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Generalized Manifolds
A generalization is a form of abstraction whereby common properties of specific instances are formulated as general concepts or claims. Generalizations posit the existence of a domain or set theory, set of elements, as well as one or more common characteristics shared by those elements (thus creating a conceptual model). As such, they are the essential basis of all valid deductive inferences (particularly in logic, mathematics and science), where the process of falsifiability, verification is necessary to determine whether a generalization holds true for any given situation. Generalization can also be used to refer to the process of identifying the parts of a whole, as belonging to the whole. The parts, which might be unrelated when left on their own, may be brought together as a group, hence belonging to the whole by establishing a common relation between them. However, the parts cannot be generalized into a whole—until a common relation is established among ''all'' parts. T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abstraction
Abstraction in its main sense is a conceptual process wherein general rules and concepts are derived from the usage and classification of specific examples, literal ("real" or "concrete") signifiers, first principles, or other methods. "An abstraction" is the outcome of this process—a concept that acts as a common noun for all subordinate concepts and connects any related concepts as a ''group'', ''field'', or ''category''. Suzanne K. Langer (1953), ''Feeling and Form: a theory of art developed from Philosophy in a New Key'' p. 90: " Sculptural form is a powerful abstraction from actual objects and the three-dimensional space which we construe ... through touch and sight." Conceptual abstractions may be formed by filtering the information content of a concept or an observable phenomenon, selecting only those aspects which are relevant for a particular purpose. For example, abstracting a leather soccer ball to the more general idea of a ball selects only the information on gen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
