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140-398: Existence is the state of having being or reality in contrast to nonexistence and nonbeing . Existence is often contrasted with essence : the essence of an entity is its essential features or qualities, which can be understood even if one does not know whether the entity exists. Ontology is the philosophical discipline studying the nature and types of existence. Singular existence

280-413: A collection or family , especially when its elements are themselves sets. Roster or enumeration notation defines a set by listing its elements between curly brackets , separated by commas: This notation was introduced by Ernst Zermelo in 1908. In a set, all that matters is whether each element is in it or not, so the ordering of the elements in roster notation is irrelevant (in contrast, in

420-429: A sequence , a tuple , or a permutation of a set, the ordering of the terms matters). For example, {2, 4, 6} and {4, 6, 4, 2} represent the same set. For sets with many elements, especially those following an implicit pattern, the list of members can be abbreviated using an ellipsis ' ... '. For instance, the set of the first thousand positive integers may be specified in roster notation as An infinite set

560-576: A TOE, it would necessarily be a set of equations. He wrote, "What is it that breathes fire into the equations and makes a universe for them to describe?" On a much broader and more subjective level, private experiences, curiosity, inquiry, and the selectivity involved in personal interpretation of events shapes reality as seen by one and only one person and hence is called phenomenological . While this form of reality might be common to others as well, it could at times also be so unique to oneself as to never be experienced or agreed upon by anyone else. Much of

700-399: A belief or we don't have a belief") with the more permissive, probabilistic notion of credence ("there is an entire spectrum of degrees of belief, not a simple dichotomy between belief and non-belief"). Philosophy addresses two different aspects of the topic of reality: the nature of reality itself, and the relationship between the mind (as well as language and culture) and reality. On

840-497: A building and being 443.2 meters tall , express what an object is like but do not directly describe whether or not that building exists. According to this view, existence is more fundamental than regular properties because an object cannot have any properties if it does not exist. According to second-order theorists, quantifiers rather than predicates express existence. Predicates are expressions that apply to and classify objects, usually by attributing features to them, such as "is

980-403: A butterfly" and "is happy". Quantifiers are terms that talk about the quantity of objects that have certain properties. Existential quantifiers express that there is at least one object, like the expressions "some" and "there exists", as in "some cows eat grass" and "there exists an even prime number". In this regard, existence is closely related to counting because to assert that something exists

1120-419: A certain amount. Constructivism and intuitionism are realistic about objects that can be explicitly constructed, but reject the use of the principle of the excluded middle to prove existence by reductio ad absurdum . The traditional debate has focused on whether an abstract (immaterial, intelligible) realm of numbers has existed in addition to the physical (sensible, concrete) world. A recent development

1260-466: A definition is called a semantic description . Set-builder notation specifies a set as a selection from a larger set, determined by a condition on the elements. For example, a set F can be defined as follows: F = { n ∣ n  is an integer, and  0 ≤ n ≤ 19 } . {\displaystyle F=\{n\mid n{\text{ is an integer, and }}0\leq n\leq 19\}.} In this notation,

1400-429: A different thick concept of existence; he stated: "to be is to be perceived", meaning all existence is mental. Existence contrasts with nonexistence, a lack of reality. Whether objects can be divided into existent and nonexistent objects is a subject of controversy. This distinction is sometimes used to explain how it is possible to think of fictional objects like dragons and unicorns but the concept of nonexistent objects

1540-415: A distinction between reality and existence. In fact, many analytic philosophers today tend to avoid the term "real" and "reality" in discussing ontological issues. But for those who would treat "is real" the same way they treat "exists", one of the leading questions of analytic philosophy has been whether existence (or reality) is a property of objects. It has been widely held by analytic philosophers that it

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1680-703: A firm basis for all human knowledge , including scientific knowledge , and could establish philosophy as a "rigorous science". Husserl's conception of phenomenology has been criticised and developed by his student and assistant Martin Heidegger (1889–1976), by existentialists like Maurice Merleau-Ponty (1908–1961) and Jean-Paul Sartre (1905–1980), and by other philosophers, such as Paul Ricoeur (1913–2005), Emmanuel Levinas (1906–1995), and Dietrich von Hildebrand (1889–1977). Skeptical hypotheses in philosophy suggest that reality could be very different from what we think it is; or at least that we cannot prove it

1820-526: A hierarchical structure. They believed a transcendent entity, called "the One" or "the Good", is responsible for all existence. From it emerges the intellect, which in turn gives rise to the soul and the material world. In medieval philosophy , Anselm of Canterbury (1033–1109 CE) formulated the influential ontological argument , which aims to deduce the existence of God from the concept of God. Anselm defined God as

1960-677: A higher degree than others. The orthodox position in ontology is that existence is a second-order property or a property of properties. For example, to say that lions exist means that the property of being a lion is possessed by an entity. A different view states that existence is a first-order property or a property of individuals . This means existence is similar to other properties of individuals, like color and shape. Alexius Meinong and his followers accept this idea and say that not all individuals have this property; they state that there are some individuals, such as Santa Claus , that do not exist. Universalists reject this view; they see existence as

2100-406: A logical property that every existing thing shares; they do not include any substantial content about the metaphysical implications of having existence. According to one view, existence is the same as the logical property of self-identity . This view articulates a thin concept of existence because it merely states what exists is identical to itself without discussing any substantial characteristics of

2240-530: A long philosophical tradition in relation to the existence of universals. According to Platonists , universals have general existence as Platonic forms independently of the particulars that exemplify them. According to this view, the universal of redness exists independently of the existence or nonexistence of red objects. Aristotelianism also accepts the existence of universals but says their existence depends on particulars that instantiate them and that they are unable to exist by themselves. According to this view,

2380-455: A negative singular existential is true if the individual it refers to does not exist. Meinongianism has important implications for understandings of quantification. According to an influential view defended by Willard Van Orman Quine , the domain of quantification is restricted to existing objects. This view implies quantifiers carry ontological commitments about what exists and what does not exist. Meinongianism differs from this view by saying

