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Логика. Логическая операция обобщения и ограничения понятий (самое важное)

Lecture notes, cheat sheets

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14. LOGICAL OPERATION OF GENERALIZATION AND LIMITATIONS OF CONCEPTS

Of great importance for achieving the certainty of our thinking are the logical operations of generalization and limitation of concepts, based on the law of the inverse relationship between the content and scope of the concept.

Generalize the concept - means to move from a concept with a smaller volume, but a large content to a concept with more volume but less content. For example, generalizing the concept of "city court", we get the concept of "court", the scope of the new concept is wider than the original, since the first relates to the second as a species to a genus. At the same time, the content of the new concept has decreased, since we have excluded its specific features. Generalization of the concept can be multi-stage, for example. "criminal offence", "crime", "wrongful act", "act". However, the generalization of concepts cannot be infinite. The limit of generalization is categories - concepts with an extremely wide scope: matter, consciousness, movement, property, etc. Categories do not have a generic concept.

Restricting a concept is the opposite of generalization.

Restrict concept - means moving from a concept with a larger volume, but less content, to a concept with a smaller volume, but more content. For example, “lawyer”, “investigator”, “investigator of the prosecutor’s office”, “investigator of the prosecutor’s office Petrov”. The limit of limitation of a concept is a single concept.

The logical operations of generalizing and restricting concepts are widely used in the practice of thinking: moving from the concept of one volume to the concept of another volume, we clarify the subject of our thought, make our thinking more defined and consistent.

Generalization and limitation of concepts must not be confused with a mental transition from a part to a whole and the separation of a part from a whole. For example, a day is divided into hours, hours into minutes, minutes into seconds. Each subsequent concept is not a kind of the previous one, which in turn cannot be considered as generic. Therefore, the transition from the concept of "hour" to the concept of "day" is not a generalization, but a transition from part to whole.

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Scientists from the National Institute of Standards and Technology (NIST) have upgraded the optical microscopy technology they developed several years ago and adapted it to observe nano-sized objects, which allows them to control the production of elements of three-dimensional semiconductor chips of a new generation. With the help of this technology, called TSOM (Through-Focus Scanning Optical Micr), one can not only examine the nanoscale components of chips, which until recently were two-dimensional structures, but also determine differences in their shapes and sizes with a sufficiently high accuracy, which is required for carrying out technological control.

New generations of semiconductor chips are composed of three-dimensional elements that are superimposed on each other. For the correct and reliable operation of the chip as a whole, it is required that all components have the correct shape and strictly specified dimensions. Existing methods of microscopy - electron, atomic force and others - can provide control of the shape and size of chip elements, but they do it extremely slowly, with the risk of damaging the fragile structure of the chip, and they are also extremely expensive. And the use of optical microscopy methods is limited by the fact that the dimensions of the chip elements are much smaller than half the wavelength of visible light (250 nm for green light), so an optical microscope cannot physically see such small objects.

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"Our research has shown that with TSOM, we can view elements as small as 10 nm, which is enough to control semiconductor manufacturing processes for the next decade," says Ravikiran Attota, a scientist at NIST. TSOM technology can be used not only in the electronics industry, but also in other industries, in science and everywhere where it is necessary to analyze and control the shapes of tiny three-dimensional objects."

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