View source for Dialetheism

{{Short description|View that there are statements that are both true and false}}

'''Dialetheism''' ({{IPAc-en|d|aɪ|ə|ˈ|l|ɛ|θ|i|ɪ|z|əm}}; from [[Ancient Greek|Greek]] {{lang|grc|δι-}} {{Transliteration|grc|di-}} 'twice' and {{lang|grc|ἀλήθεια}} {{Transliteration|grc|alḗtheia}} 'truth') is the view that there are [[statement (logic)|statements]] that are both true and false. More precisely, it is the belief that there can be a true statement whose [[negation]] is also true. Such statements are called "true [[contradiction]]s", ''dialetheia'', or [[Nonduality (spirituality)|nondualism]]s.

Dialetheism is not a [[formal system|system of formal logic]]; instead, it is a thesis about [[truth]] that influences the construction of a formal logic, often based on pre-existing systems. Introducing dialetheism has various consequences, depending on the theory into which it is introduced. A common mistake resulting from this is to reject dialetheism on the basis that, in traditional systems of logic (e.g., [[classical logic]] and [[intuitionistic logic]]), every statement becomes a [[theorem (logic)|theorem]] if a contradiction is true, [[trivialism|trivialising]] such systems when dialetheism is included as an [[axiom]].<ref name=Why>Ben Burgis, Visiting Professor of Philosophy at the University of Ulsan in South Korea, in [http://blogandnot-blog.blogspot.co.za/2007/11/why-contradictions-dont-explode-or-how.html Blog&~Blog].</ref> Other logical systems, however, do not [[principle of explosion|explode]] in this manner when contradictions are introduced; such contradiction-tolerant systems are known as [[paraconsistent logic]]s. Dialetheists who do not want to allow that every statement is true are free to favour these over traditional, explosive logics.

[[Graham Priest]] defines dialetheism as the view that there are true contradictions.<ref name="Dialetheism, logical consequence and hierarchy">Whittle, Bruno. "[https://ora.ox.ac.uk/objects/uuid:88139a8f-646b-4927-bc9d-5af0e869bf99/download_file?safe_filename=Dialetheism%252C%2Blogical%2Bconsequence%2Band%2Bhierarchy&file_format=application%2Fpdf&type_of_work=Journal+article Dialetheism, Logical Consequence and Hierarchy]." [[Analysis (journal)|Analysis]] Vol. 64 Issue 4 (2004): 318–326.</ref> [[Jc Beall]] is another advocate; his position differs from Priest's in advocating constructive (methodological) [[deflationism]] regarding the truth predicate.<ref name="True and False-As If,">Jc Beall in ''The Law of Non-Contradiction: New Philosophical Essays'' (Oxford: Oxford University Press, 2004), pp.&nbsp;197–219.</ref>

The term was coined by Graham Priest and [[Richard Sylvan|Richard Sylvan (then Routley)]].{{citation needed|date=December 2024}}

==Motivations==
===Dialetheism resolves certain paradoxes===
The [[liar paradox]] and [[Russell's paradox]] deal with self-contradictory statements in classical logic and [[naïve set theory]], respectively. Contradictions are problematic in these theories because they cause the theories to [[principle of explosion|explode]]—if a contradiction is true, then every proposition is true. The classical way to solve this problem is to ban contradictory statements: to revise the axioms of the logic so that self-contradictory statements do not appear (just as with [[Russell's paradox]]). Dialetheists, on the other hand, respond to this problem by accepting the contradictions as true. Dialetheism allows for the unrestricted [[Axiom schema of specification#Unrestricted comprehension|axiom of comprehension]] in [[set theory]], claiming that any resulting contradiction is a [[theorem]].<ref name="Transfinite Numbers in Paraconsistent Set Theory">''Transfinite Numbers in Paraconsistent Set Theory'' [[Review of Symbolic Logic]] 3(1), 2010, pp. 71-92.</ref>

However, self-referential [[paradox]]es, such as the Strengthened Liar can be avoided without revising the axioms by abandoning [[classical logic]] and accepting more than two [[truth value]]s with the help of [[many-valued logic]], such as [[fuzzy logic]] or [[Łukasiewicz logic]].

===Human reasoning===
Ambiguous situations may cause humans to affirm both a proposition and its negation. For example, if John stands in the doorway to a room, it may seem reasonable both to affirm that ''John is in the room'' and to affirm that ''John is not in the room''.

