By the end of the 16th century, all the preconditions had formed in European philosophy for its transition to rationalist positions, for an experimental-experimental method of cognizing the world. Among the thinkers who were the first to advance the ideas of experimental science were F. Bacon and R. Descartes.
Those principles of scientific knowledge that were substantiated by these scientists created an almost new philosophical and methodological attitude. To a large extent, it overcame the limitations of the Aristotelian organon and medieval scholasticism, which did not recognize experience as a source of knowledge of reality.
According to Bacon, in order to consistently and really explore the natural world, the method of induction and deduction should be applied. In the framework of the inductive method, it is necessary, in his opinion, to follow from the particular to the general, from particular facts to move towards the generalizing conclusions to which F. Bacon gave the name - average axioms. This will make it possible to ensure accuracy and gradualness in the cognitive process, since Bacon saw a great danger in the transition from individual facts recorded in the mind immediately to generalizations. This mechanism of the movement of thought was not opposed to the deductive-syllogistic model of reasoning, but rather effectively supplemented it. In a word, induction and deduction were organically combined within the framework of a single methodological tool. This approach significantly expanded the scope of application of each of the components of the inductive-deductive method, which were previously used independently of each other.
Bacon claimed that there is complete and incomplete induction-deduction, and thanks to this, he clearly defined their methodological capabilities and their place in the general system of cognitive resources of modern science. The thinker considered true induction to be the highest form of this method, which, according to Bacon, is capable of leading a person not only to reliable conclusions, but also to conclusions completely new. As their verification, it is recommended to resort to another method - the experiment, which acts as the highest authority in relation to the thesis being proved.
As you know, today the definition of induction is formulated quite clearly - this is the process of ascension in reasoning from many separate judgments to single conclusions generalizing them. Deduction involves the movement in a different direction - from generalized conclusions to individual conclusions that are valid for all objects that make up this set.
If we consider the categories of induction and deduction in the context of their historical development, then the picture is somewhat more complicated.
In the era of antiquity and the Middle Ages, scientists used mainly deduction, the main achievement and form of which was the syllogistics of Aristotle. As already mentioned, here the thought is directed from axioms to private judgments. To know the laws of nature, the use of such a method is not effective, because this method is completely not based on experience. Reliance on experience can only be given by induction, which involves the movement of learning from single facts that can be verified experimentally to general principles. It is interesting that it was Aristotle himself who described induction, however, at one time he did not attach any scientific and applied significance to it. But F. Bacon considered the most powerful methodological tool in it, and R. Descartes developed the principles of practical application on the basis of experimental verification of the reliability of facts. These scientists proved that induction and deduction can perform universal functions in cognition.
Induction, acting as a formal logical conclusion, is very widely used in the cognitive process. The logic of the inductive algorithm is as follows: by discovering the identical properties of objects of one class, the cognizing subject formulates the conclusion that all of them belong to all objects that make up this class. Thanks to such an algorithm for the development of thought, the law of universal gravitation was discovered, the laws of atmospheric pressure dependencies and other empirical dependencies existing in the observed nature were substantiated.
Deduction, which is a movement of thinking from the general to the unit, played an enduring role in the development of theoretical science at the stage of formulating the idea hypothesis. In this case, it represents the starting point for the formation of a new system of knowledge.
In modern scientific methodology, induction and deduction interact with each other in approximately the same way as, for example, synthesis and analysis, and their use implies the need for a competent choice of the exact area where the place of each method gives the greatest effect.