Logical possibility refers to a logical proposition that cannot be disproved, using the axioms 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. However, when talking about logical possibility, it is often assumed that the system in question is

classical propositional logic Propositional calculus is a branch of logic. It is also called propositional logic, statement logic, sentential calculus, sentential logic, or sometimes zeroth-order logic. It deals with propositions (which can be true or false) and relations ...

. 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 collection of formal systems developed to represent statements about necessity and possibility. It plays a major role in philosophy of language, epistemology, metaphysics, and natural language semantics. Modal logics extend ot ...

, a logical proposition is possible if it is true in some possible world. The universe of "possible worlds" depends upon the axioms and rules of the

logical system A formal system is an abstract structure used for inferring theorems from axioms according to a set of rules. These rules, which are used for carrying out the inference of theorems from axioms, are the logical calculus of the formal system. A for ...

in which one is working, but given some logical system, any

logically consistent In classical deductive logic, a consistent theory is one that does not lead to a logical contradiction. The lack of contradiction can be defined in either semantic or syntactic terms. The semantic definition states that a theory is consiste ...

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 should be distinguished from other sorts of subjunctive possibilities. But 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 studies the fundamental nature of reality, the first principles of being, identity and change, space and time, causality, necessity, and possibility. It includes questions about the nature of conscio ...

, for example, many philosophers following

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

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. However, it is nonetheless ''logically'' possible for “Hesperus = Phosphorus” to be false, since denying it doesn't violate a logical rule such as consistency. Other philosophers are also of the view that logical possibility is broader than metaphysical possibility, so that anything which is metaphysically possible is also logically possible.

References

* {{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