A logically possible proposition is one which is consistent with the axioms of a given system of logic. In other words, the logical possibility of a proposition will depend on the system of logic being considered, rather than violation of any single rule. Some systems of logic tolerate inconsistent propositions or even true contradictions, while other logical systems have truth-value gaps instead of a binary of such values. However, when talking about logical possibility it is often understood that the system in question is classical propositional logic.
Logical possibility should be distinguished from other sorts of subjunctive possibilities. For example, it may be logically possible for the universe's physical laws to be different from what they actually are. If it is, then many things which we would normally consider to be demonstrably impossible can be logically possible: for example, traveling faster-than-light might be possible or escaping from black holes is not impossible. Many philosophers, then, have held that these scenarios are logically possible but nomologically impossible (impossible under the actual laws of nature).
With this understanding of logical possibility in mind, other logical modalities may be defined in terms of it: a proposition is logically necessary if it is not logically possible for it to be false within some system of logic, logically impossible if it is not logically possible for it to be true in a system of logic, and logically contingent if it is logically possible for it to be true and logically possible for it to be false in some system of logic. Logical possibility can be further distinguished from metaphysical possibility, as the former refers to what is permissible in a system of logic, while the latter concerns what can be true at (or exist in) some possible world. Given the aforementioned description of logical possibility, some propositions can be logically possible (in a system of logic) and yet metaphysically impossible, or even logically impossible (in a system of logic) and yet be true of the world.
- Vaidya, Anand. "The Epistemology of Modality". Stanford Encyclopedia of Philosophy. Stanford Encyclopedia of Philosophy. Retrieved 10/10/205. Check date values in:
- Do Modal Claims Imply the Existence of Possible Worlds?, paper criticizing David Lewis' theory of possibility.