Critics argue that this merely reflects an ambiguity in our language rather than a dialetheic quality in our thoughts; if we replace the given statement with one that is less ambiguous (such as "John is halfway in the room" or "John is in the doorway"), the contradiction disappears. The statements appeared contradictory only because of a syntactic play; here, the actual meaning of "being in the room" is not the same in both instances, and thus each sentence is not the exact logical negation of the other: therefore, they are not necessarily contradictory.

Moreover, John appears to be standing in a [[Logical conjunction|conjunction]] of two concepts. He is in '''''x''''' and '''''not''' '''x''''' at the same time, but not in '''x''' and ''not in'' '''x''' at the same time (that would result in a [[contradiction]]). He is on his [[logical connective]] truth-functional operator, which shows the recurrent ambiguity of human language that often fails to capture the nature of some [[Logical sentence|logical statements]].

===Apparent dialetheism in other philosophical doctrines===
The [[Jain]] philosophical doctrine of [[anekantavada]]—non-one-sidedness—states that all statements are true in some sense and false in another.<ref>Matilal, Bimal Krishna. (1998), "The Character of Logic in India" (Albany, State University of New York Press), 127-139.</ref> Some interpret this as saying that dialetheia not only exist but are ubiquitous. Technically, however, a ''logical contradiction'' is a proposition that is true and false in the ''same'' sense; a proposition which is true in one sense and false in another does not constitute a logical contradiction. (For example, although in one sense a man cannot both be a "father" and "celibate"—leaving aside such cases as either a celibate man adopting a child or a man fathering a child and only later adopting celibacy—there is no contradiction for a man to be a ''spiritual'' father and also celibate; the sense of the word father is different here. In another example, although at the same time George W. Bush cannot both be president and not be president, he was president from 2001-2009, but was not president before 2001 or after 2009, so in different times he was both president and not president.)

The [[Buddhist]] logic system, named "[[Catuṣkoṭi]]", similarly implies that a statement and its negation may possibly co-exist.<ref>{{Cite web|url=http://www.iep.utm.edu/nagarjun/#H2|title = Nagarjuna &#124; Internet Encyclopedia of Philosophy}}</ref><ref>Ganeri, J. (2002), "The Collected Essays of [[Bimal Krishna Matilal]]: Mind, Language and World" (Oxford University Press), 77-79.</ref>

[[Graham Priest]] argues in ''Beyond the Limits of Thought'' that dialetheia arise at the borders of expressibility, in a number of philosophical contexts other than formal semantics.

==Formal consequences==
In classical logics, taking a contradiction <math>p \wedge \neg p</math> (see [[List of logic symbols]]) as a premise (that is, taking as a premise the truth of both <math>p</math> and <math>\neg p</math>), allows us to prove any statement <math>q</math>. Indeed, since <math>p</math> is true, the statement <math>p \vee q</math> is true (by generalization). Taking <math>p \vee q</math> together with <math>\neg p</math> is a [[disjunctive syllogism]] from which we can conclude <math>q</math>. (This is often called the ''[[principle of explosion]]'', since the truth of a contradiction is imagined to make the number of theorems in a system "explode".)<ref name="Why"/>

==Advantages==
The proponents of dialetheism mainly advocate its ability to avoid problems faced by other more orthodox resolutions as a consequence of their appeals to hierarchies. According to Graham Priest, "the whole point of the dialetheic solution to the semantic paradoxes is to get rid of the distinction between object language and meta-language".<ref name="Dialetheism, logical consequence and hierarchy"/> Another possibility is to utilize dialetheism along with a [[paraconsistent logic]] to resurrect the program of [[logicism]] advocated for by [[Gottlob Frege|Frege]] and [[Bertrand Russell|Russell]].<ref name="Inconsistent Mathematics">Mortensen, Chris, [https://plato.stanford.edu/archives/fall2017/entries/mathematics-inconsistent/ "Inconsistent Mathematics"], The Stanford Encyclopedia of Philosophy (Fall 2017 Edition), Edward N. Zalta (ed.).</ref> This even allows one to prove the truth of otherwise unprovable theorems such as the [[well-ordering theorem]] and the falsity of others such as the [[continuum hypothesis]].{{citation needed|date=April 2025}}

There are also dialetheic solutions to the [[sorites paradox]].{{citation needed|date=July 2024}}

==Criticisms==
One criticism of dialetheism is that it fails to capture a crucial feature about [[negation]], known as absoluteness of disagreement.<ref>{{cite journal|last1=Wang|first1=W.|date=2011|title=Against Classical Dialetheism|journal=Frontiers of Philosophy in China|volume=6|issue=3|pages=492–500|doi=10.1007/s11466-011-0152-4|s2cid=195310673 }}</ref>

Imagine John's utterance of ''P''. Sally's typical way of disagreeing with John is a consequent utterance of ¬''P''. Yet, if we accept dialetheism, Sally's so uttering does not prevent her from also accepting ''P''; after all, ''P'' may be a dialetheia and therefore it and its negation are both true. The absoluteness of disagreement is lost.

