Reflexivity (social theory)

Reflexivity refers to circular relationships between cause and effect. A reflexive relationship is bidirectional with both the cause and the effect affecting one another in a relationship in which neither can be assigned as causes or effects. In sociology, reflexivity therefore comes to mean an act of self-reference where examination or action "bends back on", refers to, and affects the entity instigating the action or examination.

To this extent it commonly refers to the capacity of an agent to recognize forces of socialization and alter their place in the social structure. A low level of reflexivity would result in an individual shaped largely by their environment (or "society"). A high level of social reflexivity would be defined by an individual shaping their own norms, tastes, politics, desires, and so on. This is similar to the notion of autonomy. (See also Structure and agency and Social mobility.)

In economics, reflexivity refers to the self-reinforcing effect of market sentiment, whereby rising prices attract buyers whose actions drive prices higher still until the process becomes unsustainable and the same process operates in reverse leading to a catastrophic collapse in prices. This is an instance of a positive feedback loop.

Social theory

Social theories are frameworks of empirical evidence used to study and interpret social phenomena. A tool used by social scientists, social theories relate to historical debates over the most valid and reliable methodologies (e.g. positivism and antipositivism), as well as the primacy of either structure or agency. Certain social theories attempt to remain strictly scientific, descriptive, and objective. Conflict theories, by contrast, present ostensibly normative positions, and often critique the ideological aspects inherent in conventional, traditional thought.

Тhe origins of social theory are difficult to pinpoint, but debates frequently return to Ancient Greece (Berberoglu 2005, p. xi). From these foundations in Western philosophy arose Enlightenment social contract theory, sociological positivism, and modern social science. Today, 'social science' is used as an umbrella term to refer to sociology, economics, political science, jurisprudence, and other disciplines. Social theory is interdisciplinary and draws upon ideas from fields as diverse as anthropology and media studies. Social theory of an informal nature, or authorship based outside of academic social and political science, may be referred to instead as "social criticism" or "social commentary". Similarly, "cultural criticism" may be associated both with formal cultural and literary scholarship, as well as other non-academic or journalistic forms of writing.

Theory

Theory is a contemplative and rational type of abstract or generalizing thinking, or the results of such thinking. Depending on the context, the results might for example include generalized explanations of how nature works. The word has its roots in ancient Greek, but in modern use it has taken on several different related meanings. A theory is not the same as a hypothesis. A theory provides an explanatory framework for some observation, and from the assumptions of the explanation follows a number of possible hypotheses that can be tested in order to provide support for, or challenge, the theory.

A theory can be normative (or prescriptive), meaning a postulation about what ought to be. It provides "goals, norms, and standards". A theory can be a body of knowledge, which may or may not be associated with particular explanatory models. To theorize is to develop this body of knowledge.

As already in Aristotle's definitions, theory is very often contrasted to "practice" (from Greek praxis, πρᾶξις) a Greek term for "doing", which is opposed to theory because pure theory involves no doing apart from itself. A classical example of the distinction between "theoretical" and "practical" uses the discipline of medicine: medical theory involves trying to understand the causes and nature of health and sickness, while the practical side of medicine is trying to make people healthy. These two things are related but can be independent, because it is possible to research health and sickness without curing specific patients, and it is possible to cure a patient without knowing how the cure worked.

Chess theory

The game of chess is commonly divided into three phases: the opening, middlegame, and endgame. There is a large body of theory regarding how the game should be played in each of these phases, especially the opening and endgame. Those who write about chess theory, who are often but not necessarily also eminent players, are referred to as "theorists" or "theoreticians".

"Opening theory" commonly refers to consensus, broadly represented by current literature on the openings. "Endgame theory" consists of statements regarding specific positions, or positions of a similar type, though there are few universally applicable principles. "Middlegame theory" often refers to maxims or principles applicable to the middlegame. The modern trend, however, is to assign paramount importance to analysis of the specific position at hand rather than to general principles.

The development of theory in all of these areas has been assisted by the vast literature on the game. In 1913, preeminent chess historian H. J. R. Murray wrote in his 900-page magnum opus A History of Chess that, "The game possesses a literature which in contents probably exceeds that of all other games combined." He estimated that at that time the "total number of books on chess, chess magazines, and newspapers devoting space regularly to the game probably exceeds 5,000". In 1949, B. H. Wood opined that the number had increased to about 20,000.David Hooper and Kenneth Whyld wrote in 1992 that, "Since then there has been a steady increase year by year of the number of new chess publications. No one knows how many have been printed..." The world's largest chess library, the John G. White Collection at the Cleveland Public Library, contains over 32,000 chess books and serials, including over 6,000 bound volumes of chess periodicals. Chess players today also avail themselves of computer-based sources of information.

Theory (mathematical logic)

In mathematical logic, a theory (also called a formal theory) is a set of sentences in a formal language. Usually a deductive system is understood from context. An element of a theory is then called an axiom of the theory, and any sentence that follows from the axioms () is called a theorem of the theory. Every axiom is also a theorem. A first-order theory is a set of first-order sentences.

Theories expressed in formal language generally

When defining theories for foundational purposes, additional care must be taken and normal set-theoretic language may not be appropriate.

The construction of a theory begins by specifying a definite non-empty conceptual class , the elements of which are called statements. These initial statements are often called the primitive elements or elementary statements of the theory, to distinguish them from other statements which may be derived from them.

A theory is a conceptual class consisting of certain of these elementary statements. The elementary statements which belong to are called the elementary theorems of and said to be true. In this way, a theory is a way of designating a subset of which consists entirely of true statements.