Editing Principle of bivalence (section)

== Relationship to the law of the excluded middle ==

The principle of bivalence is related to the [[law of excluded middle]] though the latter is a [[syntactic]] expression of the language of a logic of the form "P ∨ ¬P". The difference between the principle of bivalence and the law of excluded middle is important because there are logics that validate the law but not the principle.<ref name="Tomassi1999"/> For example, the [[three-valued logic|three-valued]] [[Logic of Paradox]] (LP) validates the law of excluded middle, and yet also validates the [[law of non-contradiction]], ¬(P ∧ ¬P), and its [[intended interpretation|intended semantics]] is not bivalent.<ref name="Priest2008">{{cite book|author=Graham Priest|title=An introduction to non-classical logic: from if to is|url=https://books.google.com/books?id=rMXVbmAw3YwC&pg=PA124|year=2008|publisher=Cambridge University Press|isbn=978-0-521-85433-7|pages=124–125}} (see also ''[[An Introduction to Non-Classical Logic]]'')</ref>  In [[Intuitionistic logic]] the law of excluded middle does not hold. In [[classical logic|classical]] two-valued logic both the law of excluded middle and the [[law of non-contradiction]] hold.<ref name="Goble2001bis">{{cite book|author=Lou Goble|title=The Blackwell guide to philosophical logic|url=https://books.google.com/books?id=aaO2f60YAwIC&pg=PA309|year=2001|publisher=Wiley-Blackwell|isbn=978-0-631-20693-4|page=309}}</ref>