Editing Truth (section)

===Logic===
{{Main|Logical truth|Criteria of truth|Truth value}}

[[Logic]] is concerned with the patterns in [[reason]] that can help tell if a [[proposition]] is true or not. Logicians use [[formal language]]s to express the truths they are concerned with, and as such there is only truth under some [[interpretation (logic)|interpretation]] or truth within some [[logical system]].<ref>{{Cite book |last=Novaes |first=Catarina Dutilh |url=https://books.google.com/books?id=5ZV7AAAAQBAJ |title=Formal Languages in Logic: A Philosophical and Cognitive Analysis |date=2012 |publisher=Cambridge University Press |isbn=978-1-107-02091-7 |language=en}}</ref>

A logical truth (also called an analytic truth or a necessary truth) is a statement that is true in all logically possible worlds<ref>[[Ludwig Wittgenstein]], ''[[Tractatus Logico-Philosophicus]]''.</ref> or under all possible interpretations, as contrasted to a ''[[fact]]'' (also called a ''[[Analytic-synthetic distinction|synthetic claim]]'' or a ''[[Necessary and sufficient condition|contingency]]''), which is only true in this [[World (philosophy)|world]] as it has historically unfolded. A proposition such as "If p and q, then p" is considered to be a logical truth because of the meaning of the [[symbol (formal)|symbols]] and [[well-formed formula|words]] in it and not because of any fact of any particular world. They are such that they could not be untrue.

[[Degree of truth|Degrees]] of [[truth values|truth]] in logic may be represented using two or more discrete values, as with [[principle of bivalence|bivalent logic]] (or [[Boolean logic|binary logic]]), [[three-valued logic]], and other forms of [[finite-valued logic]].<ref>{{cite book| last=Kretzmann| first=Norman| title=William of Sherwood's Treatise on Syncategorematic Words| chapter=IV, section<nowiki>=</nowiki>2. 'Infinitely Many' and 'Finitely Many'| publisher=University of Minnesota Press| year=1968| chapter-url=https://books.google.com/books?id=fW5rlSy-5D8C&pg=PA42| isbn=978-0-8166-5805-3}}</ref><ref>{{cite book| last=Smith| first=Nicholas J.J.| chapter=Article 2.6| title=Many-Valued Logics| publisher=Routledge| year=2010| chapter-url=https://www-personal.usyd.edu.au/~njjsmith/papers/smith-many-valued-logics.pdf| access-date=2018-05-25| archive-date=2018-04-08| archive-url=https://web.archive.org/web/20180408200831/http://www-personal.usyd.edu.au/~njjsmith/papers/smith-many-valued-logics.pdf| url-status=live}}</ref> Truth in logic can be represented using numbers comprising a [[continuous or discrete variable|continuous]] range, typically between 0 and 1, as with [[fuzzy logic]] and other forms of [[infinite-valued logic]].<ref>{{cite book| title=The Development of Modern Logic| last1=Mancosu| first1=Paolo| last2=Zach| first2=Richard| last3=Badesa| first3=Calixto| chapter=9. The Development of Mathematical Logic from Russell to Tarski 1900-1935" §7.2 "Many-valued logics| publisher=Oxford University Press| pages=418–420| year=2004| url=https://books.google.com/books?id=0jXavKsArnIC| isbn=978-0-19-972272-3}}</ref><ref>{{cite web| last=Garrido| first=Angel| title=A Brief History of Fuzzy Logic| publisher=Revista EduSoft| year=2012| url=https://www.edusoft.ro/brain/index.php/brain/article/viewFile/308/390| access-date=2018-05-25| archive-date=2018-05-17| archive-url=https://web.archive.org/web/20180517152622/https://www.edusoft.ro/brain/index.php/brain/article/viewFile/308/390| url-status=live}}, Editorial</ref> In general, the concept of representing truth using more than two values is known as [[many-valued logic]].<ref>{{cite book| last=Rescher| first=Nicholas| publisher=Humanities Press Synthese Library volume 17| year=1968| doi=10.1007/978-94-017-3546-9_6| title=Topics in Philosophical Logic|pages = 54–125|isbn = 978-90-481-8331-9| chapter=Many-Valued Logic}}</ref>