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All sciences use theory as a tool to explain. It is useful to think of theory as a conceptual model of some aspect of life. The term theory is used in the empirical sciences and is also used in philosophy, logic, and many other fields, like we may have a theory of mate selection, or the emergence of capitalism in societies, or of criminal behavior, or of the content of dreams. In each case the theory consists of a set of concepts and their nominal definition, assertions about the relationships between these concepts, assumptions and knowledge claims. Theory, in the scientific sense of the word, is an analytic structure designed to explain a set of empirical observations. The word 'theory' is generally considered to derive from Greek theoria.
Carl Jung's theory of the self, for example, begins by asserting the key concepts, introversion and extroversion, and the relationship between these two components, one is dominant and the other subordinate. It assumes that the dominant characteristic will be displayed in behavior and the subordinate one in our dreams or unconscious.
The content of dreams can be explained by bringing Jung's model to the inquiry. In the classic model of how science is conducted, the scientist begins with a theory, deduces a hypothesis about the real world from the theory and then engages in the necessary research to determine if the hypothesis is true or false. In this way science is always about theory testing.
Theories are distinct from theorems which are derived deductively from theories according to a formal system of rules, generally as a first step in testing or applying the theory in a concrete situation. Theories are abstract and conceptual and are never considered right or wrong. They are supported or challenged by observations in the world.
Fields of study such as game theory and number theory are sometimes named "theory" because their basis is some initial set of assumptions describing the field's approach to a subject matter.