2520-461: A nonexisting object. Closely related to the problem of different types of entities is the question of whether their modes of existence also vary. This is the case according to ontological pluralism, which states entities belonging to different types differ in both their essential features and in the ways they exist. This position is sometimes found in theology; it states God is radically different from his creation and emphasizes his uniqueness by saying

2660-400: A particular function ( Hilary Putnam ). Some have also attempted to offer significant revisions to our notion of belief, including eliminativists about belief who argue that there is no phenomenon in the natural world which corresponds to our folk psychological concept of belief ( Paul Churchland ) and formal epistemologists who aim to replace our bivalent notion of belief ("either we have

2800-455: A person who if asked about the color of snow would assert "snow is white"). There are various ways that contemporary philosophers have tried to describe beliefs, including as representations of ways that the world could be ( Jerry Fodor ), as dispositions to act as if certain things are true ( Roderick Chisholm ), as interpretive schemes for making sense of someone's actions ( Daniel Dennett and Donald Davidson ), or as mental states that fill

2940-457: A physically 'real' world". The hypothesis suggests that worlds corresponding to different sets of initial conditions, physical constants, or altogether different equations should be considered real. The theory can be considered a form of Platonism in that it posits the existence of mathematical entities, but can also be considered a mathematical monism in that it denies that anything exists except mathematical objects. The problem of universals

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3080-423: A property of individuals while second-order theories say existence is a second-order property, that is, a property of properties. A central challenge for theories of the nature of existence is an understanding of the possibility of coherently denying the existence of something, like the statement: "Santa Claus does not exist". One difficulty is explaining how the name "Santa Claus" can be meaningful even though there

3220-481: A property of some but not all entities, was first formulated by Alexius Meinong . Its main assertion is that there are some entities that do not exist, meaning objecthood is independent of existence. Proposed examples of nonexistent objects are merely possible objects such as flying pigs, as well as fictional and mythical objects like Sherlock Holmes and Zeus. According to this view, these objects are real and have being, even though they do not exist. Meinong states there

3360-410: A robust explanation of why statements about what is possible and necessary are true. According to him, possible objects exist in possible worlds while actual objects exist in the actual world. Lewis says the only difference between possible worlds and the actual world is the location of the speaker; the term "actual" refers to the world of the speaker, similar to the way the terms "here" and "now" refer to

3500-456: A rock falls on a plant and damages it, or a plant grows through rock and breaks it. Abstract objects, like numbers, sets, and types, have no location in space and time, and lack causal powers. The distinction between concrete objects and abstract objects is sometimes treated as the most-general division of being. The existence of concrete objects is widely agreed upon but opinions about abstract objects are divided. Realists such as Plato accept

3640-436: A second-order property. According to second-order theories, to talk about existence is to talk about which properties have instances. For example, this view says that the sentence "God exists" means "Godhood is instantiated" rather than "God has the property of existing". A key reason against characterizing existence as a property of individuals is that existence differs from regular properties. Regular properties, such as being

3780-441: A set S , denoted | S | , is the number of members of S . For example, if B = {blue, white, red} , then | B | = 3 . Repeated members in roster notation are not counted, so | {blue, white, red, blue, white} | = 3 , too. More formally, two sets share the same cardinality if there exists a bijection between them. The cardinality of the empty set is zero. The list of elements of some sets

3920-465: A set A to a set B is a rule that assigns to each "input" element of A an "output" that is an element of B ; more formally, a function is a special kind of relation , one that relates each element of A to exactly one element of B . A function is called An injective function is called an injection , a surjective function is called a surjection , and a bijective function is called a bijection or one-to-one correspondence . The cardinality of

4060-524: A single value be produced with certainty). A closely related term is counterfactual definiteness (CFD), used to refer to the claim that one can meaningfully speak of the definiteness of results of measurements that have not been performed (i.e. the ability to assume the existence of objects, and properties of objects, even when they have not been measured). Local realism is a significant feature of classical mechanics, of general relativity , and of classical electrodynamics ; but not quantum mechanics . In

4200-406: A special position. The founders of quantum mechanics debated the role of the observer, and of them, Wolfgang Pauli and Werner Heisenberg believed that quantum mechanics expressed the observers knowledge and when an experiment was completed the additional knowledge should be incorporated in the wave function, an effect that came to be called state reduction or collapse . This point of view, which

4340-416: A strict sense, all negative singular existentials are false, including the assertion that "Ronald McDonald does not exist". Universalists can interpret such sentences slightly differently in relation to the context. In everyday life, for example, people use sentences like "Ronald McDonald does not exist" to express the idea that Ronald McDonald does not exist as a concrete object, which is true. Another approach

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4480-400: A subclass of possible objects; creationists say that they are artifacts that depend for their existence on the authors who first conceived them. Intentional inexistence is a similar phenomenon concerned with the existence of objects within mental states. This happens when a person perceives or thinks about an object. In some cases, the intentional object corresponds to a real object outside

4620-428: A subconscious set of mental filters formed from their beliefs and experiences, every individual interprets the same world differently, hence "Truth is in the eye of the beholder". His ideas influenced the work of his friend Robert Anton Wilson . The status of abstract entities, particularly numbers, is a topic of discussion in mathematics. In the philosophy of mathematics, the best known form of realism about numbers

4760-540: A systematic framework we use to structure our experience. Spatial measurements are used to quantify how far apart objects are, and temporal measurements are used to quantitatively compare the interval between (or duration of) events . Although space and time are held to be transcendentally ideal in this sense, they are also empirically real , i.e. not mere illusions. Idealist writers such as J. M. E. McTaggart in The Unreality of Time have argued that time

4900-448: A tendency: in the way that glass objects tend to break, or are disposed to break, even if they do not actually break. Likewise, the mind-independent properties of quantum systems could consist of a tendency to respond to particular measurements with particular values with ascertainable probability. Such an ontology would be metaphysically realistic, without being realistic in the physicist's sense of "local realism" (which would require that

5040-636: A universal property of every individual. The concept of existence has been discussed throughout the history of philosophy and already played a role in ancient philosophy , including Presocratic philosophy in Ancient Greece , Hindu and Buddhist philosophy in Ancient India , and Daoist philosophy in ancient China . It is relevant to fields such as logic , mathematics , epistemology , philosophy of mind , philosophy of language , and existentialism . Dictionaries define existence as

