Necessity and Possibility: What Will Be Must Be?

Core idea

We often claim not merely that something is so but that it must be so, or that it could be so. Logicians write "necessarily a" as □a and "possibly a" as ◊a. These are modal operators — they express the mode in which a sentence is true. They are interdefinable: to say something must be true is to say it cannot fail to be true, so □a means the same as "not possibly not-a".

Unlike "and", "or", and "not", modal operators are not truth functions. Knowing that a sentence is false tells you nothing about whether it is possibly true. "I will rise before 7am" and "I will hover 2m above the bed" may both be false today, yet the first is possible and the second is not. The truth value of a simply does not fix the truth value of ◊a.

Why it matters

Possible worlds

The standard modern account explains modality through possible worlds, a term from Leibniz. Each situation s comes equipped with a set of situations that are possible relative to it — those that could arise without violating the laws of physics. Then ◊a is true in s if a is true in at least one of those worlds, and □a is true in s if a is true in all of them.

This neatly explains why modality is not truth-functional: two sentences false in s can differ wildly across the associated worlds. It also gives a test for modal inference. From "possibly a" and "possibly b" you may not infer "possibly a-and-b" — a might hold in one world, b in another, with no world holding both. But from "necessarily a" and "necessarily b" you may infer "necessarily a-and-b", since both hold in every world.

Aristotle's argument for fatalism

Fatalism is the view that whatever happens must happen — nothing could have been prevented. Aristotle argued for it like this. Either I will have an accident tomorrow or I will not. Suppose I will: then it is true that I will, and "if it is true that I will, then it cannot fail to be that I will" — so it must happen. The same reasoning covers the other case. So whatever happens, must happen.

Priest's argument: Aristotle's argument trades on an ambiguity — "if a then it cannot fail that b" can mean "if a is true, then b is necessary" or "necessarily, if a then b" — and only the second is correct here.

The correct reading is that necessarily, if a statement is true then what it says is the case — a fixed link across all worlds. The argument needs the other reading: that given the statement is true, the outcome is necessary. That step does not follow. So Aristotle's argument, resting on a quantifier-of-modality confusion, is invalid.

The crack: fatalism from the fixed past

Defusing Aristotle is not the end. There is a stronger argument. Statements about the past, if true, are now necessarily true — nothing can make the Battle of Hastings have been fought in 1067. Now take a claim about tomorrow. If it is true, then anyone who had uttered it 100 years ago would have spoken truly — so it was true a century ago. That makes it a true statement about the past, hence necessarily true now. The same goes for any future event. This argument does not commit Aristotle's fallacy. So is fatalism true after all? Priest leaves the question open.

Key takeaways

Mental model

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Practical application

When an argument moves from "it is true that X" to "X is necessary" or "X is unavoidable", pause. Distinguish necessarily, if the report is accurate then the event occurs — a harmless logical link — from given that the report is accurate, the event is now fixed. Conflating these is the engine of fatalism, and of much fatalistic comfort-thinking after the fact.

Example

A project lead says: "The launch slipped, and since it slipped, it was bound to slip — there was nothing we could do." The reasoning mirrors Aristotle. It is indeed necessarily true that if the launch slipped, then the launch slipped. But that does not make slipping unavoidable: in many possible worlds — better staffing, earlier testing — the launch held. The team's powerlessness does not follow from the bare truth of "it slipped." Treating a realised outcome as a necessary one converts hindsight into false consolation.

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