Possibility

What could be the case, whether or not it is - and the question of what makes such a claim true.

Theme: Being and reality
Tradition: Western
Term fixed: c. 330 BC

In plain terms

Some things are not the case but could have been. You could have caught an earlier train. There could have been no rain today. Claims like these are used constantly, taken to be true or false, and they are not about anything that happened.

So what makes one of them true? Not observation, since there is nothing to observe. Saying it is possible because we can imagine it will not do either, since people have imagined plenty of impossible things and failed to imagine perfectly possible ones.

And possible has several senses that get run together. Not ruled out by logic is one. Not ruled out by physics is a much narrower one. Not ruled out by circumstances is narrower again, and it is usually the one people mean.

As a philosopher would put it

Aristotle's account ties possibility to potentiality in things: what is possible is what some actual thing has the power to become. The modern treatment detaches it - a proposition is possible if true at some possible world - which gives a clean semantics for modal logic and immediately raises the question of what possible worlds are.

Lewis's modal realism takes them to be as real as this one, differing only in that we are here; the ontological cost is enormous and the theory is otherwise well behaved. Actualists take them to be constructions out of the actual - maximal consistent sets of propositions, or ways things could have been - which is cheaper and makes the truthmaker harder to identify.

The kinds have to be kept apart. Logical possibility is freedom from contradiction; metaphysical possibility is what could have been the case given the natures of things, and on Kripke's account water could not have failed to be H₂O even though no contradiction is involved in saying so; epistemic possibility is only what we do not know to be false, which is why it might be raining and it could have rained are different claims.

Where you meet it

A patent office has to decide, every working day, what is possible. An application is refused if the invention lacks industrial applicability or if the description does not enable a skilled person to make it work, and the burden falls on the applicant.

Perpetual motion machines are the standing case. The United States Patent Office has required a working model for them since the nineteenth century, and the European Patent Office refuses them under the enablement requirement rather than by arguing thermodynamics with the applicant. The refusal is not that the device does not exist - almost nothing in a patent application exists yet - but that the description could not be made to work.

What the office is doing is drawing a line between not yet actual and not possible, on evidence, with money and legal consequences attached. And its criterion is neither logic nor imagination: the applications are perfectly coherent and were imagined in detail. The criterion is the natures of the things involved, which is metaphysical possibility being applied by clerks.

What is actually disputed

What makes a possibility claim true.

If possible worlds are real, the semantics is clean and the ontology is extravagant beyond anything else in philosophy. If they are constructions out of the actual world, the ontology is modest and the account risks circularity, since a maximal consistent set is defined using a notion of consistency that is itself modal.

A second dispute concerns whether metaphysical possibility is a real category at all, or whether it collapses into either logical possibility or physical possibility, with the intermediate cases being disguised claims about meaning. And a third asks how anyone could know: unlike facts about the actual world, modal facts have no obvious causal contact with us, which makes modal knowledge as puzzling as mathematical knowledge and for similar reasons.

Defined against

Necessity The two are interdefinable - what is necessary is what could not have been otherwise - and neither is analysable without the other

Philosophers

Aristotle Possibility as the potentiality of actual things
Gottfried Wilhelm Leibniz Possible worlds, and the best of them
David Hume Whatever is distinctly conceivable is possible - the criterion, and its trouble
Immanuel Kant The modal categories as forms of judgement rather than features of things
Willard Van Orman Quine The case that modal notions should be avoided altogether

Works

Metaphysics The modal vocabulary in its first systematic form
Monadology Possible worlds, and why this one was chosen
A Treatise of Human Nature Conceivability as the test
Naming and Necessity The separation of the metaphysical from the epistemic
Critique of Pure Reason Modality as a category of judgement

Schools

Peripatetic school (Aristotelianism) Possibility grounded in things rather than in worlds
Avicennism The possible-in-itself, and the argument from contingency
British Empiricism Conceivability as the criterion
Vienna Circle Where modal talk is regarded with suspicion

Related concepts

Necessity c. 330 BC · Contingency c. 1020 · Potentiality c. 330 BC · Actuality c. 330 BC · Imagination c. 330 BC

Aristotle sets out the modal vocabulary; the modern treatment begins with Leibniz's possible worlds and becomes formal machinery in the twentieth century.