5180-419: A universal that is not present in the space and time does not exist. According to nominalists , only particulars have existence and universals do not exist. There is an influential distinction in ontology between concrete and abstract objects . Many concrete objects, like rocks, plants, and other people, are encountered in everyday life. They exist in space and time. They have effects on each other, like when

5320-696: A work now called the EPR paradox , Einstein relied on local realism to suggest that hidden variables were missing in quantum mechanics. However, John S. Bell subsequently showed that the predictions of quantum mechanics are inconsistent with hidden variables, a result known as Bell's theorem . The predictions of quantum mechanics have been verified: Bell's inequalities are violated, meaning either local realism or counterfactual definiteness must be incorrect. Different interpretations of quantum mechanics violate different parts of local realism and/or counterfactual definiteness . The transition from "possible" to "actual"

5460-399: Is Platonic realism , which grants them abstract, immaterial existence. Other forms of realism identify mathematics with the concrete physical universe. Anti-realist stances include formalism and fictionalism . Some approaches are selectively realistic about some mathematical objects but not others. Finitism rejects infinite quantities. Ultra-finitism accepts finite quantities up to

5600-552: Is not a property at all, though this view has lost some ground in recent decades. On the other hand, particularly in discussions of objectivity that have feet in both metaphysics and epistemology, philosophical discussions of "reality" often concern the ways in which reality is, or is not, in some way dependent upon (or, to use fashionable jargon , "constructed" out of) mental and cultural factors such as perceptions, beliefs, and other mental states, as well as cultural artifacts, such as religions and political movements , on up to

5740-420: Is a difference between entities and the fundamental characteristics that make them the entities they are. Martin Heidegger (1889–1976) introduced this concept; he calls it the ontological difference and contrasts individual beings with being. According to his response to the question of being, being is not an entity but the background context that makes all individual entities intelligible. Many discussions of

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5880-403: Is a graphical representation of a collection of sets; each set is depicted as a planar region enclosed by a loop, with its elements inside. If A is a subset of B , then the region representing A is completely inside the region representing B . If two sets have no elements in common, the regions do not overlap. A Venn diagram , in contrast, is a graphical representation of n sets in which

6020-401: Is a major topic of quantum physics , with related theories including quantum darwinism . The quantum mind –body problem refers to the philosophical discussions of the mind–body problem in the context of quantum mechanics. Since quantum mechanics involves quantum superpositions , which are not perceived by observers , some interpretations of quantum mechanics place conscious observers in

6160-460: Is a perennial topic in metaphysics. For instance, Parmenides taught that reality was a single unchanging Being, whereas Heraclitus wrote that all things flow. The 20th-century philosopher Heidegger thought previous philosophers have lost sight of the question of Being (qua Being) in favour of the questions of beings (existing things), so he believed that a return to the Parmenidean approach

6300-422: Is a set with an infinite number of elements. If the pattern of its elements is obvious, an infinite set can be given in roster notation, with an ellipsis placed at the end of the list, or at both ends, to indicate that the list continues forever. For example, the set of nonnegative integers is and the set of all integers is Another way to define a set is to use a rule to determine what the elements are: Such

6440-506: Is a set with exactly one element; such a set may also be called a unit set . Any such set can be written as { x }, where x is the element. The set { x } and the element x mean different things; Halmos draws the analogy that a box containing a hat is not the same as the hat. If every element of set A is also in B , then A is described as being a subset of B , or contained in B , written A ⊆ B , or B ⊇ A . The latter notation may be read B contains A , B includes A , or B

6580-410: Is a subjective attitude that a proposition is true or a state of affairs is the case. A subjective attitude is a mental state of having some stance , take, or opinion about something. In epistemology , philosophers use the term "belief" to refer to attitudes about the world which can be either true or false . To believe something is to take it to be true; for instance, to believe that snow

6720-435: Is a superset of A . The relationship between sets established by ⊆ is called inclusion or containment . Two sets are equal if they contain each other: A ⊆ B and B ⊆ A is equivalent to A = B . If A is a subset of B , but A is not equal to B , then A is called a proper subset of B . This can be written A ⊊ B . Likewise, B ⊋ A means B is a proper superset of A , i.e. B contains A , and

6860-421: Is an ancient problem in metaphysics about whether universals exist. Universals are general or abstract qualities, characteristics, properties , kinds or relations , such as being male/female, solid/liquid/gas or a certain colour, that can be predicated of individuals or particulars or that individuals or particulars can be regarded as sharing or participating in. For example, Scott, Pat, and Chris have in common

7000-399: Is an elementary concept, meaning it cannot be defined in other terms without involving circularity. This would imply characterizing existence or talking about its nature in a non-trivial manner may be difficult or impossible. Disputes about the nature of existence are reflected in the distinction between thin and thick concepts of existence. Thin concepts of existence understand existence as

7140-521: Is an illusion. As well as differing about the reality of time as a whole, metaphysical theories of time can differ in their ascriptions of reality to the past , present and future separately. Time, and the related concepts of process and evolution are central to the system-building metaphysics of A. N. Whitehead and Charles Hartshorne . The term " possible world " goes back to Leibniz's theory of possible worlds, used to analyse necessity, possibility , and similar modal notions . Modal realism

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7280-403: Is an object corresponding to any combination of properties. A more specific criticism rejects the idea that there are incomplete and impossible objects. Universalists agree with Meinongians that existence is a property of individuals but deny there are nonexistent entities. Instead, universalists state existence is a universal property; all entities have it, meaning everything exists. One approach

7420-510: Is an object for any combination of properties. For example, there is an object that only has the single property of "being a singer" with no other properties. This means neither the attribute of "wearing a dress" nor the absence of it applies to this object. Meinong also includes impossible objects like round squares in this classification. According to Meinongians, sentences describing Sherlock Holmes and Zeus refer to nonexisting objects. They are true or false depending on whether these objects have

