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In philosophy, **events** are objects in time or instantiations of properties in objects.

**Philosophy** is the study of general and fundamental questions about existence, knowledge, values, reason, mind, and language. Such questions are often posed as problems to be studied or resolved. The term was probably coined by Pythagoras. Philosophical methods include questioning, critical discussion, rational argument, and systematic presentation. Classic philosophical questions include: Is it possible to know anything and to prove it? What is most real? Philosophers also pose more practical and concrete questions such as: Is there a best way to live? Is it better to be just or unjust? Do humans have free will?

**Time** is the indefinite continued progress of existence and events that occur in apparently irreversible succession from the past, through the present, to the future. Time is a component quantity of various measurements used to sequence events, to compare the duration of events or the intervals between them, and to quantify rates of change of quantities in material reality or in the conscious experience. Time is often referred to as a fourth dimension, along with three spatial dimensions.

In mathematics, logic, and philosophy, a **property** is a characteristic of an object; a red object is said to have the property of redness. The property may be considered a form of object in its own right, able to possess other properties. A property, however, differs from individual objects in that it may be instantiated, and often in more than one thing. It differs from the logical/mathematical concept of class by not having any concept of extensionality, and from the philosophical concept of class in that a property is considered to be distinct from the objects which possess it. Understanding how different individual entities can in some sense have some of the same properties is the basis of the problem of universals. The terms **attribute** and quality have similar meanings.

Jaegwon Kim theorized that events are structured.

They are composed of three things:

**Jaegwon Kim** is a Korean-American philosopher who is now an emeritus professor at Brown University, but who also taught at several other leading American universities. He is best known for his work on mental causation, the mind-body problem and the metaphysics of supervenience and events. Key themes in his work include: a rejection of Cartesian metaphysics, the limitations of strict psychophysical identity, supervenience, and the individuation of events. Kim's work on these and other contemporary metaphysical and epistemological issues is well represented by the papers collected in *Supervenience and Mind: Selected Philosophical Essays* (1993).

- Object(s) ,
- a property and
- time or a temporal interval .

Events are defined using the operation .

A unique event is defined by two principles:

An **operational definition** is the articulation of operationalization used in defining the terms of a process needed to determine the nature of an item or phenomenon and its properties such as duration, quantity, extension in space, chemical composition, etc. Since the degree of operationalization can vary itself, it can result in a more or less operational definition. The procedures included in definitions should be repeatable by anyone or at least by peers.

- a) the existence condition and
- b) the identity condition.

The existence condition states “ exists if and only if object exemplifies the -adic at time .” This means a unique event exists if the above is met. The identity condition states “ is if and only if , and .”

Kim uses these to define events under five conditions:

- One, they are unrepeatable, unchangeable particulars that include changes and the states and conditions of that event.
- Two, they have a semi-temporal location.
- Three, only their constructive property creates distinct events.
- Four, holding a constructive property as a generic event creates a type-token relationship between events, and events are not limited to their three requirements (i.e. ). Critics of this theory such as Myles Brand have suggested that the theory be modified so that an event had a spatiotemporal region; consider the event of a flash of lightning. The idea is that an event must include both the span of time of the flash of lightning and the area in which it occurred.

Other problems exist within Kim’s theory, as he never specified what properties were (e.g. universals, tropes, natural classes, etc.). In addition, it is not specified if properties are few or abundant. The following is Kim’s response to the above.

The term "**trope**" is both a term which denotes figurative and metaphorical language and one which has been used in various technical senses. The term *trope* derives from the Greek τρόπος (*tropos*), "a turn, a change", related to the root of the verb τρέπειν (*trepein*), "to turn, to direct, to alter, to change"; this means that the term is used metaphorically to denote, among other things, metaphorical language. Perhaps the term can be explained as meaning the same thing as *a turn of phrase* in its original sense.

