Editing Existence (section)

== In various disciplines ==
=== Formal logic ===
{{main|Logic}}

Formal logic studies [[Deductive validity|deductively valid arguments]].<ref>{{multiref |1={{harvnb|MacFarlane|2017}} |2={{harvnb|Corkum|2015|pp=753–767}} |3={{harvnb|Blair|Johnson|2000|pp=93–95}} |4={{harvnb|Magnus|2005|loc=§ 1.6 Formal Languages|pp=12–14}} }}</ref> In [[first-order logic]], which is the most-commonly used system of formal logic, existence is expressed using the [[existential quantifier]] (<math>\exists</math>). For example, the formula <math>\exists x \text{Horse}(x)</math> can be used to state horses exist. The variable ''x'' ranges over all elements in the [[Domain of discourse|domain of quantification]] and the existential quantifier expresses that at least one element in this domain is a horse. In first-order logic, all singular terms like names refer to objects in the domain and imply the object exists. Because of this, one can deduce <math>\exists x \text{Honest}(x)</math> (someone is honest) from <math>\text{Honest}(Bill)</math> (Bill is honest).<ref>{{multiref |1={{harvnb|Shapiro|Kouri Kissel|2022|loc=§2.1 Building Blocks}} |2={{harvnb|Cook|2009|p=[https://books.google.com/books?id=JfaqBgAAQBAJ&pg=PA111 111]}} |3={{harvnb|Montague|2018|p=214}} |4={{harvnb|Casati|Fujikawa|loc=Lead Section, §1. Existence as a Second-Order Property and Its Relation to Quantification}} }}</ref> If only one object matching the description exists, the [[Uniqueness quantification|unique existential quantifier]] <math>\exists !</math> can be used.<ref>{{multiref | {{harvnb|Roberts|2009|p=[https://books.google.com/books?id=NjBLnLyE4jAC&pg=PA52 52]}} | {{harvnb|Johar|2024|p=[https://books.google.com/books?id=JnPsEAAAQBAJ&pg=PA38 38]}} }}</ref>

Many logical systems that are based on first-order logic also follow this idea. [[Free logic]] is an exception because it allows the presence of empty names that do not refer to an object in the domain.<ref>{{harvnb|Nolt|2021|loc=Lead Section, §1. The Basics}}</ref> With this modification, it is possible to apply [[logical reasoning]] to fictional objects instead of limiting it to regular objects.<ref>{{harvnb|Nolt|2021|loc=§5.4 Logics of Fiction}}</ref> In free logic one can express that Pegasus is a flying horse using the formula <math>\text{Flyinghorse}(Pegasus)</math>. As a consequence of this modification, one cannot infer from this type of statement that something exists. This means the inference from <math>\text{Flyinghorse}(Pegasus)</math> to <math>\exist x \text{Flyinghorse}(x)</math> is invalid in free logic, even though it is valid in first-order logic. Free logic uses an additional existence predicate (<math>E!</math>) to say a singular term refers to an existing object. For example, the formula <math>E!(Homer)</math> can be used to say [[Homer]] exists while the formula <math>\lnot E!(Pegasus)</math> states Pegasus does not exist.<ref>{{multiref |1={{harvnb|Lenzen|2013|p=[https://books.google.com/books?id=zn3oCAAAQBAJ&pg=PA118 118]}} |2={{harvnb|Nolt|2021|loc=Lead Section, §1. The Basics, §5.4 Logics of Fiction}} |3={{harvnb|Sider|2010|p=[https://books.google.com/books?id=GK8SEAAAQBAJ&pg=PA129 129]}} }}</ref>

=== Others ===
The disciplines of [[epistemology]], [[philosophy of mind]], and [[philosophy of language]] deal with [[Mental representation|mental]] and linguistic representations in their attempt to understand the nature of knowledge, the mind, and language. This brings with it the problem of reference or how representations can refer to existing objects. Examples of such representations are beliefs, thoughts, perceptions, words, and sentences. For instance, in the sentence "Barack Obama is a Democrat", the name "Barack Obama" refers to a particular individual. The problem of reference also affects the epistemology of perception. In particular, this concerns the problem of whether perceptual impressions establish a direct contact with reality.<ref>{{multiref |1={{harvnb|Urban|2014|p=[https://books.google.com/books?id=xLS3AwAAQBAJ&pg=PT33 33]}} |2={{harvnb|Raftopoulos|Machamer|2012|pp=[https://books.google.com/books?id=80ZitZBNao4C&pg=PA1 1–2, 142]}} |3={{harvnb|Michaelson|Reimer|2022|loc=Lead Section, § 1. Introduction}} |4={{harvnb|Audi|2006|loc=§ Epistemology, § Philosophy of Mind, § Philosophy of Language}} }}</ref>