7560-500: Is between merely possible, contingent , and necessary existence. An entity has necessary existence if it must exist or could not fail to exist. This means that it is not possible to newly create or destroy necessary entities. Entities that exist but could fail to exist are contingent; merely possible entities do not exist but could exist. Most entities encountered in ordinary experience, like telephones, sticks, and flowers, have contingent existence. The contingent existence of telephones

7700-493: Is called negative singular existential and the expression Ronald McDonald is a singular term that seems to refer to an individual. It is not clear how the expression can refer to an individual if, as the sentence asserts, this individual does not exist. According to a solution philosopher Bertrand Russell (1872–1970) proposed, singular terms do not refer to individuals but are descriptions of individuals . This theory states negative singular existentials deny an object matching

7840-453: Is closely related to the problem of modes of existence. This topic is based on the idea that some entities exist to a higher degree or have more being than other entities, similar to the way some properties, such as heat and mass, have degrees. According to philosopher Plato (428/427–348/347 BCE), for example, unchangeable Platonic forms have a higher degree of existence than physical objects. The view that there are different types of entities

7980-417: Is common in metaphysics but the idea that they differ from each other in their modes or degrees of existence is often rejected, implying that a thing either exists or does not exist without in-between alternatives. Metaphysician Peter van Inwagen (1942–present) uses the idea that there is an intimate relationship between existence and quantification to argue against different modes of existence. Quantification

8120-477: Is contradictory. This conclusion follows from the premises that one can only deny the existence of something by referring to that entity and that one can only refer to entities that exist. Universalists have proposed different ways of interpreting negative singular existentials. According to one view, names of fictional entities like "Ronald McDonald" refer to abstract objects , which exist even though they do not exist in space and time. This means, when understood in

8260-399: Is endless, or infinite . For example, the set N {\displaystyle \mathbb {N} } of natural numbers is infinite. In fact, all the special sets of numbers mentioned in the section above are infinite. Infinite sets have infinite cardinality . Some infinite cardinalities are greater than others. Arguably one of the most significant results from set theory is that

8400-611: Is fundamentally immaterial (e.g. idealism ), whether hypothetical unobservable entities posited by scientific theories exist, whether a god or gods exist, whether numbers and other abstract objects exist, and whether possible worlds exist. Epistemology is concerned with what can be known or inferred as likely and how, whereby in the modern world emphasis is put on reason , empirical evidence and science as sources and methods to determine or investigate reality. A common colloquial usage would have reality mean "perceptions, beliefs, and attitudes toward reality", as in "My reality

8540-505: Is impossible because the world needs to contain at least all necessary entities. Entities that exist on a physical level include objects encountered in everyday life, like stones, trees, and human bodies, as well as entities discussed in modern physics , like electrons and protons. Physical entities can be observed and measured; they possess mass and a location in space and time. Mental entities like perceptions, experiences of pleasure and pain as well as beliefs, desires, and emotions belong to

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8680-482: Is in B ". The statement " y is not an element of B " is written as y ∉ B , which can also be read as " y is not in B ". For example, with respect to the sets A = {1, 2, 3, 4} , B = {blue, white, red} , and F = { n | n is an integer, and 0 ≤ n ≤ 19} , The empty set (or null set ) is the unique set that has no members. It is denoted ∅ , ∅ {\displaystyle \emptyset } , { }, ϕ , or ϕ . A singleton set

8820-457: Is known as direct realism when developed to counter indirect or representative realism, also known as epistemological dualism , the philosophical position that our conscious experience is not of the real world itself but of an internal representation, a miniature virtual-reality replica of the world. Timothy Leary coined the influential term Reality Tunnel , by which he means a kind of representative realism . The theory states that, with

8960-500: Is made between existence and essence . Essence refers to the intrinsic nature or defining qualities of an entity. The essence of something determines what kind of entity it is and how it differs from other kinds of entities. Essence corresponds to what an entity is, while existence corresponds to the fact that it is. For instance, it is possible to understand what an object is and grasp its nature even if one does not know whether this object exists. According to some philosophers, there

9100-479: Is no Santa Claus. Second-order theories understand existence as a second-order property rather than a first-order property. They are often seen as the orthodox position in ontology. For instance, the Empire State Building is an individual object and "being 443.2 meters (1,454 ft) tall" is a first-order property of it. "Being instantiated" is a property of "being 443.2 meters tall" and therefore

9240-523: Is no mind or soul over and above such mental events . Finally, anti-realism became a fashionable term for any view which held that the existence of some object depends upon the mind or cultural artifacts. The view that the so-called external world is really merely a social, or cultural, artifact, called social constructionism , is one variety of anti-realism. Cultural relativism is the view that social issues such as morality are not absolute, but at least partially cultural artifact . The nature of being

9380-428: Is not equal to A . A third pair of operators ⊂ and ⊃ are used differently by different authors: some authors use A ⊂ B and B ⊃ A to mean A is any subset of B (and not necessarily a proper subset), while others reserve A ⊂ B and B ⊃ A for cases where A is a proper subset of B . Examples: The empty set is a subset of every set, and every set is a subset of itself: An Euler diagram

9520-457: Is not generally accepted; some philosophers say the concept is contradictory. Closely related contrasting terms are nothingness and nonbeing. Existence is commonly associated with mind-independent reality but this position is not universally accepted because there could also be forms of mind-dependent existence, such as the existence of an idea inside a person's mind. According to some idealists , this may apply to all of reality. Another contrast

9660-470: Is not your reality." This is often used just as a colloquialism indicating that the parties to a conversation agree, or should agree, not to quibble over deeply different conceptions of what is real. For example, in a religious discussion between friends, one might say (attempting humor), "You might disagree, but in my reality, everyone goes to heaven." Reality can be defined in a way that links it to worldviews or parts of them (conceptual frameworks): Reality

9800-405: Is not. Examples include: Jain philosophy postulates that seven tattva (truths or fundamental principles) constitute reality. These seven tattva are: Scientific realism is, at the most general level, the view that the world (the universe) described by science (perhaps ideal science) is the real world, as it is, independent of what we might take it to be. Within philosophy of science , it