. . . [T]he basic generic events may be best picked out relative to a scientific theory, whether the theory is a common-sense theory of the behavior of middle-sized objects or a highly sophisticated physical theory. They are among the important properties, relative to the theory, in terms of which lawful regularities can be discovered, described, and explained. The basic parameters in terms of which the laws of the theory are formulated would, on this view, give us our basic generic events, and the usual logical, mathematical, and perhaps other types of operations on them would yield complex, defined generic events. We commonly recognize such properties as motion, colors, temperatures, weights, pushing, and breaking, as generic events and states, but we must view this against the background of our common-sense explanatory and predictive scheme of the world around us. I think it highly likely that we cannot pick out generic events completely

a priori.^{ [1] }

There is also a major debate about the essentiality of a constitutive object. There are two major questions involved in this: If one event occurs, could it have occurred in the same manner if it were another person, and could it occur in the same manner if it would have occurred at a different time? Kim holds that neither are true and that different conditions (i.e. a different person or time) would lead to a separate event. However, some consider it natural to assume the opposite.

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Donald Davidson and John Lemmon proposed a theory of events that had two major conditions, respectively: a causal criterion and a spatiotemporal criterion.

**Donald Herbert Davidson** was an American philosopher. He served as Slusser Professor of Philosophy at the University of California, Berkeley from 1981 to 2003 after having also held teaching appointments at Stanford University, Rockefeller University, Princeton University, and the University of Chicago. Davidson was known for his charismatic personality and the depth and difficulty of his thought. His work exerted considerable influence in many areas of philosophy from the 1960s onward, particularly in philosophy of mind, philosophy of language, and action theory. While Davidson was an analytic philosopher, and most of his influence lies in that tradition, his work has attracted attention in continental philosophy as well, particularly in literary theory and related areas.

**Edward John Lemmon** was a logician and philosopher born in Sheffield, England. He is most well known for his work on modal logic, particularly his joint text with Dana Scott published posthumously.

The causal criterion defines an event as two events being the same if and only if they have the same cause and effect.

The spatiotemporal criterion defines an event as two events being the same if and only if they occur in the same space at the same time. Davidson however provided this scenario; if a metal ball becomes warmer during a certain minute, and during the same minute rotates through 35 degrees, must we say that these are the same event? However, one can argue that the warming of the ball and the rotation are possibly temporally separated and are therefore separate events.

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David Lewis theorized that events are merely spatiotemporal regions and properties (i.e. membership of a class). He defines an event as “e is an event only if it is a class of spatiotemporal regions, both thisworldly (assuming it occurs in the actual world) and otherworldly.” The only problem with this definition is it only tells us what an event could be, but does not define a unique event. This theory entails modal realism, which assumes possible worlds exist; worlds are defined as sets containing all objects that exist as a part of that set. However, this theory is controversial. Some philosophers have attempted to remove possible worlds, and reduce them to other entities. They hold that the world we exist in is the only world that actually exists, and that possible worlds are only possibilities.

Lewis’ theory is composed of four key points. Firstly, the non-duplication principle; it states that x and y are separate events if and only if there is one member of x that is not a member of y (or vice versa). Secondly, there exist regions that are subsets of possible worlds and thirdly, events are not structured by an essential time.

In *Being and Event*, Alain Badiou writes that the event (*événement*) is a multiple which basically does not make sense according to the rules of the "situation," in other words existence. Hence, the event "is not," and therefore, in order for there to be an event, there must be an "intervention" which changes the rules of the situation in order to allow that particular event to be ("to be" meaning to be a multiple which belongs to the multiple of the situation — these terms are drawn from or defined in reference to set theory). In his view, there is no "one," and everything that is is a "multiple." "One" happens when the situation "counts," or accounts for, acknowledges, or defines something: it "counts it as one." For the event to be counted as one by the situation, or counted in the one of the situation, an intervention needs to decide its belonging to the situation. This is because his definition of the event violates the prohibition against self-belonging (in other words, it is a set-theoretical definition which violates set theory's rules of consistency), thus does not count as extant on its own.^{ [2] }

Gilles Deleuze lectured on the concept of *event* on March 10, 1987. A sense of the lecture is described by James Williams.^{ [3] } Williams also wrote, "From the point of view of the difference between two possible worlds, the event is all important".^{ [4] } He also stated, "Every event is revolutionary due to an integration of signs, acts and structures through the whole event. Events are distinguished by the intensity of this revolution, rather than the types of freedom or chance."^{ [5] } In 1988 Deleuze published a magazine article "Signes et événements"^{ [6] }

In his book *Nietszche and Philosophy*, he addresses the question "Which one is beautiful?" In the preface to the English translation he wrote:

- The one that ... does not refer to an individual, to a person, but rather to an event, that is, to the forces in their various relationships to a proposition or phenomenon, and the genetic relationship that determines these forces (power).
^{ [7] }

The Danish philosopher Ole Fogh Kirkeby deserves mentioning, as he has written a comprehensive trilogy about the event, or in Danish "begivenheden". In the first work of the trilogy "Eventum tantum – begivenhedens ethos"^{ [8] } (Eventum tantum - the ethos of the event) he distinguishes between three levels of the event, inspired from Nicola Cusanus: Eventum tantum as non aliud, the alma-event and the proto-event.

