Editing Logical possibility

{{original research|date=February 2015}}

'''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  [[Paraconsistent logic|inconsistent propositions]] or even allow for [[Dialetheism|true contradictions]]. Other logical systems have [[Many-valued logic|more than two truth-values]] instead of a [[Principle_of_bivalence|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]], 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]] in which one is working, but given some logical system, any [[Logical consistency|logically consistent]] collection of statements is a possible world. The modal diamond operator <math>\lozenge</math> is used to express possibility: <math>\lozenge P</math> denotes "proposition <math>P</math> is possible".<ref name=Vaidya322>{{cite web|last1=Vaidya|first1=Anand|title=The Epistemology of Modality|url=http://stanford.library.usyd.edu.au/archives/sum2014/entries/modality-epistemology/|website=Stanford Encyclopedia of Philosophy|date=5 December 2007 |publisher=[[Stanford Encyclopedia of Philosophy]]|access-date=10 October 2015|ref=Vaidya}}</ref>

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]], for example, many philosophers following [[Saul Kripke]] have held that [[A posteriori necessity|discovered identities]] such as "Hesperus =  Phosphorus" are metaphysically necessary because they pick out the [[Rigid designator|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{{who?|date=April 2023}} are 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]]

==References==
{{reflist}}

==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}}

[[Category:Modal logic]]
[[Category:Possibility]]