9940-557: Is often framed as an answer to the question "how is the success of science to be explained?" The debate over what the success of science involves centers primarily on the status of entities that are not directly observable discussed by scientific theories . Generally, those who are scientific realists state that one can make reliable claims about these entities (viz., that they have the same ontological status) as directly observable entities, as opposed to instrumentalism . The most used and studied scientific theories today state more or less

10080-400: Is only one empty set. Sets are ubiquitous in modern mathematics. Indeed, set theory , more specifically Zermelo–Fraenkel set theory , has been the standard way to provide rigorous foundations for all branches of mathematics since the first half of the 20th century. Mathematical texts commonly denote sets by capital letters in italic , such as A , B , C . A set may also be called

10220-418: Is reflected in the fact that they exist in the present but did not exist in the past, meaning that it is not necessary that they exist. It is an open question whether any entities have necessary existence. According to some nominalists , all concrete objects have contingent existence while all abstract objects have necessary existence. According to some theorists, one or several necessary beings are required as

10360-498: Is related to alethic logic : a proposition is necessary if it is true in all possible worlds, and possible if it is true in at least one. The many worlds interpretation of quantum mechanics is a similar idea in science. The philosophical implications of a physical TOE are frequently debated. For example, if philosophical physicalism is true, a physical TOE will coincide with a philosophical theory of everything. The "system building" style of metaphysics attempts to answer all

10500-409: Is related to the counting of objects; according to Inwagen, if there were different modes of entities, people would need different types of numbers to count them. Because the same numbers can be used to count different types of entities, he concludes all entities have the same mode of existence. Theories of the nature of existence aim to explain what it means for something to exist. A central dispute in

10640-405: Is said not to depend on perceptions, beliefs, language, or any other human artifact, one can speak of "realism about " that object. A correspondence theory of knowledge about what exists claims that "true" knowledge of reality represents accurate correspondence of statements about and images of reality with the actual reality that the statements or images are attempting to represent. For example,

10780-556: Is studied by the subdiscipline of metaphysics known as ontology . The terms "being", "reality", and "actuality" are often used as synonyms of "existence", but the exact definition of existence and its connection to these terms is disputed. According to metaphysician Alexius Meinong (1853–1920), all entities have being but not all entities have existence. He argues merely possible objects like Santa Claus have being but lack existence. Ontologist Takashi Yagisawa (20th century–present) contrasts existence with reality; he sees "reality" as

10920-511: Is that singular existence can be expressed in terms of general existence. For instance, the sentence "Angela Merkel exists" can be expressed as "entities that are identical to Angela Merkel exist", where the expression "being identical to Angela Merkel" is understood as a general term. Philosopher Willard Van Orman Quine (1908–2000) defends a different position by giving primacy to singular existence and arguing that general existence can be expressed in terms of singular existence. A related question

11060-448: Is that there simply and literally is no reality beyond the perceptions or beliefs we each have about reality. Such attitudes are summarized in popular statements, such as "Perception is reality" or "Life is how you perceive reality" or "reality is what you can get away with" ( Robert Anton Wilson ), and they indicate anti-realism  – that is, the view that there is no objective reality, whether acknowledged explicitly or not. Many of

11200-525: Is the mathematical universe hypothesis , the theory that only a mathematical world exists, with the finite, physical world being an illusion within it. An extreme form of realism about mathematics is the mathematical multiverse hypothesis advanced by Max Tegmark . Tegmark's sole postulate is: All structures that exist mathematically also exist physically . That is, in the sense that "in those [worlds] complex enough to contain self-aware substructures [they] will subjectively perceive themselves as existing in

11340-545: Is the existence of individual entities while general existence refers to the existence of concepts or universals . Entities present in space and time have concrete existence in contrast to abstract entities, like numbers and sets. Other distinctions are between possible , contingent , and necessary existence and between physical and mental existence. The common view is that an entity either exists or not with nothing in between, but some philosophers say that there are degrees of existence, meaning that some entities exist to

11480-571: Is the predicate. Quantifier constructions can also be used to express negative existential statements; for instance, the sentence "talking tigers do not exist" can be expressed as "it is not the case that there exist talking tigers". Many ontologists accept that second-order theories provide a correct analysis of many types of existential sentences. It is, however, controversial whether it is correct for all cases. Some problems relate to assumptions associated with everyday language about sentences like " Ronald McDonald does not exist". This type of statement

11620-588: Is the totality of a system, known and unknown. Philosophical questions about the nature of reality or existence or being are considered under the rubric of ontology , which is a major branch of metaphysics in the Western philosophical tradition. Ontological questions also feature in diverse branches of philosophy , including the philosophy of science , of religion , of mathematics , and philosophical logic . These include questions about whether only physical objects are real (i.e., physicalism ), whether reality

11760-404: Is the totality of all things, structures (actual and conceptual), events (past and present) and phenomena, whether observable or not. It is what a world view (whether it be based on individual or shared human experience) ultimately attempts to describe or map. Certain ideas from physics, philosophy, sociology, literary criticism , and other fields shape various theories of reality. One such theory

11900-495: Is the view, notably propounded by David Kellogg Lewis , that all possible worlds are as real as the actual world. In short: the actual world is regarded as merely one among an infinite set of logically possible worlds, some "nearer" to the actual world and some more remote. Other theorists may use the Possible World framework to express and explore problems without committing to it ontologically. Possible world theory

12040-422: Is to assert that the corresponding concept has one or more instances. Second-order views imply a sentence like " egg-laying mammals exist" is misleading because the word "exist" is used as a predicate in them. These views say the true logical form is better expressed in reformulations like "there exist entities that are egg-laying mammals". This way, "existence" has the role of a quantifier and "egg-laying mammals"

12180-403: Is to say existence is the same as self-identity. According to the law of identity , every object is identical to itself or has the property of self-identity. This can be expressed in predicate logic as ∀ x ( x = x ) {\displaystyle \forall x(x=x)} . An influential argument in favor of universalism is that the denial of the existence of something

12320-557: Is to understand negative singular existentials as neither true nor false but meaningless because their singular terms do not refer to anything. Western philosophy originated with the Presocratic philosophers , who aimed to replace earlier mythological accounts of the universe by providing rational explanations based on foundational principles of all existence. Some, like Thales (c. 624–545 BCE) and Heraclitus (c. 540–480 BCE), suggested concrete principles like water and fire are

