linguistic:paraphrasing, structural:summarization, structural:scholar_edition
Possibility and necessity

The concepts of possibility and necessity convey what can or must be the case, expressed in statements like "it is possible to find a cure for cancer" and "it is necessary that two plus two equals four". They belong to modal metaphysics, which investigates the metaphysical principles underlying them, in particular, why it is the case that some modal statements are true while others are false. Some metaphysicians hold that modality is a fundamental aspect of reality, meaning that besides facts about what is the case, there are additional facts about what could or must be the case. A different view argues that modal truths are not about an independent aspect of reality but can be reduced to non-modal characteristics, for example, to facts about what properties or linguistic descriptions are compatible with each other or to fictional statements.

Borrowing a term from German philosopher Gottfried Wilhelm Leibniz 's theodicy, many metaphysicians use the concept of possible worlds to analyze the meaning and ontological ramifications of modal statements. A possible world is a complete and consistent way of how things could have been. For example, the dinosaurs were wiped out in the actual world but there are possible worlds in which they are still alive. According to possible world semantics, a statement is possibly true if it is true in at least one possible world while it is necessarily true if it is true in all possible worlds. Modal realists argue that possible worlds exist as concrete entities in the same sense as the actual world, with the main difference being that the actual world is the world we live in while other possible worlds are inhabited by counterparts. This view is controversial and various alternatives have been suggested, for example, that possible worlds only exist as abstract objects or that they are similar to stories told in works of fiction.