Possibility and Necessity, Informally

The previous article leaned on a sentence that describes nothing actual. "Had the match not been struck, it would not have lit" is not made true by the match, which was struck, and is not made true by the lighting, which happened. Whatever makes it true, it is something about how things could have gone rather than about how they went. That is the subject matter of this article, and it is used constantly outside philosophy: engineers ask what a bridge could withstand, lawyers ask what a reasonable person could have foreseen, and doctors ask what might have prevented a death.

The basic vocabulary

The last phrase is the point of the whole subject. "The window is broken" reports how the world stands. "The window could have survived" and "the window had to break, given the speed of the ball" say something further about the standing of that fact, and no amount of looking at the window settles them.

Possibility and necessity are each definable from the other, and the equivalence is worth having explicitly. Something is necessary exactly when its denial is not possible, and something is possible exactly when its denial is not necessary. Impossibility is then necessary falsehood. One primitive notion suffices, and which one is taken as primitive is a matter of convenience.

Almost everything anyone knows is contingent in this sense. That there are eight planets, that Rome was founded, that you are reading this. Each is true and each could have been otherwise. The interesting claims are the ones on the other side of the line, and the argument is always about where the line falls.

Kinds of possibility

The single word "possible" covers several standards at once, and most confusion about modality comes from sliding between them.

By this standard a great deal is possible. A person can jump to the moon without contradiction. Nothing in the meanings of the words rules it out, and the reason it will not happen is a fact about legs and gravity rather than about logic. What logical possibility excludes is very little: round squares, married bachelors, and the like.

A narrower standard takes the laws of nature as fixed. What is possible in this sense is what those laws permit, so the jump to the moon is out and a hundred-metre sprint in seven seconds is out, while a great deal that has never happened remains in. This standard is often called physical or nomological possibility, and it is the one working scientists mostly use.

The third standard is the philosophically contested one, and the case for needing it comes from examples that the other two classify wrongly.

Consider water. Nothing in logic rules out water being an element rather than a compound, since no contradiction is derivable from the supposition, so it is logically possible. Yet Saul Kripke argued that if water is in fact H₂O, then it could not have been anything else, because being that compound is what water is. The impossibility is not logical and it is not a matter of the laws of nature either, since we are not asking what the laws allow but what water is. Something narrower than logical possibility and different in kind from physical possibility is doing the work.

The three standards are usually taken to nest, with logical possibility the widest, metaphysical possibility narrower, and physical possibility narrower still. That ordering is the working picture rather than a settled result. Whether every metaphysical possibility is a logical one, and whether the boundary between the first two is sharp at all, remain live questions, and the intermediate tier takes them up with better tools.

What modal claims are about

Two accounts of what makes modal claims true dominate the literature, and both are developed later.

The first treats them as claims about complete alternative situations. On this way of speaking, a claim is possible when it holds in at least one such situation and necessary when it holds in all of them. The apparatus is enormously useful and it postpones rather than answers the question, since what those situations are, and whether any of them exist, is itself disputed. The logic ladder develops the formal machinery, and the metaphysics intermediate tier asks what the machinery commits you to.

The second takes modal facts to be grounded in the natures of the things involved, so that a claim is necessary because of what its subject matter is. The water example above has this shape. This approach was largely displaced during the twentieth century and has been revived, and the advanced tier follows the revival.

Where this leads

Two consequences carry into the next article.

Once possibility is available, questions can be asked about a thing that no examination of it will answer. Not what colour it is, but whether it could have been another colour. Not what it is made of, but whether it could have been made of something else and still been that thing.

Those questions divide a thing's properties into two groups, and the division is the oldest use to which modal notions have been put.