Today is sunny at Waitarere Beach. The sea is sparkling, the sky is blue, the air is calm and it feels good to be alive.

(1) But it wasn't sunny yesterday. Yesterday was grey, wet and windy, and we were depressed.

(2) But it didn't have to be sunny today. It might have been grey, wet and windy, and we would have been depressed.

What have (1) and (2) in common? Begin with (1). Suppose that today is Tuesday, meaning obviously some particular Tuesday. Then (1) is true on Tuesday because there was rain (and it was grey and windy and so on …) on Monday. That seems like common sense. It also seems common sense that rain is something that can occur on one day – Monday – and fail to occur on another day – Tuesday. What then should be said about (2)? We shall assume in this book that sentences about what is necessary or about what is possible have literal truth values. Our aim is to introduce you to a way of dealing with (2) which is exactly parallel with the way of dealing with (1) that we have just mentioned. This came about with the advent of the possible-worlds semantics for modal logic – the logic of necessity and possibility – in the early 1960s. Corresponding to the times Monday and Tuesday and so on, at which things happen, philosophers began to speak of the possible worlds in which they happen – so that (2) is true because in some possible but non-actual world there is rain today (at Waitarere), even though in the actual world it is sunny.