Logical possibility

Logical possibilityrefers to alogical propositionthat cannot be disproved, using theaxiomsand 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 frominconsistent propositionsor even allow fortrue contradictions.Other logical systems havemore than two truth-valuesinstead of abinaryof such values. Some assume the system in question isclassical 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.

Inmodal logic,alogical propositionis possible if it is true in somepossible world.The universe of "possible worlds" depends upon the axioms and rules of thelogical systemin which one is working, but given some logical system, anylogically consistentcollection 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 andmetaphysics,for example, many philosophers followingSaul Kripkehave held thatdiscovered identitiessuch as "Hesperus = Phosphorus" are metaphysically necessary because they pick out thesame objectin 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 philosophersare of the view that logical possibility is broader than metaphysical possibility, so that anything which is metaphysically possible is also logically possible.

See also

• Modal logic
• Paraconsistent logic
• Paradox
• Possibility theory
• Possible world
• Subjunctive possibility

Bibliography

• Brian F. Chellas (1980).Modal Logic: An Introduction.Cambridge University Press.ISBN978-0-521-29515-4.