Editing Modal logic (section)

===Alethic logic===
{{main|Subjunctive possibility}}
Modalities of necessity and possibility are called ''alethic'' modalities. They are also sometimes called ''special'' modalities, from the [[Latin]] ''species''. Modal logic was first developed to deal with these concepts, and only afterward was extended to others. For this reason, or perhaps for their familiarity and simplicity, necessity and possibility are often casually treated as ''the'' subject matter of modal logic. Moreover, it is easier to make sense of relativizing necessity, e.g. to legal, physical, [[nomological]], [[epistemic]], and so on, than it is to make sense of relativizing other notions.

In [[classical modal logic]], a proposition is said to be
*'''possible''' if it is ''not necessarily false'' (regardless of whether it is actually true or actually false);
*'''necessary''' if it is ''not possibly false'' (i.e. true and necessarily true);
*'''contingent''' if it is ''not necessarily false'' and ''not necessarily true'' (i.e. possible but not necessarily true);
*'''impossible''' if it is ''not possibly true'' (i.e. false and necessarily false).

In classical modal logic, therefore, the notion of either possibility or necessity may be taken to be basic, where these other notions are defined in terms of it in the manner of [[De Morgan duality]]. [[Intuitionistic modal logic]] treats possibility and necessity as not perfectly symmetric.

For example, suppose that while walking to the convenience store we pass Friedrich's house, and observe that the lights are off. On the way back, we observe that they have been turned on.
* "Somebody or something turned the lights on" is ''necessary''.
* "Friedrich turned the lights on", "Friedrich's roommate Max turned the lights on" and "A burglar named Adolf broke into Friedrich's house and turned the lights on" are ''contingent''.
* All of the above statements are ''possible''.
* It is ''impossible'' that [[Socrates]] (who has been dead for over two thousand years) turned the lights on.
(Of course, this analogy does not apply alethic modality in a ''truly'' rigorous fashion; for it to do so, it would have to axiomatically make such statements as "human beings cannot rise from the dead", "Socrates was a human being and not an immortal vampire", and "we did not take hallucinogenic drugs which caused us to falsely believe the lights were on", ''ad infinitum''. Absolute certainty of truth or falsehood exists only in the sense of logically constructed abstract concepts such as "it is impossible to draw a triangle with four sides" and "all bachelors are unmarried".)

For those having difficulty with the concept of something being possible but not true, the meaning of these terms may be made more comprehensible by thinking of multiple "possible worlds" (in the sense of [[Gottfried Wilhelm Leibniz|Leibniz]]) or "alternate universes"; something "necessary" is true in all possible worlds, something "possible" is true in at least one possible world. 

====Physical possibility====
Something is physically, or nomically, possible if it is permitted by the [[physical law|laws of physics]].{{citation needed|date=January 2016}} For example, current theory is thought to allow for there to be an [[atom]] with an [[atomic number]] of 126,<ref>{{cite news|title=Press release: Superheavy Element 114 Confirmed: A Stepping Stone to the Island of Stability|url=http://newscenter.lbl.gov/2009/09/24/114-confirmed/|work=Lawrence Berkeley National Laboratory|date=24 September 2009}}</ref> even if there are no such atoms in existence. In contrast, while it is logically possible to accelerate beyond the [[speed of light]],<ref name="Feinberg67">{{cite journal |last=Feinberg |first=G. |year=1967 |title=Possibility of Faster-Than-Light Particles |journal=[[Physical Review]] |volume=159 |issue=5 |pages=1089–1105 |bibcode=1967PhRv..159.1089F |doi=10.1103/PhysRev.159.1089}} See also Feinberg's later paper: Phys. Rev. D 17, 1651 (1978)</ref> modern science stipulates that it is not physically possible for material particles or information.<ref>{{cite journal | last = Einstein | first = Albert | author-link = Albert Einstein | title = Zur Elektrodynamik bewegter Körper | journal = Annalen der Physik | volume = 17 | pages = 891–921 | date = 1905-06-30|bibcode = 1905AnP...322..891E |doi = 10.1002/andp.19053221004 | issue = 10 | url = http://sedici.unlp.edu.ar/handle/10915/2786 | doi-access = free }}</ref> Physical possibility does not coincide with empirical possibility.<ref>{{cite journal | last = Gyenis | first = Balazs | author-link = Balazs Gyenis | title = Physical, Empirical, and Conditional Inductive Possibility | journal = Philosophy of Physics | volume = 3 | pages = 1-22 | date = 2025-03-03|doi = 10.31389/pop.148 | issue = 1 | url = https://philosophyofphysics.lse.ac.uk/articles/10.31389/pop.148 | doi-access = free | url-access = subscription }}</ref>

====Metaphysical possibility====
{{Main|Modal metaphysics}}
[[Philosophers]]{{who|date=April 2012}} debate if objects have properties independent of those dictated by scientific laws. For example, it might be metaphysically necessary, as some who advocate [[physicalism]] have thought, that all thinking beings have bodies<ref>{{cite web|last1=Stoljar|first1=Daniel|title=Physicalism|url=http://plato.stanford.edu/entries/physicalism/|website=The Stanford Encyclopedia of Philosophy|access-date=16 December 2014}}</ref> and can experience the passage of [[time]]. [[Saul Kripke]] has argued that every person necessarily has the parents they do have: anyone with different parents would not be the same person.<ref>Saul Kripke ''Naming and Necessity'' Harvard University Press, 1980, p. 113.</ref>

[[Metaphysical possibility]] has been thought to be more restricting than bare logical possibility<ref>{{cite book|last1=Thomson|first1=Judith and Alex Byrne|title=Content and Modality : Themes from the Philosophy of Robert Stalnaker|date=2006|publisher=[[Oxford University Press]]|location=Oxford|page=107|url=https://books.google.com/books?id=JXeOkXnCwb8C|access-date=16 December 2014|isbn=9780191515736}}</ref> (i.e., fewer things are metaphysically possible than are logically possible). However, its exact relation (if any) to logical possibility or to physical possibility is a matter of dispute. Philosophers{{who|date=April 2012}} also disagree over whether metaphysical truths are necessary merely "by definition", or whether they reflect some underlying deep facts about the world, or something else entirely.