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Inference... description and analysis

Description and analysis

1 - Different types of reasoning

Inference is a mental act consisting of successive rulings, which, if they are established, require another ruling in and of themselves. The connection between the rulings that make up inference is of three types: deduction, induction, and representation.

1 - Conclusion

Reasoning is the most complete type of reasoning. It has two forms: analogy and structural inference.

Le Syllogisme An analogy is a statement made up of statements that, if they are stated, are necessary by themselves, not by accident, another statement other than them by necessity (2), such as your saying: Every lion is a vertebrate, and every lion calf is a vertebrate, so every calf is a vertebrate. This analogy consists of three statements, that is, two introductions and a conclusion. The two premises share one term, and are separated by two terms. The limits are three: the largest, the middle, and the smallest. The premise that contains the largest term (the largest term is the most comprehensive of the three terms) is called the major term, and the one that contains the smallest term (the smallest term is the least comprehensive of the three terms) is called the minor term, and the common term between the two premise is called the middle term. This term would be removed from the result, and would connect the other two terms.

Therefore, the result combines the larger term and the smaller term, and is necessarily necessary in relation to the two premises. The meaning of this necessity is that if you state the two premises, you are forced to accept the result, and if you do not accept it, you fall into contradiction. The conclusion is not only necessary in relation to the two premises, but rather it is implied and included in them. You can reach it through analysis, because it only applies the general ruling that was made in the major case to a single, special case. We will talk about this analysis in logic, and show that analogy is a formal deduction.

Constructive deduction or proof (Déduction constructive ou démonstration) Descartes distinguished in his book: Discourse de la method (Discourse de la method) between logical analogy and mathematical proof, saying: Analogy is sterile, and mathematical proof is productive. In fact, these two types of deduction share the necessity of the conclusion from the premises. The conclusion is necessary from the principles in mathematical proof, just as the conclusion is necessary from the premises in logical analogy. Otherwise, this inference would not be a conclusion, but the result of mathematical proof is not included in the principles.
But it is added to it. In proof, the mathematician does not limit himself to analyzing the principles and extracting the elements in them. Rather, he creates the results in a comprehensive manner and synthesizes them. We often follow this method in synthesizing the facts that have been transmitted to us, or that we have forgotten, so we rely on some of the elements known to us, and construct the rest.

Definition of conclusion. - For every conclusion, the result is necessarily necessary from the premises. It is a transition from principles to results. Measurement is a formal, analytical conclusion, while proof is a constructive, synthetic conclusion.

2 - Induction - L'induction

Induction is a judgment about a whole, because that judgment exists in the details of that whole. It is applied in experimental sciences, for example: every body falls towards the center of the Earth. Because each thing is like a stone, or water, or wood, and the stone, water, and wood all fall toward the center of the earth. We are not relying here on abstract principles, but rather on specific phenomena, and we move from these phenomena to laws, that is, to general, fixed, and comprehensive relationships. For all phenomena that are of one type, such as the phenomena of falling bodies, or the phenomena of light reflection or refraction, then induction is the inference by which we move from phenomena to laws.

And induction, as is clear from this example. It expands the scope of observation, because observation only includes a limited number of phenomena, but the law extracted from it is general and includes an indefinite number of phenomena. It is as if we are judging the particular over the universal, or the limited over the infinite, due to the existence of the general in the particular, and this expansion is not a pretext. In induction and its results, because it is based on rational axioms that we will mention in logic.

3- Acting by analogy

Representation is a judgment about a specific thing, due to the existence of that judgment in another specific thing, or certain other things, provided that that judgment is comprehensive in its similar meaning. Example: Mars, like Earth, has a breezy atmosphere, and therefore, like Earth, it is populated. If we find in one thing an attribute associated with another attribute, and then we find this attribute in another thing, we expect the presence of the second attribute along with it. Such as our ruling on impure milk as causing typhoid fever, by analogy with impure water that causes this fever, due to its similarity in impurity. The example against which an analogy is made is called a root, the example against which it is measured is called a branch, and the attribute or attributes that are the basis of the ruling are called comprehensive. It is as if the mind realizes by this analogy that there is a connection between the common characteristic and the other characteristic, so it tends to generalize this connection, and rules that the second characteristic exists for everything in which the first characteristic is present.

But two examples may share an attribute, or even many attributes, and it does not follow that they share the other attributes. Therefore, inference by representation only serves conjecture, or mere possibility.

Although representation only benefits probability, it is the most common type of reasoning among people. Indeed, Ribot has shown that it is the basic way of thinking in children and elementary humans. Carson said: This inference plays a great role in the lives of higher animals. Yes, despite the suspicion, because the behavior of these animals indicates that their thinking is representational.

4 - Definition of inference

Two basic things emerge from this analysis:

1 - All types of reasoning are theoretical (discursives), which means that they require an intellectual movement and a transition from one rule to another.

2 - There is a connection between the rulings included in inference that leads to extracting a result, and by result I mean a statement that ends the movement of thought and leads to the goal.

Inference, then, is linking different rulings to each other, such that they produce a result. It can be investigated, like all other mental processes, from two points of view: the logical point of view, and the psychological point of view.

The logician studies complete reasoning consisting of a set of propositions without researching its formation and emergence. He distinguishes between the different types of reasoning, and arranges them according to their value and degrees of relationship to each other. He neglects weak inferences or analogies despite their popularity among people.

The psychologist studies the movement of thought in reasoning, and investigates how it is formed and arises. For him, there is no difference in that between one reasoning and another. Rather, all types of reasoning are alike to him. The values ​​of arguments that are fried in the eyes of the logician may differ in terms of their closeness to the truth, or their distance from it. ; However, its value to psychologists is the same, because they only look at the movement of thought and how rational arguments are formed and arise, not at their validity or corruption.