12460-440: Is uncountable. Moreover, the power set is always strictly "bigger" than the original set, in the sense that any attempt to pair up the elements of S with the elements of P ( S ) will leave some elements of P ( S ) unpaired. (There is never a bijection from S onto P ( S ) .) A partition of a set S is a set of nonempty subsets of S , such that every element x in S is in exactly one of these subsets. That is,

12600-405: Is whether there can be general existence without singular existence. According to philosopher Henry S. Leonard (1905–1967), a property only has general existence if there is at least one actual object that instantiates it. Philosopher Nicholas Rescher (1928–2024), by contrast, states that properties can exist if they have no actual instances, like the property of "being a unicorn". This question has

12740-405: Is white is comparable to accepting the truth of the proposition "snow is white". However, holding a belief does not require active introspection . For example, few individuals carefully consider whether or not the sun will rise tomorrow, simply assuming that it will. Moreover, beliefs need not be occurrent (e.g. a person actively thinking "snow is white"), but can instead be dispositional (e.g.

12880-588: The Greek phainómenon , meaning "that which appears", and lógos , meaning "study". In Husserl's conception, phenomenology is primarily concerned with making the structures of consciousness, and the phenomena which appear in acts of consciousness, objects of systematic reflection and analysis. Such reflection was to take place from a highly modified " first person " viewpoint, studying phenomena not as they appear to "my" consciousness, but to any consciousness whatsoever. Husserl believed that phenomenology could thus provide

13020-460: The absolute a positive one. The question of direct or "naïve" realism , as opposed to indirect or "representational" realism , arises in the philosophy of perception and of mind out of the debate over the nature of conscious experience ; the epistemological question of whether the world we see around us is the real world itself or merely an internal perceptual copy of that world generated by neural processes in our brain. Naïve realism

13160-842: The n loops divide the plane into 2 zones such that for each way of selecting some of the n sets (possibly all or none), there is a zone for the elements that belong to all the selected sets and none of the others. For example, if the sets are A , B , and C , there should be a zone for the elements that are inside A and C and outside B (even if such elements do not exist). There are sets of such mathematical importance, to which mathematicians refer so frequently, that they have acquired special names and notational conventions to identify them. Many of these important sets are represented in mathematical texts using bold (e.g. Z {\displaystyle \mathbf {Z} } ) or blackboard bold (e.g. Z {\displaystyle \mathbb {Z} } ) typeface. These include Each of

13300-510: The scientific method can verify that a statement is true based on the observable evidence that a thing exists. Many humans can point to the Rocky Mountains and say that this mountain range exists, and continues to exist even if no one is observing it or making statements about it. One can also speak of anti -realism about the same objects. Anti-realism is the latest in a long series of terms for views opposed to realism. Perhaps

13440-458: The types of existing entities revolve around the definitions of different types, the existence or nonexistence of entities of a specific type, the way entities of different types are related to each other, and whether some types are more fundamental than others. Examples are the existence or nonexistence of souls ; whether there are abstract, fictional, and universal entities; and the existence or nonexistence of possible worlds and objects besides

13580-462: The vertical bar "|" means "such that", and the description can be interpreted as " F is the set of all numbers n such that n is an integer in the range from 0 to 19 inclusive". Some authors use a colon ":" instead of the vertical bar. Philosophy uses specific terms to classify types of definitions: If B is a set and x is an element of B , this is written in shorthand as x ∈ B , which can also be read as " x belongs to B ", or " x

13720-414: The 20th century, views similar to Berkeley's were called phenomenalism . Phenomenalism differs from Berkeleyan idealism primarily in that Berkeley believed that minds, or souls, are not merely ideas nor made up of ideas, whereas varieties of phenomenalism, such as that advocated by Russell , tended to go farther to say that the mind itself is merely a collection of perceptions, memories, etc., and that there

13860-399: The above sets of numbers has an infinite number of elements. Each is a subset of the sets listed below it. Sets of positive or negative numbers are sometimes denoted by superscript plus and minus signs, respectively. For example, Q + {\displaystyle \mathbf {Q} ^{+}} represents the set of positive rational numbers. A function (or mapping ) from

14000-452: The academic discourse about the nature of existence is whether existence is a property of individuals. An individual is a unique entity, like Socrates or a particular apple. A property is something that is attributed to an entity, like "being human" or "being red", and usually expresses a quality or feature of that entity. The two main theories of existence are first-order and second-order theories. First-order theories understand existence as

14140-480: The actual world. These discussions cover the topics of the basic stuff or constituents underlying all reality and the most general features of entities. There is a distinction between singular existence and general existence. Singular existence is the existence of individual entities. For example, the sentence " Angela Merkel exists" expresses the existence of one particular person. General existence pertains to general concepts, properties, or universals . For instance,

14280-400: The cardinality of a straight line (i.e., the number of points on a line) is the same as the cardinality of any segment of that line, of the entire plane , and indeed of any finite-dimensional Euclidean space . The continuum hypothesis, formulated by Georg Cantor in 1878, is the statement that there is no set with cardinality strictly between the cardinality of the natural numbers and

14420-470: The cardinality of a straight line. In 1963, Paul Cohen proved that the continuum hypothesis is independent of the axiom system ZFC consisting of Zermelo–Fraenkel set theory with the axiom of choice . (ZFC is the most widely-studied version of axiomatic set theory.) The power set of a set S is the set of all subsets of S . The empty set and S itself are elements of the power set of S , because these are both subsets of S . For example,

14560-487: The comprehension of reality. Out of all the realities, the reality of everyday life is the most important one since our consciousness requires us to be completely aware and attentive to the experience of everyday life. In philosophy , potentiality and actuality are a pair of closely connected principles which Aristotle used to analyze motion , causality , ethics , and physiology in his Physics , Metaphysics , Nicomachean Ethics , and De Anima . A belief

14700-400: The concepts of science and philosophy are often defined culturally and socially . This idea was elaborated by Thomas Kuhn in his book The Structure of Scientific Revolutions (1962). The Social Construction of Reality , a book about the sociology of knowledge written by Peter L. Berger and Thomas Luckmann , was published in 1966. It explained how knowledge is acquired and used for

