What Is Inductive Reasoning?

Inductive reasoning is a reasoning from individual to general. From a certain degree of view on individual things to a wider range of views, general principles and principles of interpretation are derived from specific and specific cases. General in nature and society exists in individual, special, and exists through individual. Generally exist in specific objects and phenomena, so only by knowing the individual can we know the general. When people explain a larger thing, they summarize and generalize a variety of general principles or principles from individual and special things, and then it is possible to start from these principles and principles and draw conclusions about individual things. in conclusion. This order of understanding runs through people's interpretation activities, and continuously rises from individual to general, that is, from the recognition of individual things to the general regularity of things. For example, according to the backwardness of social life caused by the unproductive development of productive forces in various regions and historical periods, it can be concluded that the development of productive forces is the driving force for social progress. This is the reasoning of general conclusions drawn from the study of individual things. Process, that is, inductive reasoning. Obviously, inductive reasoning is an inferential process from the study of individual things to the conclusion and generalization of general laws. In the process of induction and generalization, the interpreter not only uses inductive reasoning, but also uses deductive methods. In people's explanatory thinking, induction and deduction are interconnected, complementary and indivisible. ^[1]

For example: in a plane,

Inductive reasoning and

The empirical materials obtained through observation, experiment, and other methods need to be processed and organized to form scientific conclusions. The methods for organizing empirical materials include comparison, classification, analysis and synthesis, and abstraction and generalization.

M. Klein wrote in "Mathematics in Western Culture": "Needless to say about our future, even after an hour from now, there is nothing certain that exists. One minute later, under our feet The ground may crack. However, claiming this possibility does not scare us, because we know that the probability of this happening is extremely small.

In other words, it is the probability that an event will happen that determines our attitude and action towards the event. "The phenomenon that may or may not occur under certain conditions, we call it a random event or an accidental event, such as drawing a red peach K from a bridge. In fact, when we observe a large number of similar random After the incident, it will be found that there is a certain regularity.

Probability is the quantitative characterization of the regularity presented by a large number of random events, which is usually represented by P (A). Using probabilistic reasoning, we can learn how likely an event is, or how likely it is. In this sense, we can say that probabilistic reasoning is the inference of opportunity.

Inductive reasoning probability

In daily life, we are only satisfied with estimating whether the probability of an event is high or low. However, this estimate is too broad to meet the needs of many issues such as industry, economy, insurance, medical, sociology, psychology, and so on. Because in the above case, you must know the exact probability value. To do this, you need help with mathematics. Reliance on mathematically calculated probability values can reliably guide our actions.

Generally, the definition of the calculated probability value is: if there are n kinds of possibilities, and the situation that is conducive to the occurrence of an event is m, the probability of the event occurring is m / n , and the probability of not occurring is (nm) / n . Under this definition, if the event is impossible, the probability of the event is 0 / n, which is 0; if the event is completely certain, the probability is n / n , which is 1.

Therefore, the probability value varies from 0 to 1, that is, from improbability to certainty. The so-called possibility means that the possibility of occurrence is the same. For example, a dice has 6 faces. If there is no factor in the shape of the dice or the way of throwing the dice that is conducive to the appearance of a certain face, the possibility of the 6 faces of the dice is the same, that is, there are 6 types of dice, etc. possibility.

According to this definition of calculating the probability value, the probability of selecting a card "A" from a deck of 52 ordinary unwashed cards is 4/52, which is 1/13. Because there are 52 such possibilities here, 4 of them are advantageous. However, if all possibilities are not equal, the definition of the calculated probability value does not apply. For example, there are only two possibilities for a person to cross the street: either safely or without safety. However, it cannot be concluded that the probability of a person crossing the street safely is 1/2, because the two possibilities of "safe crossing" and "no safe crossing" are not equally possible.

It should be noted that probability tells us what is happening in a large number of choices. For example, the probability of selecting "A" from 52 decks of cards is 1/13, which does not mean that if a person takes 13 times in this deck of cards, he will definitely choose an "A" ". He may have taken it 30 or 40 times and did not get an "A". However, the more times he takes, the ratio of the number of A's to the total number of cards drawn will approach 1/13. In addition, this does not mean that if a person takes an "A", for example, it happens to be obtained for the first time, the probability of taking out an "A" next time must be less than 1/13. The probability will still be the same, which is 1/13, even when 3 "A" s are taken out continuously. Because a deck of cards has neither memory nor consciousness, what has happened will not affect the future.