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Varieties of analysis are classification and periodization.
Synthesis is a research method that involves the mental connection of the constituent parts or elements of the object under study, its study as a whole.
Methods of analysis and synthesis are interconnected, they are equally used in scientific research.
Induction is the movement of thought (cognition) from facts, individual cases to a general position. Induction leads to universal concepts and laws that can be taken as the basis of deduction.
Deduction is the derivation of a single, particular from any general position; the movement of thought (cognition) from general statements to statements about individual objects or phenomena. Through deductive reasoning, a certain thought is «deduced» from other thoughts.
Analogy is a way of obtaining knowledge about objects and phenomena based on the fact that they are similar to others; reasoning in which, from the similarity of the studied objects in some features, a conclusion is made about their similarity in other features.
The methods of the theoretical level include axiomatic, hypothetical, formalization, abstraction, ranking, generalization, ascent from the abstract to the concrete, historical, method of system analysis.
In scientific research, the method of abstraction is widely used, that is, abstraction from secondary facts in order to focus on the most important features of the phenomenon under study. For example, when studying the operation of a mechanism, a calculation scheme is analyzed that displays the main, essential properties of the mechanism. Sometimes, when analyzing phenomena and processes, there is a need to consider a large number of facts (signs). Here it is important to be able to highlight the main thing. In this case, a ranking method can be applied, with the help of which everything secondary, which does not significantly affect the phenomenon under consideration, is excluded.
The axiomatic method consists in the fact that some statements (axioms, postulates) are accepted without proof and then, according to certain logical rules, the rest of the knowledge is derived from them.
In some cases, a formalization method is used. Its essence lies in the fact that the main provisions of processes and phenomena are presented in the form of formulas and special symbols. Through operations with formulas of artificial languages, one can obtain new formulas, prove the truth of any proposition. Formalization is the basis for algorithmization and programming, without which the computerization of knowledge and the research process cannot do. The use of symbols and other familiar systems allows you to establish patterns between the studied facts.
The hypothetical method is based on the development of a hypothesis, a scientific assumption containing elements of novelty and originality. A hypothesis must more fully and better explain phenomena and processes, be confirmed experimentally, and comply with the general laws of dialectics and natural science. This research method is the main and most common in applied sciences.