Knowledge in the Psychology of Thinking and Mathematics

Knowledge in the Psychology of Thinking and Mathematics

Xenia Naidenova (Military Medical Academy, Russia)
DOI: 10.4018/978-1-60566-810-9.ch001
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This chapter offers a view on the history of developing the concepts of knowledge and human reasoning both in mathematics and psychology. Mathematicians create the formal theories of correct thinking; psychologists study the cognitive mechanisms that underpin knowledge construction and thinking as the most important functions of human existence. They study how the human mind works. The progress in understanding human knowledge and thinking will be undoubtedly related to combining the efforts of scientists in these different disciplines. Believing that it is impossible to study independently the problems of knowledge and human reasoning we strive to cover in this chapter the central ideas of knowledge and logical inference that have been manifested in the works of outstanding thinkers and scientists of past time. These ideas reveal all the difficulties and obstacles on the way to comprehending the human mental processes.
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This chapter acquaints the reader with the circle of ideas about the human thinking and its laws. If we know something in general about the world, then this is due to the fact that we know how to reason. While the logic or science about how to think correctly and how to come to true conclusions was developed in the course of millenniums, the science of knowledge as the result of reasoning arose in our time within the framework of a scientific direction called ‘artificial intelligence’. The use of computers in all spheres of our life requires studying and a fundamental understanding of how men extract knowledge from observations. Plausible reasoning, «fuzzy» reasoning reflecting the properties of human thinking in everyday life, became the subject of study in computer sciences, cognitive psychology, logic, and mathematics. The problem of the synthesis of knowledge and reasoning is not yet solved, but it is the forward edge of studies, and the experience of past times is extremely valuable for these studies.

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