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Composition (objects)
Compositional objects are wholes instantiated by collections of parts. If an ontology wishes to permit the inclusion of compositional objects it must define which collections of objects are to be considered parts composing a whole. Mereology, the study of relationships between parts and their wholes, provides specifications on how parts must relate to one another in order to compose a whole. Mereology of material objects Ontological disputes do not revolve around what particular matter is present; rather, the center of disputation is what objects can be said to be instantiated by a given collection of matter. The token objects posited by a given ontology may be classified as instances of one or more distinct object types. As the types of objects accepted proliferate, so do the possible tokens that a given collection of matter can be said to instantiate. This creates variations in size between ontologies, which serve as an arena for disputes among philosophers. The ontologies o ...
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Ontology
In metaphysics, ontology is the philosophical study of being, as well as related concepts such as existence, becoming, and reality. Ontology addresses questions like how entities are grouped into categories and which of these entities exist on the most fundamental level. Ontologists often try to determine what the categories or highest kinds are and how they form a system of categories that encompasses classification of all entities. Commonly proposed categories include substances, properties, relations, states of affairs and events. These categories are characterized by fundamental ontological concepts, including particularity and universality, abstractness and concreteness, or possibility and necessity. Of special interest is the concept of ontological dependence, which determines whether the entities of a category exist on the most fundamental level. Disagreements within ontology are often about whether entities belonging to a certain category exist and, if so, how they ...
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Gunk (mereology)
In mereology, an area of philosophical logic, the term gunk applies to any whole whose parts all have further proper parts. That is, a gunky object is not made of indivisible ''atoms'' or '' simples''. Because parthood is transitive, any part of gunk is itself gunk. If point-sized objects are always simple, then a gunky object does not have any point-sized parts. By usual accounts of gunk, such as Alfred Tarski's in 1929, three-dimensional gunky objects also do not have other degenerate parts shaped like one-dimensional curves or two-dimensional surfaces. (See also ''Whitehead's point-free geometry''.) Gunk is an important test case for accounts of the composition of material objects: for instance, Ted Sider has challenged Peter van Inwagen's account of composition because it is inconsistent with the possibility of gunk. Sider's argument also applies to a simpler view than van Inwagen's: mereological ''nihilism'', the view that only material simples exist. If nihilism is necess ...
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Paradigm
In science and philosophy, a paradigm () is a distinct set of concepts or thought patterns, including theories, research methods, postulates, and standards for what constitute legitimate contributions to a field. Etymology ''Paradigm'' comes from Greek παράδειγμα (''paradeigma''), "pattern, example, sample" from the verb παραδείκνυμι (''paradeiknumi''), "exhibit, represent, expose" and that from παρά (''para''), "beside, beyond" and δείκνυμι (''deiknumi''), "to show, to point out". In classical (Greek-based) rhetoric, a paradeigma aims to provide an audience with an illustration of a similar occurrence. This illustration is not meant to take the audience to a conclusion, however it is used to help guide them get there. One way of how a ''paradeigma'' is meant to guide an audience would be exemplified by the role of a personal accountant. It is not the job of a personal accountant to tell a client exactly what (and what not) to spend money on ...
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Determination
Determination is a positive emotional feeling that involves persevering towards a difficult goal in spite of obstacles.Kirby, L.D., Morrow, J., & Yih, J. (2014). The challenge of challenge: Pursuing determination as an emotion. In M. M. Tugade, M. N. Shiota, & L. D. Kirby (Eds.), Handbook of Positive Emotions. New York: Guilford Publications, Inc.Smith, C. A. (1991). The self, appraisal, and coping. In C. R. Snyder & D. R. Forsyth (Eds.), Handbook of Social and Clinical Psychology: The Health Perspective. New York: Pergamon press. Determination occurs prior to goal attainment and serves to motivate behavior that will help achieve one's goal. Empirical research suggests that people consider determination to be an emotion; in other words, determination is not just a cognitive state, but rather an affective state. In the psychology literature, researchers have studied determination under other terms, including challenge and anticipatory enthusiasm; this may explain one reason for th ...
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Arbitrary
Arbitrariness is the quality of being "determined by chance, whim, or impulse, and not by necessity, reason, or principle". It is also used to refer to a choice made without any specific criterion or restraint. Arbitrary decisions are not necessarily the same as random decisions. For example, during the 1973 oil crisis, Americans were allowed to purchase gasoline only on odd-numbered days if their license plate was odd, and on even-numbered days if their license plate was even. The system was well-defined and not random in its restrictions; however, since license plate numbers are completely unrelated to a person's fitness to purchase gasoline, it was still an arbitrary division of people. Similarly, schoolchildren are often organized by their surname in alphabetical order, a non-random yet an arbitrary method—at least in cases where surnames are irrelevant. Philosophy Arbitrary actions are closely related to teleology, the study of purpose. Actions lacking a ''telos'', a go ...
