Logical possibility refers to a logical proposition that cannot be disproved, using the

axioms An axiom, postulate, or assumption is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments. The word comes from the Ancient Greek word (), meaning 'that which is thought worthy or f ...

and rules of a given system of logic. The logical possibility of a proposition will depend upon the system of logic being considered, rather than on the violation of any single rule. Some systems of logic restrict inferences from inconsistent propositions or even allow for true contradictions. Other logical systems have more than two truth-values instead of a binary of such values. Some assume the system in question is classical propositional logic. Similarly, the criterion for logical possibility is often based on whether or not a proposition is contradictory and as such, is often thought of as the broadest type of possibility. In

modal logic Modal logic is a kind of logic used to represent statements about Modality (natural language), necessity and possibility. In philosophy and related fields it is used as a tool for understanding concepts such as knowledge, obligation, and causality ...

, a logical proposition is possible if it is true in some

possible world A possible world is a complete and consistent way the world is or could have been. Possible worlds are widely used as a formal device in logic, philosophy, and linguistics in order to provide a semantics for intensional and modal logic. Their met ...

. The universe of "possible worlds" depends upon the axioms and rules of the

logical system A formal system is an abstract structure and formalization of an axiomatic system used for deducing, using rules of inference, theorems from axioms. In 1921, David Hilbert proposed to use formal systems as the foundation of knowledge in math ...

in which one is working, but given some logical system, any logically consistent collection of statements is a possible world. The modal diamond operator

\lozenge

is used to express possibility:

\lozenge P

denotes "proposition

P

is possible". Logical possibility is different from other sorts of subjunctive possibilities. The relationship between modalities (if there is any) is the subject of debate and may depend upon how one views logic, as well as the relationship between logic and

metaphysics Metaphysics is the branch of philosophy that examines the basic structure of reality. It is traditionally seen as the study of mind-independent features of the world, but some theorists view it as an inquiry into the conceptual framework of ...

, for example, many philosophers following

Saul Kripke Saul Aaron Kripke (; November 13, 1940 – September 15, 2022) was an American analytic philosophy, analytic philosopher and logician. He was Distinguished Professor of Philosophy at the Graduate Center of the City University of New York and emer ...

have held that discovered identities such as "Hesperus = Phosphorus" are metaphysically necessary because they pick out the same object in all possible worlds where the terms have a referent. It is logically possible for “Hesperus = Phosphorus” to be false, since denying it does not violate a logical rule such as consistency. Other philosophers are of the view that logical possibility is broader than metaphysical possibility, so that anything which is metaphysically possible is also logically possible.

References

Bibliography

* {{cite book, author=Brian F. Chellas, title=Modal Logic: An Introduction, url=https://books.google.com/books?id=YupiXWV5j6cC, date=1980, publisher=Cambridge University Press, isbn=978-0-521-29515-4 Modal logic Possibility

See also

References

Bibliography