Closely related to the problem of reference is the relationship between true representations and existence. According to [[truthmaker theory]], true representations require a truthmaker, i.e., an entity whose existence is responsible for the representation being true. For example, the sentence "kangaroos live in Australia" is true because there are kangaroos in Australia; the existence of these kangaroos is the truthmaker of the sentence. Truthmaker theory states there is a close relationship between truth and existence; there exists a truthmaker for every true representation.<ref>{{multiref |1={{harvnb|Asay|loc=Lead Section}} |2={{harvnb|Smith|Mulligan|Simons|2013|pp=[https://books.google.com/books?id=RNg2n2yVrCUC&pg=PA9 9–10]}} }}</ref>

Many of the individual sciences are concerned with the existence of particular types of entities and the laws governing them, such as physical things in physics and living entities in biology.<ref>{{harvnb|Ney|2014|p=xiii}}</ref> The [[natural science]]s employ a great variety of concepts to classify entities; these are known as [[natural kinds]], and include categories like protons, gold, and elephants. According to [[Scientific realism|scientific realists]], these entities have mind-independent being; [[Scientific anti-realism|scientific anti-realists]] say the existence of these entities and categories is based on human perceptions, theories, and social constructs.<ref>{{multiref | {{harvnb|Brzović|loc=Lead Section, § 3. Metaphysics of Natural Kinds}} | {{harvnb|Bird|Tobin|2024|loc=Lead Section, § 1.2 Natural Kind Realism}} | {{harvnb|Liston|loc=Lead Section}} }}</ref>

A similar problem concerns the existence of social kinds, which are basic concepts used in the [[social sciences]], such as race, gender, disability, money, and nation state.<ref>{{multiref | {{harvnb|Ásta|2017|pp=[https://www.taylorfrancis.com/chapters/edit/10.4324/9781315768571-27/social-kinds-%C3%A1sta 290–291]}} | {{harvnb|Ney|2014|pp=259–263}} | {{harvnb|Rea|2021|pp=185–186}} | {{harvnb|Killmister|2020|p=[https://books.google.com/books?id=-MrhDwAAQBAJ&pg=PA472 472]}} }}</ref> Social kinds are often understood as social constructions that, while useful for describing the complexities of human social life, do not form part of objective reality on the most fundamental level.<ref>{{multiref|{{harvnb|Ney|2014|pp=259–263}}|{{harvnb|Rea|2021|pp=185–186}}}}</ref> According to the controversial [[Sapir–Whorf hypothesis]], the social institution of language influences or fully determines how people perceive and understand the world.<ref>{{multiref | {{harvnb|Trask|2007|p=[https://books.google.com/books?id=PHt-gNzagikC&pg=PA154 154]}} | {{harvnb|Parkin|2013|p=[https://books.google.com/books?id=cbEpAAAAQBAJ&pg=PA238 238]}} }}</ref>

