Editing Thought (section)

===Laws of thought===
Traditionally, the term "[[laws of thought]]" refers to three fundamental laws of logic: the [[law of contradiction]], the [[law of excluded middle]], and the [[principle of identity]].<ref name="BritannicaLaws"/><ref name="BorchertLaws"/> These laws by themselves are not sufficient as axioms of logic but they can be seen as important precursors to the modern [[Axiomatic system|axiomatization]] of logic. The ''law of contradiction'' states that for any proposition, it is impossible that both it and its negation are true: <math>\lnot (p \land \lnot p)</math>. According to the ''law of excluded middle'', for any proposition, either it or its opposite is true: <math>p \lor \lnot p</math>. The principle of identity asserts that any object is identical to itself: <math>\forall x (x = x)</math>.<ref name="BritannicaLaws"/><ref name="BorchertLaws"/> There are different conceptions of how the laws of thought are to be understood. The interpretations most relevant to thinking are to understand them as prescriptive laws of how one should think or as formal laws of propositions that are true only because of their form and independent of their content or context.<ref name="BorchertLaws"/> [[Metaphysics|Metaphysical]] interpretations, on the other hand, see them as expressing the nature of "being as such".<ref name="BorchertLaws"/>

While there is a very wide acceptance of these three laws among logicians, they are not universally accepted.<ref name="BritannicaLaws"/><ref name="BorchertLaws"/> Aristotle, for example, held that there are some cases in which the law of excluded middle is false. This concerns primarily uncertain future events. On his view, it is currently "not ... either true or false that there will be a naval battle tomorrow".<ref name="BritannicaLaws">{{cite web |title=Laws of thought |url=https://www.britannica.com/topic/laws-of-thought |website=Encyclopedia Britannica |access-date=28 October 2021 |language=en}}</ref><ref name="BorchertLaws"/> Modern [[intuitionist logic]] also rejects the law of excluded middle. This rejection is based on the idea that mathematical truth depends on verification through a [[Mathematical proof|proof]]. The law fails for cases where no such proof is possible, which exist in every sufficiently strong formal system, according to [[Gödel's incompleteness theorems]].<ref>{{cite web |last1=Moschovakis |first1=Joan |title=Intuitionistic Logic: 1. Rejection of Tertium Non Datur |url=https://plato.stanford.edu/entries/logic-intuitionistic/#RejTerNonDat |website=The Stanford Encyclopedia of Philosophy |publisher=Metaphysics Research Lab, Stanford University |access-date=28 October 2021 |date=2021}}</ref><ref>{{cite web |last1=McKubre-Jordens |first1=Maarten |title=Constructive Mathematics: 1b Constructivism as Philosophy |url=https://iep.utm.edu/con-math/#SH1b |website=Internet Encyclopedia of Philosophy |access-date=28 October 2021}}</ref><ref name="BritannicaLaws"/><ref name="BorchertLaws"/> [[Dialetheism|Dialetheists]], on the other hand, reject the law of contradiction by holding that some propositions are both true and false. One motivation of this position is to avoid certain paradoxes in classical logic and set theory, like the [[liar's paradox]] and [[Russell's paradox]]. One of its problems is to find a formulation that circumvents the [[principle of explosion]], i.e. that anything follows from a contradiction.<ref>{{cite web |last1=Priest |first1=Graham |last2=Berto |first2=Francesco |last3=Weber |first3=Zach |title=Dialetheism |url=https://plato.stanford.edu/entries/dialetheism/ |website=The Stanford Encyclopedia of Philosophy |publisher=Metaphysics Research Lab, Stanford University |date=2018}}</ref><ref>{{cite web |last1=Horn |first1=Laurence R. |title=Contradiction |url=https://plato.stanford.edu/entries/contradiction/ |website=The Stanford Encyclopedia of Philosophy |publisher=Metaphysics Research Lab, Stanford University |date=2018}}</ref><ref>{{cite web |last1=Weber |first1=Zach |title=Dialetheism |url=https://www.oxfordbibliographies.com/view/document/obo-9780195396577/obo-9780195396577-0310.xml |website=Oxford Bibliographies |access-date=28 October 2021 |language=en}}</ref>

Some formulations of the laws of thought include a fourth law: the [[principle of sufficient reason]].<ref name="BorchertLaws"/> It states that everything has a sufficient [[reason]], ground, or [[cause]]. It is closely connected to the idea that everything is intelligible or can be explained in reference to its sufficient reason.<ref name="BritannicaSufficient"/><ref name="Melamed"/> According to this idea, there should always be a full explanation, at least in principle, to questions like why the sky is blue or why [[World War II]] happened. One problem for including this principle among the laws of thought is that it is a metaphysical principle, unlike the other three laws, which pertain primarily to logic.<ref name="Melamed">{{cite web |last1=Melamed |first1=Yitzhak Y. |last2=Lin |first2=Martin |title=Principle of Sufficient Reason |url=https://plato.stanford.edu/entries/sufficient-reason/ |website=The Stanford Encyclopedia of Philosophy |publisher=Metaphysics Research Lab, Stanford University |access-date=28 October 2021 |date=2021}}</ref><ref name="BorchertLaws">{{cite book |last1=Borchert |first1=Donald |title=Macmillan Encyclopedia of Philosophy, 2nd Edition |date=2006 |publisher=Macmillan |url=https://philpapers.org/rec/BORMEO |chapter=Laws of Thought }}</ref><ref name="BritannicaSufficient">{{cite web |title=principle of sufficient reason |url=https://www.britannica.com/topic/principle-of-sufficient-reason |website=Encyclopædia Britannica |access-date=28 October 2021 |language=en}}</ref>