conflict”), an expectation (“the package should arrive today”), or a model-based prediction (“this index should make lookup constant-time”). It is usually analyzed as weak necessity — necessity across the best alternatives rather than all of them — which is why should tolerates exceptions that must does not. That softness quietly disposes of responsibility. “The backup should run nightly” leaves an operator unable to say whether nightly execution is required, expected, or merely a good idea, and it will be read as whichever reading is most convenient after the backup fails to run. A requirement says shall or is required to and names its enforcement condition. A forecast names its assumptions.

Negation lands on one side or the other

Negation can sit inside the modal’s scope or outside it, and the two produce opposite instructions.

Same modal, same negative, opposite guidance. The pattern repeats across the vocabulary: “The key cannot be valid” rules validity out, while “The key may not be valid” leaves invalidity merely open — and in a deontic setting shifts to prohibition. “The service is not able to recover every file” denies complete recovery and says nothing against partial recovery; “the service is able to recover no file” is the other claim entirely.

English does hand you unambiguous pairs for the common cases — must not against need not, cannot against might not. When a writer uses one negative modal for both jobs, the ambiguity is manufactured, not inherited.

Time and aspect

Modality and time interact, and the combination decides whether anything actually happened.

“She must have left” is a present inference about a past departure — epistemic, and the departure is asserted only as the conclusion of the inference. “She had to leave” reports past necessity; context often suggests that she left, but an obligation alone does not entail compliance. “She should have left” usually marks an unfulfilled obligation and carries criticism, though in the right context it is an expectation about what probably occurred. “She was allowed to leave” records a past permission and tells you nothing about whether she used it.

Aspect matters too, in ways that are easy to miss. Could in the past leaves the event open — “she could swim across” does not say she did — while the perfective “she was able to swim across” usually reports that she did, an effect known as an actuality entailment. Similarly “the job was supposed to finish” does not entail completion, while “the job managed to finish” does. Before treating a modal sentence as a report of events, check whether it asserts an outcome, expects one, requires one, or merely permits one.

Backgrounds are where the argument is hiding

Modal disagreements almost never turn out to be disagreements about force. They turn out to be disagreements about background that were never surfaced.

We must retain all logs.

Four backgrounds fit that sentence. Retention may be what every action compliant with the regulation involves; what every action consistent with current internal policy involves; what every action preserving our forensic options involves; or what every action compatible with the present storage design involves. The first is a legal requirement, the second a revisable choice made by people in this building, the third a goal-relative recommendation, and the fourth a contingent technical fact that a migration could erase. Four arguments, four different counterparties, one word.

That compression is easy to exploit, and the exploitations are recognizable:

The repair is never to strip out modal language, which would make ordinary planning impossible. It is to name the parameter: “Under the regulation, retention is required.” “Given the current evidence, expiry is likely.” “With existing hardware, throughput cannot exceed X.” “To preserve the launch date, scope reduction is necessary.” Each of those can now be checked by someone, which is the entire point.

Four readings, worked

An incident report. “The database must have rejected the write.” The force is necessity and the background is epistemic: whatever logs, invariants, and architectural assumptions the speaker is reasoning from. What would defeat it is evidence of an accepted write, an alternative path producing the same symptom, or a bad assumption about what the logs record. What it does not establish is that rejection was correct, or required by anything. This is where the chapter opened, and the reply about policy failed because it attacked a background the speaker was never using.

An employment policy. “Managers may review employee messages when necessary.” May here grants permission; it does not predict that reviews will happen. Then necessary smuggles in a second modal, and its background is entirely unstated — necessary for what objective, judged against what standard, and decided by whom? Note also what the sentence leaves unbounded: all messages, or only those relevant to whatever triggered the necessity? The clause looks constrained and in fact delegates its own limits to an undefined modal judgment made later by the party it constrains.

A product claim. “The model can detect fraud.” On the weakest existential ability reading this is satisfied by conditions under which detection succeeds — perhaps one demonstration on one dataset. The reading a buyer takes away is that the model reliably detects fraud in their population, which the sentence never said. Everything that matters is in the background: the definition of fraud, the base rate, the decision threshold, the cost of false positives, the data distribution, and the criterion for calling performance adequate. Can clears a very low bar. Operational use needs a calibrated tendency claim instead.

An executive claim. “We cannot miss the quarter.” Literal impossibility is not on offer; quarters get missed. So the sentence is doing something else — expressing a goal, forecasting a severe consequence, or issuing a prohibition — and until it says which, no plan can be built on it. Compare “missing the quarter would trigger the debt covenant” with “leadership will not accept missing the quarter.” The first is a fact about a contract with a determinate consequence. The second is a fact about people, negotiable by talking to them. Cannot covers both and commits to neither.

Modality gets precise when four questions have answers: what force, which background, whose authority or ability, and what would change the set of live alternatives. Until then, can and must are reporting a frame someone chose, and presenting it as a fact about the world.