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Spatial Dimension
In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of one (1D) because only one coordinate is needed to specify a point on itfor example, the point at 5 on a number line. A surface, such as the boundary of a cylinder or sphere, has a dimension of two (2D) because two coordinates are needed to specify a point on itfor example, both a latitude and longitude are required to locate a point on the surface of a sphere. A two-dimensional Euclidean space is a two-dimensional space on the plane. The inside of a cube, a cylinder or a sphere is three-dimensional (3D) because three coordinates are needed to locate a point within these spaces. In classical mechanics, space and time are different categories and refer to absolute space and time. That conception of the world is a four-dimensional space but not the one that was found necessary ...
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Molecule
A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and biochemistry, the distinction from ions is dropped and ''molecule'' is often used when referring to polyatomic ions. A molecule may be homonuclear, that is, it consists of atoms of one chemical element, e.g. two atoms in the oxygen molecule (O2); or it may be heteronuclear, a chemical compound composed of more than one element, e.g. water (two hydrogen atoms and one oxygen atom; H2O). In the kinetic theory of gases, the term ''molecule'' is often used for any gaseous particle regardless of its composition. This relaxes the requirement that a molecule contains two or more atoms, since the noble gases are individual atoms. Atoms and complexes connected by non-covalent interactions, such as hydrogen bonds or ionic bonds, are typically not consid ...
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Spatial Analysis
Spatial analysis or spatial statistics includes any of the formal techniques which studies entities using their topological, geometric, or geographic properties. Spatial analysis includes a variety of techniques, many still in their early development, using different analytic approaches and applied in fields as diverse as astronomy, with its studies of the placement of galaxies in the cosmos, to chip fabrication engineering, with its use of "place and route" algorithms to build complex wiring structures. In a more restricted sense, spatial analysis is the technique applied to structures at the human scale, most notably in the analysis of geographic data or transcriptomics data. Complex issues arise in spatial analysis, many of which are neither clearly defined nor completely resolved, but form the basis for current research. The most fundamental of these is the problem of defining the spatial location of the entities being studied. Classification of the techniques of spatial ...
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Stipulation
In United States law, a stipulation is a formal legal acknowledgment and agreement made between opposing parties before a pending hearing or trial. For example, both parties might stipulate to certain facts and so not have to argue them in court. After the stipulation is entered into, it is presented to the judge. The term can also refer to a special rule in a professional wrestling match, which can force the loser to do something (such as retire) or to any other change to the basic rules of the match type. The word is derived from the Latin word ''stipula'' "straw." The Ancient Roman In modern historiography, ancient Rome refers to Roman civilisation from the founding of the city of Rome in the 8th century BC to the collapse of the Western Roman Empire in the 5th century AD. It encompasses the Roman Kingdom (753–509 BC ... custom was that the negotiating parties, upon reaching an agreement, broke a straw as a sign of their mutual agreement and wrote down the agreement's ...
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Atom
Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons. Every solid, liquid, gas, and plasma is composed of neutral or ionized atoms. Atoms are extremely small, typically around 100 picometers across. They are so small that accurately predicting their behavior using classical physics, as if they were tennis balls for example, is not possible due to quantum effects. More than 99.94% of an atom's mass is in the nucleus. The protons have a positive electric charge, the electrons have a negative electric charge, and the neutrons have no electric charge. If the number of protons and electrons are equal, then the atom is electrically neutral. If an atom has more or fewer electrons than protons, then it has an overall negative or positive charge, respectively – such atoms are called ions. The electrons of an atom are a ...
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Decomposition Method (constraint Satisfaction)
In constraint satisfaction, a decomposition method translates a constraint satisfaction problem into another constraint satisfaction problem that is binary and acyclic. Decomposition methods work by grouping variables into sets, and solving a subproblem for each set. These translations are done because solving binary acyclic problems is a tractable problem. Each structural restriction defined a measure of complexity of solving the problem after conversion; this measure is called ''width''. Fixing a maximal allowed width is a way for identifying a subclass of constraint satisfaction problems. Solving problems in this class is polynomial for most decompositions; if this holds for a decomposition, the class of fixed-width problems form a tractable subclass of constraint satisfaction problems. Overview Decomposition methods translate a problem into a new one that is easier to solve. The new problem only contains binary constraints; their scopes form a directed acyclic graph. Th ...
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Counterintuitive
A paradox is a logically self-contradictory statement or a statement that runs contrary to one's expectation. It is a statement that, despite apparently valid reasoning from true premises, leads to a seemingly self-contradictory or a logically unacceptable conclusion. A paradox usually involves contradictory-yet-interrelated elements that exist simultaneously and persist over time. They result in "persistent contradiction between interdependent elements" leading to a lasting "unity of opposites". In logic, many paradoxes exist that are known to be invalid arguments, yet are nevertheless valuable in promoting critical thinking, while other paradoxes have revealed errors in definitions that were assumed to be rigorous, and have caused axioms of mathematics and logic to be re-examined. One example is Russell's paradox, which questions whether a "list of all lists that do not contain themselves" would include itself, and showed that attempts to found set theory on the identification ...
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