A response is that disagreement can be displayed by uttering "¬''P'' and, furthermore, ''P'' is not a dialetheia". However, the most obvious codification of "''P'' is not a dialetheia" is ¬(''P'' <math>\wedge</math> ¬''P''). But ''this itself'' could be a dialetheia as well. One dialetheist response is to offer a distinction between [[Logical assertion|assertion]] and rejection. This distinction might be hashed out in terms of the traditional distinction between [[logical quality|logical qualities]], or as a distinction between two [[illocutionary force|illocutionary]] [[speech acts]]: [[Logical assertion|assertion]] and rejection. Another criticism is that dialetheism cannot describe [[logical consequence]]s, once we believe in the relevance of logical consequences, because of its inability to describe hierarchies.<ref name="Dialetheism, logical consequence and hierarchy"/>{{clarify|reason=The phrase 'inability to describe hierarchies' is unclear and needs further explanation.|date=August 2024}}

==History==
Before Priest, both [[Nicholas of Cusa]] and [[Hegel]] were dialetheists. [[Heraclitus]] and [[Protagoras]] were both accused of being.

Heraclitus states:

"one cannot step into the same river twice." 

Protagoras states:

"Man is the measure of all things: of things which are, that they are, and of things which are not, that they are not".<ref>(80B1 [[Diels-Kranz|DK]]). According to Plato's ''[[Theaetetus (dialogue)|Theaetetus]]'', section 152a. [https://www.perseus.tufts.edu/cgi-bin/ptext?lookup=Plat.+Theaet.+152a]</ref>

Cusa states:

...there cannot be several things exactly the same, for in that case there would not be several things, but the same thing itself. Therefore all things both agree with and differ from one another.<ref>De Venatione Sapientiae, 23.</ref>

==See also==
{{Portal|Philosophy}}
* [[Catuskoti]]
* [[Compossibility]]
* [[Doublethink]]
* [[Oxymoron]]
* [[Paraconsistent logic]]
* [[Subvaluationism]]
* [[Tetralemma]]
* [[Trivialism]]

==References==
{{Reflist|1}}

==Sources==
* [[Gottlob Frege|Frege, Gottlob]]. "Negation." ''Logical Investigations''. Trans. P. Geach and R. H Stoothoff. New Haven, Conn.: Yale University Press, 1977. 31–53.
* [[Terence Parsons|Parsons, Terence]]. "Assertion, Denial, and the Liar Paradox." ''Journal of Philosophical Logic'' 13 (1984): 137–152.
* Parsons, Terence. "[https://www.tandfonline.com/doi/pdf/10.1080/00455091.1990.10716495 True Contradictions]." ''Canadian Journal of Philosophy'' 20 (1990): 335–354.
* [[Graham Priest|Priest, Graham]]. ''In Contradiction''. Dordrecht: Martinus Nijhoff (1987). (Second Edition, Oxford: Oxford University Press, 2006.)
* [[Graham Priest|Priest, Graham]]. "What Is So Bad About Contradictions?" ''Journal of Philosophy'' 95 (1998): 410–426.

==External links==
* {{cite SEP|url-id=dialetheism|title=Dialetheism|last=Berto|first=Francesco|last2=Priest|first2=Graham}}
* [https://web.archive.org/web/20140228151217/http://homepages.uconn.edu/~jcb02005/ JC Beall UCONN Homepage]
* [http://blogandnot-blog.blogspot.com/ (Blog & ~Blog)] 
* [https://web.archive.org/web/20100805185531/http://www.paulkabay.com/ Paul Kabay on dialetheism and trivialism] (includes both published and unpublished works)

{{Non-classical logic}}

{{Philosophical logic}}

[[Category:Modal metaphysics]]
[[Category:Non-classical logic]]
[[Category:Theories of deduction]]
[[Category:Theories of truth]]