Editing Many-valued logic (section)

==History==
It is ''wrong'' that the first known classical logician who did not fully accept the [[law of excluded middle]] was [[Aristotle]] (who, ironically, is also generally considered to be the first classical logician and the "father of [two-valued] logic"<ref>Hurley, Patrick. ''A Concise Introduction to Logic'', 9th edition. (2006).</ref>). In fact, Aristotle did ''not'' contest the universality of the law of excluded middle, but the universality of the bivalence principle: he admitted that this principle did not all apply to future events (''De Interpretatione'', ''ch. IX''),<ref>Jules Vuillemin, ''Necessity or Contingency'', CSLI Lecture Notes, N°56, Stanford, 1996, pp. 133-167</ref> but he didn't create a system of multi-valued logic to explain this isolated remark. Until the coming of the 20th century, later logicians followed [[Aristotelian logic]], which includes or assumes the [[Law of excluded middle|law of the excluded middle]].

The 20th century brought back the idea of multi-valued logic. The Polish logician and philosopher [[Jan Łukasiewicz]] began to create systems of many-valued logic in 1920, using a third value, "possible", to deal with Aristotle's [[Problem of future contingents|paradox of the sea battle]]. Meanwhile, the American mathematician, [[Emil Post|Emil L. Post]] (1921), also introduced the formulation of additional truth degrees with ''n''&nbsp;≥ 2, where ''n'' are the truth values. Later, Jan Łukasiewicz and [[Alfred Tarski]] together formulated a logic on ''n'' truth values where ''n''&nbsp;≥ 2. In 1932, [[Hans Reichenbach]] formulated a logic of many truth values where ''n''→∞. [[Kurt Gödel]] in 1932 showed that [[intuitionistic logic]] is not a [[finitely-many valued logic]], and defined a system of [[Gödel logic]]s intermediate between [[classical logic|classical]] and intuitionistic logic; such logics are known as [[intermediate logics]].