[[Existentialism]] is a school of thought that explores the nature of human existence. Among its key ideas is that [[existence precedes essence]]. This means that existence is more basic than essence. As a result, the nature and purpose of human beings are not pre-existing but develop in the process of living. According to this view, humans are thrown into a world that lacks pre-existing intrinsic meaning. They must determine for themselves their purpose and what [[Meaning of life|meaning their life]] should have. Existentialists use this idea to explore the role of freedom and responsibility in actively shaping one's life.<ref>{{multiref |1={{harvnb|Burnham|Papandreopoulos|loc=Lead Section, §1c. Freedom, §1e. Existence, §1f. Irrationality/Absurdity}} |2={{harvnb|Aho|2023|loc=Lead Section}} }}</ref> [[Feminist existentialism|Feminist existentialists]] investigate the effects of [[gender]] on human existence, for example, on the experience of freedom.<ref>{{multiref | {{harvnb|Ritzer|Stepnisky|2017|pp=[https://books.google.com/books?id=xK74DQAAQBAJ&pg=PA298 298–299]}} | {{harvnb|Quinan|2016}} }}</ref> Influential existentialists include [[Søren Kierkegaard]] (1813–1855), [[Friedrich Nietzsche]] (1844–1900), [[Jean-Paul Sartre]] (1905–1980), and [[Simone de Beauvoir]] (1908–1986).<ref>{{multiref | {{harvnb|Burnham|Papandreopoulos|loc=§ Key Existentialist Philosophers}} | {{harvnb|Aho|2023|loc=Lead Section}} }}</ref> Existentialism has influenced reflections on the role of human existence in [[sociology]]. Existentialist sociology examines the ways humans experience the social world and [[Social constructionism|construct reality]].<ref>{{harvnb|Melnikov|Kotarba|2015|loc=[https://onlinelibrary.wiley.com/doi/10.1002/9781405165518.wbeose083.pub2 Existential Sociology]}}</ref> Existence theory is a relatively recent approach that focuses on the temporal aspect of existence in society. It explores how the existential milestones to which people aspire influence their lives.<ref>{{multiref | {{harvnb|Baert|Morgan|Ushiyama|2022|pp=7–8}} | {{harvnb|Flisbäck|Bengtsson|2024|pp=1–2}} }}</ref>

Mathematicians are often interested in the existence of certain [[mathematical object]]s.<ref>{{multiref | {{harvnb|Chihara|1990|p=3}} | {{harvnb|Lucas|1990|p=[https://books.google.com/books?id=jklsb5JUgoQC&pg=PA75 75]}} }}</ref> For example, number theorists ask how many [[prime number]]s exist within a certain interval.<ref>{{multiref | {{harvnb|Vinogradov|Karatsuba|1986|p=[https://books.google.com/books?id=rSay9ZPucccC&pg=PA8 8]}} | {{harvnb|Borwein|Choi|Rooney|Weirathmueller|2008|p=[https://books.google.com/books?id=Qm1aZA-UwX4C&pg=PA63 63]}} }}</ref> The statement that at least one mathematical object matching a certain description exists is called an [[existence theorem]].<ref>{{harvnb|Lucas|1990|p=[https://books.google.com/books?id=jklsb5JUgoQC&pg=PA75 75]}}</ref> Metaphysicians of mathematics investigate whether mathematical objects exist not only in relation to mathematical [[axiom]]s but also as part of the fundamental structure of reality. This position is affirmed by [[Platonists]], while [[nominalists]] believe mathematical objects lack a more-substantial form of existence, for instance, because they are merely useful fictions.<ref>{{multiref | {{harvnb|Azzouni|2015|p=[https://books.google.com/books?id=tWr_CgAAQBAJ&pg=PA133 133]}} | {{harvnb|Chihara|1990|pp=3–4}} | {{harvnb|Lucas|1990|pp=[https://books.google.com/books?id=jklsb5JUgoQC&pg=PA75 75–76]}}| {{harvnb|Balaguer|2023|loc=Lead Section}}}}</ref>

Many debates in theology revolve around the existence of the divine, and arguments have been presented for and against God's existence. [[Cosmological argument]]s state that God must exist as the first cause to explain facts about the existence and aspects of the universe.<ref>{{multiref | {{harvnb|Reichenbach|2023|loc=Lead Section}} | {{harvnb|Ratzsch|Koperski|2023|loc=§ 1. Introduction}} }}</ref> According to [[teleological argument]]s, the only way to explain the order and complexity of the universe and human life is by reference to God as the [[intelligent design]]er.<ref>{{harvnb|Ratzsch|Koperski|2023|loc=§ 1. Introduction}}</ref> An influential argument against the existence of God relies on [[the problem of evil]] since it is not clear how evil could exist if there was an all-powerful, all-knowing, and benevolent God.<ref>{{harvnb|Beebe|loc=Lead Section}}</ref> Another argument points to a lack of concrete evidence for God's existence.<ref>{{harvnb|Clark|loc=§ 2. The Evidentialist Objection to Belief in God}}</ref>