14840-533: The descriptions exists without referring to a nonexistent individual. Following this approach, the sentence "Ronald McDonald does not exist" expresses the idea: "it is not the case there is a unique happy hamburger clown". According to first-order theories, existence is a property of individuals. These theories are less-widely accepted than second-order theories but also have some influential proponents. There are two types of first-order theories: Meinongianism and universalism. Meinongianism, which describes existence as

14980-462: The difference affects both God's features and God's mode of existence. Another form of ontological pluralism distinguishes the existence of material objects from the existence of space-time . According to this view, material objects have relative existence because they exist in space-time; the existence of space-time itself is not relative in this sense because it just exists without existing within another space-time. The topic of degrees of existence

15120-495: The early modern period include the Leibniz 's Monadology , Descartes 's Dualism , Spinoza 's Monism . Hegel 's Absolute idealism and Whitehead 's Process philosophy were later systems. Other philosophers do not believe its techniques can aim so high. Some scientists think a more mathematical approach than philosophy is needed for a TOE, for instance Stephen Hawking wrote in A Brief History of Time that even if we had

15260-422: The elements outside the union of A and B are the elements that are outside A and outside B ). The cardinality of A × B is the product of the cardinalities of A and B . This is an elementary fact when A and B are finite. When one or both are infinite, multiplication of cardinal numbers is defined to make this true. The power set of any set becomes a Boolean ring with symmetric difference as

15400-436: The existence of merely possible objects. According to actualism , only actual entities have being; this includes both contingent and necessary entities but excludes merely possible entities. Possibilists reject this view and state there are also merely possible objects besides actual objects. For example, metaphysician David Lewis (1941–2001) states that possible objects exist in the same way as actual objects so as to provide

15540-415: The explanatory foundation of the cosmos. For instance, the philosophers Avicenna (980–1037) and Thomas Aquinas (1225–1274) say that God has necessary existence. A few philosophers, like Baruch Spinoza (1632–1677), see God and the world as the same thing , and say that all entities have necessary existence to provide a unified and rational explanation of everything. There are many academic debates about

15680-570: The first was idealism , so called because reality was said to be in the mind, or a product of our ideas . Berkeleyan idealism is the view, propounded by the Irish empiricist George Berkeley , that the objects of perception are actually ideas in the mind. In this view, one might be tempted to say that reality is a "mental construct"; this is not quite accurate, however, since, in Berkeley's view, perceptual ideas are created and coordinated by God. By

15820-490: The greatest conceivable being. He reasoned that an entity that did not exist outside his mind would not be the greatest conceivable being, leading him to the conclusion God exists. Reality Reality is the sum or aggregate of all that is real or existent within the universe , as opposed to that which is only imaginary , nonexistent or nonactual. The term is also used to refer to the ontological status of things, indicating their existence . In physical terms, reality

15960-642: The highest type of existence, and saw material objects as imperfect and impermanent copies of Platonic forms. Philosopher Aristotle (384–322 BCE) accepted Plato's idea that forms are different from matter, but he challenged the idea that forms have a higher type of existence. Instead, he believed forms cannot exist without matter. He stated: "being is said in many ways" and explored how different types of entities have different modes of existence. For example, he distinguished between substances and their accidents , and between potentiality and actuality . Neoplatonists like Plotinus (204–270 CE) suggested reality has

16100-414: The idea that abstract objects have independent existence. Some realists say abstract objects have the same mode of existence as concrete objects; according to others, they exist in a different way. Anti-realists state that abstract objects do not exist, a view that is often combined with the idea that existence requires a location in space and time or the ability to causally interact. A further distinction

16240-424: The important questions in a coherent way, providing a complete picture of the world. Plato and Aristotle could be said to be early examples of comprehensive systems. In the early modern period (17th and 18th centuries), the system-building scope of philosophy is often linked to the rationalist method of philosophy, that is the technique of deducing the nature of the world by pure a priori reason. Examples from

16380-664: The kind of experience deemed spiritual occurs on this level of reality. Phenomenology is a philosophical method developed in the early years of the twentieth century by Edmund Husserl (1859–1938) and a circle of followers at the universities of Göttingen and Munich in Germany. Subsequently, phenomenological themes were taken up by philosophers in France, the United States, and elsewhere, often in contexts far removed from Husserl's work. The word phenomenology comes from

16520-399: The mental state, like when accurately perceiving a tree in the garden. In other cases, the intentional object does not have a real counterpart, like when thinking about Bigfoot . The problem of intentional inexistence is the challenge of explaining how one can think about entities that do not exist since this seems to have the paradoxical implication that the thinker stands in a relation to

16660-558: The mind. Some anti-realists whose ontological position is that objects outside the mind do exist, nevertheless doubt the independent existence of time and space. Kant , in the Critique of Pure Reason , described time as an a priori notion that, together with other a priori notions such as space , allows us to comprehend sense experience . Kant denies that either space or time are substance , entities in themselves, or learned by experience; he holds rather that both are elements of

16800-463: The more-fundamental term because it equally characterizes all entities and defines existence as a relative term that connects an entity to the world it inhabits. According to philosopher Gottlob Frege (1848–1925), actuality is narrower than existence because only actual entities can produce and undergo changes, in contrast to non-actual existing entities like numbers and sets . According to some philosophers, like Edmund Husserl (1859–1938), existence

16940-516: The most-fundamental level. Materialists usually explain mental entities in terms of physical processes; for example, as brain states or as patterns of neural activation. Idealism, a minority view in contemporary philosophy, rejects matter as ultimate and views the mind as the most basic reality. Dualists like René Descartes (1596–1650) believe both physical and mental entities exist on the most-fundamental level. They state they are connected to one another in several ways but that one cannot be reduced to

17080-427: The nature of existence. Thick concepts of existence encompass a metaphysical analysis of what it means that something exists and what essential features existence implies. According to one proposal, to exist is to be present in space and time, and to have effects on other things. This definition is controversial because it implies abstract objects such as numbers do not exist. Philosopher George Berkeley (1685–1753) gave