In mathematics, **cardinal numbers**, or **cardinals** for short, are a generalization of the natural numbers used to measure the cardinality (size) of sets. The cardinality of a finite set is a natural number: the number of elements in the set. The *transfinite* cardinal numbers describe the sizes of infinite sets.

**First-order logic**—also known as **predicate logic** and **first-order predicate calculus**—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantified variables over non-logical objects and allows the use of sentences that contain variables, so that rather than propositions such as *Socrates is a man* one can have expressions in the form "there exists x such that x is Socrates and x is a man" and *there exists* is a quantifier while *x* is a variable. This distinguishes it from propositional logic, which does not use quantifiers or relations; in this sense, propositional logic is the foundation of first-order logic.

**Gilles Deleuze** was a French philosopher who, from the early 1950s until his death in 1995, wrote on philosophy, literature, film, and fine art. His most popular works were the two volumes of *Capitalism and Schizophrenia*: *Anti-Oedipus* (1972) and *A Thousand Plateaus* (1980), both co-written with psychoanalyst Félix Guattari. His metaphysical treatise *Difference and Repetition* (1968) is considered by many scholars to be his magnum opus. A. W. Moore, citing Bernard Williams's criteria for a great thinker, ranks Deleuze among the "greatest philosophers". His work has influenced a variety of disciplines across philosophy and art, including literary theory, post-structuralism and postmodernism.

In mathematics, an **ordered pair** is a pair of objects. The order in which the objects appear in the pair is significant: the ordered pair is different from the ordered pair unless *a* = *b*.

In various branches of mathematics, a useful construction is often viewed as the “most efficient solution” to a certain problem. The definition of a **universal property** uses the language of category theory to make this notion precise and to study it abstractly.

**Causality** is efficacy, by which one process or state, a *cause*, contributes to the production of another process or state, an *effect*, where the cause is partly responsible for the effect, and the effect is partly dependent on the cause. In general, a process has many causes, which are also said to be causal factors for it, and all lie in its past. An effect can in turn be a cause of, or causal factor for, many other effects, which all lie in its future. Multiple philosophers have believed that causality is metaphysically prior to notions of time and space.

**Saul Aaron Kripke** is an American philosopher and logician. He is a Distinguished Professor of Philosophy at the Graduate Center of the City University of New York and emeritus professor at Princeton University. Since the 1960s, Kripke has been a central figure in a number of fields related to mathematical logic, philosophy of language, philosophy of mathematics, metaphysics, epistemology, and set theory. Much of his work remains unpublished or exists only as tape recordings and privately circulated manuscripts. Kripke was the recipient of the 2001 Schock Prize in Logic and Philosophy.

In mathematics, specifically category theory, **adjunction** is a relationship that two functors may have. Two functors that stand in this relationship are known as **adjoint functors**, one being the **left adjoint** and the other the **right adjoint**. Pairs of adjoint functors are ubiquitous in mathematics and often arise from constructions of "optimal solutions" to certain problems, such as the construction of a free group on a set in algebra, or the construction of the Stone-Čech compactification of a topological space in topology.

In set theory, **Zermelo–Fraenkel set theory**, named after mathematicians Ernst Zermelo and Abraham Fraenkel, is an axiomatic system that was proposed in the early twentieth century in order to formulate a theory of sets free of paradoxes such as Russell's paradox. Today, Zermelo–Fraenkel set theory, with the historically controversial axiom of choice (AC) included, is the standard form of axiomatic set theory and as such is the most common foundation of mathematics. Zermelo–Fraenkel set theory with the axiom of choice included is abbreviated **ZFC**, where C stands for "choice", and **ZF** refers to the axioms of Zermelo–Fraenkel set theory with the axiom of choice excluded.

