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8. Describe the inductive and deductive methods of cognition.

Deduction

Deductive techniques of formal logic are always leading from the general to the particular and never vice versa. Inductive approaches, with a few exceptions, are aimed at an opposite direction, from the particular to the general, and allow for generalization and augmentation of existing knowledge. The fact that deductive approaches of formal logic are based on transformation “from the general to the particular” does not mean that a deductive logical mechanism necessarily produces a singular, particular statement. However, the generalization level yielded by deductive transformation cannot be higher than the original level of generalization of input information.

The ability to maintain a given validity level is a unique virtue of deductive systems: it allows to combine various deductive elements into complex compound structures based on various non-obvious particular inferences derived from a set of general premises. Verification of truthfulness of each of particular statements can indirectly provide an assessment of a general level of validity of initial premises. This kind of assessment does not, however, warrant the truthfulness of all initial premises – even in the event that most of the possible inferences are verified as truthful, there may always be left at least one false inference among those that remain unverified, while for a conjunction of initial premises to be fallacious, it needs one false inference. To overcome the effect of such an asymmetry between confirmation and refutation, Karl Popper proposed the famous demarcation criterion that separates the scientific from the unscientific.

Induction

Inductive approaches to logical transformations allow for expanding and condensing existing knowledge by adding to it a newly obtained knowledge. Formal inductive logic applies the techniques that allow for generalization of individual particular statements and, thus, production of statements of a more general character by expanding a multitude of described objects (generalizing induction), or for expansion of existing knowledge by particular statements contained in initial knowledge in a non- obvious form. According to John Stuart Mill, the term “induction” only applies to an inference of an unknown instance or a multitude of instances based on observation of known instances.

Inductive methods tend to degrade the validity level of knowledge in the end of each inductive transformation step. Therefore, the validity of initial premises upon inductive transformation in no way warrants the validity of obtained inferences.

  1. Basic principles of modeling method.

Currently in educational research is widely used modeling method.

Modeling - a method of creating and research models. The study model provides a new knowledge, a new comprehensive information about the object.

The essential features of the model are: transparency, abstract, scientific element of fantasy and imagination, the use of analogy as a logical construction method, hypothetical element. In other words, the model is a hypothesis, expressed in visual form.

An important feature of the model is the presence of her imagination.

The first - a careful study of the experience with the phenomenon of interest to researchers, the analysis and synthesis of experience and creation of hypotheses underlying the future model.

The second - the research program compilation, organization of practical work in accordance with our program, making adjustments to it, suggested by practice, refinement of the original research hypothesis, taken as a basis model.

The third - the creation of the final version of the model. If the second stage of the researcher as it offers a variety of constructed phenomenon, then the third stage it on the basis of these options create the ultimate example of the process (or project), which is going to bring.

In teaching, modeling is successfully used to solve important problems of teaching. For example, teacher-researcher can develop models: optimization of the educational process structure, enhance the cognitive independence of students, student-centered approach in the learning process.

The simulation method opens up the possibility for teaching science mathematisation pedagogical processes. Mathematisation pedagogy has a great epistemological potential. The use of mathematical modeling is closely associated with an increasingly deep knowledge of the essence of educational phenomena and processes, deepening the theoretical foundations of the study.

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