17220-430: The one hand, ontology is the study of being, and the central topic of the field is couched, variously, in terms of being, existence, "what is", and reality. The task in ontology is to describe the most general categories of reality and how they are interrelated. If a philosopher wanted to proffer a positive definition of the concept "reality", it would be done under this heading. As explained above, some philosophers draw

17360-399: The other hand, is the view that universals are real entities, but their existence is dependent on the particulars that exemplify them. Nominalism and conceptualism are the main forms of anti-realism about universals. A traditional realist position in ontology is that time and space have existence apart from the human mind. Idealists deny or doubt the existence of objects independent of

17500-575: The other. Fictional entities are entities that exist as inventions inside works of fiction . For example, Sherlock Holmes is a fictional character in Arthur Conan Doyle 's book A Study in Scarlet and flying carpets are fictional objects in the folktales One Thousand and One Nights . According to anti-realism, fictional entities do not form part of reality in any substantive sense. Possibilists, by contrast, see fictional entities as

17640-410: The power set of {1, 2, 3} is {∅, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}} . The power set of a set S is commonly written as P ( S ) or 2 . If S has n elements, then P ( S ) has 2 elements. For example, {1, 2, 3} has three elements, and its power set has 2 = 8 elements, as shown above. If S is infinite (whether countable or uncountable ), then P ( S )

17780-427: The properties ascribed to them. For instance, the sentence "Pegasus has wings" is true because having wings is a property of Pegasus, even though Pegasus lacks the property of existing. One key motivation of Meinongianism is to explain how negative singular existentials like "Ronald McDonald does not exist" can be true. Meinongians accept the idea that singular terms like "Ronald McDonald" refer to individuals. For them,

17920-403: The realm of the mind; they are primarily associated with conscious experiences but also include unconscious states like unconscious beliefs, desires, and memories. The mind–body problem concerns the ontological status of and relation between physical and mental entities and is a frequent topic in metaphysics and philosophy of mind . According to materialists , only physical entities exist on

18060-413: The root of existence. Anaximander (c. 610–545 BCE) opposed this position; he believed the source must lie in an abstract principle that is beyond the world of human perception. Plato (428/427–348/347 BCE) argued that different types of entities have different degrees of existence and that shadows and images exist in a weaker sense than regular material objects. He said unchangeable Platonic forms have

18200-406: The sentence "politicians exist" states the general term "politician" has instances without referring to a particular politician. Singular and general existence are closely related to each other, and some philosophers have tried to explain one as a special case of the other. For example, according to Frege, general existence is more basic than singular existence. One argument in favor of this position

18340-620: The set of real numbers has greater cardinality than the set of natural numbers. Sets with cardinality less than or equal to that of N {\displaystyle \mathbb {N} } are called countable sets ; these are either finite sets or countably infinite sets (sets of the same cardinality as N {\displaystyle \mathbb {N} } ); some authors use "countable" to mean "countably infinite". Sets with cardinality strictly greater than that of N {\displaystyle \mathbb {N} } are called uncountable sets . However, it can be shown that

18480-477: The spatial and temporal location of the speaker. The problem of contingent and necessary existence is closely related to the ontological question of why there is anything at all or why is there something rather than nothing . According to one view, the existence of something is a contingent fact, meaning the world could have been totally empty. This is not possible if there are necessary entities, which could not have failed to exist. In this case, global nothingness

18620-498: The state of being real and to exist as having being or participating in reality . Existence sets real entities apart from imaginary ones, and can refer both to individual entities or to the totality of reality. The word "existence" entered the English language in the late 14th century from old French and has its roots in the medieval Latin term ex(s)istere , which means "to stand forth", "to appear", and "to arise". Existence

18760-489: The subsets are pairwise disjoint (meaning any two sets of the partition contain no element in common), and the union of all the subsets of the partition is S . Suppose that a universal set U (a set containing all elements being discussed) has been fixed, and that A is a subset of U . Given any two sets A and B , Examples: The operations above satisfy many identities. For example, one of De Morgan's laws states that ( A ∪ B )′ = A ′ ∩ B ′ (that is,

18900-505: The truth. Realism in the sense used by physicists does not equate to realism in metaphysics. The latter is the claim that the world is mind-independent: that even if the results of a measurement do not pre-exist the act of measurement, that does not require that they are the creation of the observer. Furthermore, a mind-independent property does not have to be the value of some physical variable such as position or momentum . A property can be dispositional (or potential), i.e. it can be

19040-424: The universal quality of being human or humanity . The realist school claims that universals are real – they exist and are distinct from the particulars that instantiate them. There are various forms of realism. Two major forms are Platonic realism and Aristotelian realism . Platonic realism is the view that universals are real entities and they exist independent of particulars. Aristotelian realism , on

19180-450: The vague notion of a common cultural world view , or Weltanschauung . The view that there is a reality independent of any beliefs, perceptions, etc., is called realism . More specifically, philosophers are given to speaking about "realism about " this and that, such as realism about universals or realism about the external world. Generally, where one can identify any class of object, the existence or essential characteristics of which

19320-460: The widest domain of quantification includes both existing and nonexisting objects. Some aspects of Meinongianism are controversial and have received substantial criticism. According to one objection, one cannot distinguish between being an object and being an existing object. A closely related criticism states objects cannot have properties if they do not exist. A further objection is that Meinongianism leads to an "overpopulated universe" because there

19460-625: Was needed. An ontological catalogue is an attempt to list the fundamental constituents of reality. The question of whether or not existence is a predicate has been discussed since the Early Modern period, not least in relation to the ontological argument for the existence of God . Existence, that something is, has been contrasted with essence , the question of what something is. Since existence without essence seems blank, it associated with nothingness by philosophers such as Hegel. Nihilism represents an extremely negative view of being,

19600-451: Was never fully endorsed by Niels Bohr , was denounced as mystical and anti-scientific by Albert Einstein . Pauli accepted the term, and described quantum mechanics as lucid mysticism . Set (mathematics) Sets are uniquely characterized by their elements; this means that two sets that have precisely the same elements are equal (they are the same set). This property is called extensionality . In particular, this implies that there

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