Education of the republic of uzbekistan state university of world languages

Concepts in calculus: Concepts in calculus, according to Carl Benjamin Boyer⁷ in the preface of his The History of Calculus and its Conceptual Development, do not refer to perceptions. The concepts are allowed on their own as long as they are helpful and mutually compatible. The ideas of the derivative and the integral, for example, are not thought to pertain to spatial or temporal views of the external world of experience. They are also unrelated to the unexplained limits at which quantities are on the point of nascence or evanescence, that is, entering into or leaving existence.
Notable theories on the structure of concepts
Classic theory: The classical theory of concepts, also known as the empiricist theory of concepts, is the oldest hypothesis explaining the structure of concepts (dating back to Aristotle) and was widely embraced until the 1970s. According to the classical theory of concepts, concepts have a definitional structure. Often, adequate definitions of the type required by this theory take the form of a list of properties. To establish a complete definition, these traits must have two crucial qualities. The characteristics implied by a concept's definition must be both essential and sufficient for membership in the class of things covered by a specific concept. A characteristic is considered required if it is shared by all members of the designated class. A characteristic is considered required if it is shared by all members of the designated class. A feature is considered sufficient if it contains all of the components required by the definition⁸. The classic example bachelor, for example, is considered to be defined by unmarried and man. A bachelor (according to this definition) is an entity who is both unmarried and male. To determine whether anything belongs to the class, compare its characteristics to the features listed in the definition. Another important aspect of this theory is that it adheres to the concept of the excluded middle, which states that there are no partial members of a class; you are either in or out. The classical hypothesis remained uncontested for so long because it seemed intuitively true and had considerable explanatory power. It can explain how concepts are acquired, how we categorize them, and how we use a concept's structure to establish its referent class. In reality, for many years, idea analysis was one of the most important activity in philosophy⁹. The act of attempting to explain the necessary and sufficient conditions for a concept's membership in the referent class is known as concept analysis. For example, Shoemaker's famous "Time Without Change" investigated whether the concept of the flow of time might include flows in which no changes occur, despite the fact that change is commonly accepted as a description of time.