Gestalt psychology Gestalt psychology or gestaltism (German: Gestalt – "shape or form") is a theory of mind of the Berlin School. The central principle of gestalt psychology is that the mind forms a global whole with self-organizing tendencies. This principle maintains that the human mind considers objects in their entirety before, or in parallel with, perception of their individual parts; suggesting the whole is other than the sum of its parts. Gestalt psychology tries to understand the laws of our ability to acquire and maintain meaningful perceptions in an apparently chaotic world. In the domain of perception, Gestalt psychologists stipulate that perceptions are the products of complex interactions among various stimuli. Contrary to the behaviorist approach to understanding the elements of cognitive processes, gestalt psychologists sought to understand their organization (Carlson and Heth, 2010). Origins[edit] Gestalt therapy[edit] Theoretical framework and methodology[edit] Properties[edit] Reification
First principle Basic proposition or assumption In philosophy and science, a first principle is a basic proposition or assumption that cannot be deduced from any other proposition or assumption. First principles in philosophy are from first cause[1] attitudes and taught by Aristotelians, and nuanced versions of first principles are referred to as postulates by Kantians.[2] In mathematics and formal logic, first principles are referred to as axioms or postulates. In physics and other sciences, theoretical work is said to be from first principles, or ab initio, if it starts directly at the level of established science and does not make assumptions such as empirical model and parameter fitting. In a formal logical system, that is, a set of propositions that are consistent with one another, it is possible that some of the statements can be deduced from other statements. A first principle is an axiom that cannot be deduced from any other within that system. Ancient Greek philosophy [edit] Mythical cosmogonies
Normative ethics Branch of philosophical ethics that examines standards for morality Normative ethics is the study of ethical behaviour and is the branch of philosophical ethics that investigates questions regarding how one ought to act, in a moral sense. Normative ethics is distinct from meta-ethics in that the former examines standards for the rightness and wrongness of actions, whereas the latter studies the meaning of moral language and the metaphysics of moral facts. An adequate justification for a group of principles needs an explanation of those principles. Most traditional moral theories rest on principles that determine whether an action is right or wrong. Normative ethical theories[edit] There are disagreements about what precisely gives an action, rule, or disposition its ethical force. Virtue ethics[edit] Deontological ethics[edit] Deontology argues that decisions should be made considering the factors of one's duties and one's rights. Consequentialism[edit] Other theories[edit] —Philippa Foot
Problem solving Problem solving consists of using generic or ad hoc methods, in an orderly manner, for finding solutions to problems. Some of the problem-solving techniques developed and used in artificial intelligence, computer science, engineering, mathematics, medicine, etc. are related to mental problem-solving techniques studied in psychology. Definition[edit] The term problem-solving is used in many disciplines, sometimes with different perspectives, and often with different terminologies. For instance, it is a mental process in psychology and a computerized process in computer science. Psychology[edit] While problem solving accompanies the very beginning of human evolution and especially the history of mathematics,[4] the nature of human problem solving processes and methods has been studied by psychologists over the past hundred years. Clinical psychology[edit] Cognitive sciences[edit] Computer science and algorithmics[edit] Engineering[edit] Cognitive sciences: two schools[edit] Europe[edit]
Formal system Mathematical model for deduction or proof systems In 1921, David Hilbert proposed to use formal systems as the foundation of knowledge in mathematics.[2] The term formalism is sometimes a rough synonym for formal system, but it also refers to a given style of notation, for example, Paul Dirac's bra–ket notation. A formal system has the following:[3][4][5] A formal system is said to be recursive (i.e. effective) or recursively enumerable if the set of axioms and the set of inference rules are decidable sets or semidecidable sets, respectively. A formal language is a language that is defined by a formal system. A deductive system, also called a deductive apparatus,[8] consists of the axioms (or axiom schemata) and rules of inference that can be used to derive theorems of the system. The logical consequence (or entailment) of the system by its logical foundation is what distinguishes a formal system from others which may have some basis in an abstract model. Formal semantics of logical system
Entailment Logicians make precise accounts of logical consequence with respect to a given language by constructing a deductive system for , or by formalizing the intended semantics for . Formal accounts of logical consequence[edit] The most widely prevailing view on how to best account for logical consequence is to appeal to formality. are . . This is in contrast to an argument like "Fred is Mike's brother's son. is 's brother's son, therefore 's nephew" is valid in all cases, but is not a formal argument.[1] A priori property of logical consequence[edit] If you know that follows logically from no information about the possible interpretations of or will affect that knowledge. is a logical consequence of cannot be influenced by empirical knowledge.[1] Deductively valid arguments can be known to be so without recourse to experience, so they must be knowable a priori.[1] However, formality alone does not guarantee that logical consequence is not influenced by empirical knowledge. Proofs and models[edit] A formula
Symmetry Sphere symmetrical group o representing an octahedral rotational symmetry. The yellow region shows the fundamental domain. Symmetry (from Greek συμμετρία symmetria "agreement in dimensions, due proportion, arrangement")[1] has two meanings. The first is a vague sense of harmonious and beautiful proportion and balance.[2][3] The second is an exact mathematical "patterned self-similarity" that can be demonstrated with the rules of a formal system, such as geometry or physics. Although these two meanings of "symmetry" can sometimes be told apart, they are related, so they are here discussed together.[3] Mathematical symmetry may be observed This article describes these notions of symmetry from four perspectives. The opposite of symmetry is asymmetry. Geometry[edit] A geometric object is typically symmetric only under a subgroup of isometries. Reflectional symmetry[edit] An isosceles triangle with mirror symmetry. A drawing of a butterfly with bilateral symmetry Rotational symmetry[edit] .