In philosophy, **supervenience** refers to a relation between sets of properties or sets of facts. X is said to supervene on Y if and only if some difference in Y is necessary for any difference in X to be possible. Equivalently, X is said to supervene on Y if and only if X cannot vary unless Y varies. Here are some examples.

In philosophy and mathematical logic, **mereology** is the study of parts and the wholes they form. Whereas set theory is founded on the membership relation between a set and its elements, mereology emphasizes the meronomic relation between entities, which—from a set-theoretic perspective—is closer to the concept of inclusion between sets.

In mathematics, a **singleton**, also known as a **unit set**, is a set with exactly one element. For example, the set {null} is a singleton.

In the foundations of mathematics, **von Neumann–Bernays–Gödel set theory** (**NBG**) is an axiomatic set theory that is a conservative extension of Zermelo–Fraenkel set theory (ZFC). NBG introduces the notion of class, which is a collection of sets defined by a formula whose quantifiers range only over sets. NBG can define classes that are larger than sets, such as the class of all sets and the class of all ordinals. Morse–Kelley set theory (MK) allows classes to be defined by formulas whose quantifiers range over classes. NBG is finitely axiomatizable, while ZFC and MK are not.

A **definite description** is a denoting phrase in the form of "the X" where X is a noun-phrase or a singular common noun. The definite description is *proper* if X applies to a unique individual or object. For example: "the first person in space" and "the 42nd President of the United States of America", are proper. The definite descriptions "the person in space" and "the Senator from Ohio" are *improper* because the noun phrase X applies to more than one thing, and the definite descriptions "the first man on Mars" and "the Senator from some Country" are *improper* because X applies to nothing. Improper descriptions raise some difficult questions about the law of excluded middle, denotation, modality, and mental content.

A **free logic** is a logic with fewer existential presuppositions than classical logic. Free logics may allow for terms that do not denote any object. Free logics may also allow models that have an empty domain. A free logic with the latter property is an **inclusive logic**.

In mathematical logic, a **Boolean-valued model** is a generalization of the ordinary Tarskian notion of structure from model theory. In a Boolean-valued model, the truth values of propositions are not limited to "true" and "false", but instead take values in some fixed complete Boolean algebra.

This article examines the implementation of mathematical concepts in set theory. The implementation of a number of basic mathematical concepts is carried out in parallel in ZFC and in NFU, the version of Quine's New Foundations shown to be consistent by R. B. Jensen in 1969.

"**On Denoting**" is an essay by Bertrand Russell. It was published in the philosophy journal *Mind* in 1905. In it, Russell introduces and advocates his theory of denoting phrases, according to which definite descriptions and other "denoting phrases ... never have any meaning in themselves, but every proposition in whose verbal expression they occur has a meaning." This theory later became the basis for Russell's descriptivism with regard to proper names, and his view that proper names are "disguised" or "abbreviated" definite descriptions.

In mathematics, a **topos** is a category that behaves like the category of sheaves of sets on a topological space. Topoi behave much like the category of sets and possess a notion of localization; they are a direct generalization of point-set topology. The **Grothendieck topoi** find applications in algebraic geometry; the more general **elementary topoi** are used in logic.

- ↑ Jaegwon Kim (1993)
*Supervenience and Mind*, page 37, Cambridge University Press - ↑ Alain Badiou (1988)
*L'Être et l'Événement* - ↑ Charles J. Stivale (editor) (2011)
*Gilles Deleuze: Key Concepts*, 2nd edition, chapter 6: Event, pp 80–90 - ↑ James Williams (2003)
*Gilles Deleuze’s Difference and Repetition: A Critical Introduction and Guide*, page 78, Edinburgh University Press - ↑ Williams 2003 p xi
- ↑ Gilles Deleuze (1988) "Signes et événements",
*Magazine Littéraire*, #257, pages 16 to 25 - ↑ Michael Hart (1993)
*Gilles Deleuze: An apprenticeship in philosophy*, page 31, University of Minnesota Press ISBN 0-8166-2160-8 - ↑ Ole Fogh Kirkeby (2005)
*Eventum tantum : Begivenhedens ethos.*København: Samfundslitteratur

- Roberto Casati & Achille Varzi, Events, from Stanford Encyclopedia of Philosophy.
- Susan Schneider, Events, from The Internet Encyclopedia of Philosophy.
- Byron Kaldis, Events, from
*Encyclopedia of Philosophy and the Social Sciences*.

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