Axiom Statement that is taken to be true The precise definition varies across fields of study. In classic philosophy, an axiom is a statement that is so evident or well-established, that it is accepted without controversy or question.[3] In modern logic, an axiom is a premise or starting point for reasoning.[4] In mathematics, an axiom may be a "logical axiom" or a "non-logical axiom". Logical axioms are taken to be true within the system of logic they define and are often shown in symbolic form (e.g., (A and B) implies A), while non-logical axioms are substantive assertions about the elements of the domain of a specific mathematical theory, for example a + 0 = a in integer arithmetic. Any axiom is a statement that serves as a starting point from which other statements are logically derived. The root meaning of the word postulate is to "demand"; for instance, Euclid demands that one agree that some things can be done (e.g., any two points can be joined by a straight line).[8] [edit] Postulates and
Monolith In architecture, the term has considerable overlap with megalith, which is normally used for prehistory, and may be used in the contexts of rock-cut architecture that remains attached to solid rock, as in monolithic church, or for exceptionally large stones such as obelisks, statues, monolithic columns or large architraves, that may have been moved a considerable distance after quarrying. It may also be used of large glacial erratics moved by natural forces. The word derives, via the Latin monolithus, from the Ancient Greek word μονόλιθος (monolithos), from μόνος ("one" or "single") and λίθος ("stone"). Geological monoliths[edit] Large, well-known monoliths include: Africa[edit] Aso Rock, NigeriaBen Amera, MauritaniaBrandberg Mountain, NamibiaSibebe, SwazilandSphinx, EgyptZuma Rock, Nigeria Antarctica[edit] Scullin monolith Asia[edit] Bellary, IndiaMount Kelam, IndonesiaMadhugiri Betta, IndiaSangla Hill, PakistanSavandurga, IndiaSigiriya, Sri LankaYana, India Australia[edit] Europe[edit]
Eternity puzzle An empty Eternity board Eternity is a tiling puzzle created by Christopher Monckton and launched by the Ertl Company in June 1999. Consisting of 209 pieces, it was marketed as being practically unsolveable, with a £1 million prize on offer for whoever could solve it within four years. The prize was paid out in October 2000 for a winning solution arrived at by two mathematicians from Cambridge.[1] A second puzzle, Eternity II, was launched in Summer 2007 with a prize of US$2 million.[2] Puzzle[edit] The puzzle consists of filling a large almost regular dodecagon with 209 irregularly shaped smaller polygon pieces of the same color. Retail[edit] The puzzle was launched in June 1999, by Ertl, marketed to puzzle enthusiasts and 500,000 copies were sold worldwide, with the game becoming a craze at one point. Prize[edit] The puzzle's inventor Christopher Monckton put up half the prize money himself, the other half being put up by underwriters in the London insurance market. Solution[edit]
Non-classical logic Formal systems of logic that significantly differ from standard logical systems Non-classical logics (and sometimes alternative logics or non-Aristotelian logics) are formal systems that differ in a significant way from standard logical systems such as propositional and predicate logic. There are several ways in which this is commonly the case, including by way of extensions, deviations, and variations. Philosophical logic is understood to encompass and focus on non-classical logics, although the term has other meanings as well.[2] In addition, some parts of theoretical computer science can be thought of as using non-classical reasoning, although this varies according to the subject area. Examples of non-classical logics [edit] There are many kinds of non-classical logic, which include: Classification of non-classical logics according to specific authors In an extension, new and different logical constants are added, for instance the " (See also Conservative extension.)
Semantics Montague grammar[edit] In the late 1960s, Richard Montague proposed a system for defining semantic entries in the lexicon in terms of the lambda calculus. In these terms, the syntactic parse of the sentence John ate every bagel would consist of a subject (John) and a predicate (ate every bagel); Montague demonstrated that the meaning of the sentence altogether could be decomposed into the meanings of its parts and in relatively few rules of combination. The logical predicate thus obtained would be elaborated further, e.g. using truth theory models, which ultimately relate meanings to a set of Tarskiian universals, which may lie outside the logic. Despite its elegance, Montague grammar was limited by the context-dependent variability in word sense, and led to several attempts at incorporating context, such as: Dynamic turn in semantics[edit] A concrete example of the latter phenomenon is semantic underspecification – meanings are not complete without some elements of context.