The learning method of logical reasoning is different from the learning method of abstract generalization. The abstract generalization learning method involves directly analyzing experience or perceptual knowledge and summarizing it to form concepts. Its thinking process moves from vivid intuition to abstract thought. The learning method of logical reasoning involves deriving and developing new knowledge from known knowledge, and its thinking process moves from abstract thought to practice, that is, from abstraction to concrete thinking activities. The thinking activities of these two learning methods are opposite yet complementary, forming a relatively complete learning structure.\Reasoning is the scientific thinking process in which people, based on judgments formed from existing knowledge, derive a new judgment from one or several known judgments. Although the methods and approaches people use to seek new knowledge are very complex, they all rely on reasoning as a thinking method. Learning is no different: to understand systematic scientific knowledge and develop intelligence, one must frequently engage in logical reasoning activities. In the learning process, an important way to connect known knowledge with unknown knowledge is through the thinking activity of logical reasoning. This kind of connection and thinking form is composed of premises and conclusions. Known knowledge serves as the premise, and unknown knowledge serves as the conclusion. The main characteristic of this learning method lies in the fact that the conclusion derived is the result of analyzing contradictions in objective objects, and the reasoning process itself is the process of analyzing contradictions, representing the active role of subjective initiative. This active role aligns with the needs of students for understanding knowledge and developing intelligence.\Human thinking is complex, and reasoning also takes various forms; the most commonly used are deductive reasoning, analogical reasoning, and inductive reasoning.\(1) Deductive reasoning most commonly takes the form of a categorical syllogism. Its significance lies in reasoning from a general principle to a particular fact, that is, using a general principle as the premise and a particular fact as the conclusion. For example, Aristotle's syllogism is:\1. All humans are mortal (major premise)\2. Socrates is a human (minor premise)\3. Therefore, Socrates is mortal (conclusion)\In this syllogistic reasoning, both the major and minor premises are known judgments, while the conclusion is a new judgment. To derive a new judgment from known judgments, two basic conditions must be met: first, the judgments of the major and minor premises must be true; second, the reasoning process must conform to correct logical forms and rules.As Engels said: If we have correct premises and apply the laws of thought correctly to these premises, then the result must correspond to reality.\If the premises are not true, then correct conclusions cannot be drawn. Aristotle once had a line of reasoning: 'If the universe is infinite, there would be no center; the Earth is the center of the universe; therefore, the universe is finite.' The reason this reasoning arrives at the incorrect conclusion that 'the universe is finite' lies in the minor premise 'the Earth is the center of the universe,' which is a false judgment. Some people, in deriving formulas or laws, often do not pay attention to the conditions of the premises, thus spending great effort but arriving at wrong conclusions. When doing exercises, using the wrong formula can also cause fundamental errors.\If the syllogistic reasoning process violates correct logical rules, it is also impossible to obtain a correct conclusion. One rule of categorical syllogism is that the middle term must be distributed at least in one premise. For example: 'All objects with a specific gravity less than water can float on water; all porcelain bowls can float on water; therefore, all porcelain bowls have a specific gravity less than water.' The major and minor premises are obviously correct, but the problem lies in the fact that the middle term is undistributed in both the major and minor premises. The middle term refers to the term that appears in both the major and minor premises, connecting the entities in these premises but does not appear in the conclusion. In this example, 'can float on water' is the middle term. Distribution means that in a judgment, the concept in question covers the entire extension of the concept; otherwise, it is called undistributed. In this example, the major premise cannot be reversed to say: 'All objects that float on water have a specific gravity less than water.' That is to say, 'objects with a specific gravity less than water' are only part of the objects that 'can float on water,' not the whole, so in the major premise, the concept 'can float on water' is not distributed. Similarly, in the minor premise, it cannot be said that 'all objects that float on water are porcelain bowls,' so the middle term is also undistributed in the minor premise. Naturally, this will not lead to a correct conclusion.\Another important rule of categorical syllogism is that the middle term can only be one. For example: 'All metals generate a magnetic field when electrified; a magnet has a magnetic field; therefore, the magnet must be electrified.'"On the surface here, the middle term 'magnetic tide' seems to be one thing, but in reality, in the major premise it refers to the 'electromagnetic tide,' that is, the magnetic field generated by electric current, while in the minor premise it refers to the 'permanent magnetic tide,' that is, the magnetic field of a magnet. This is called 'middle term ambiguity,' where the middle term in the major and minor premises refers to different things, and the conclusion is necessarily wrong.\(2) Another form of deductive reasoning is hypothetical reasoning. Hypothetical reasoning uses a conditional judgment as the major premise and a categorical judgment as the minor premise to deduce a conclusion. Hypothetical reasoning is a form of thinking that studies natural laws through hypotheses, that is, by using known facts or laws to make hypothetical explanations about the regularities of unknown things. Scientific hypotheses are neither completely baseless conjectures nor entirely certain deductions. In our studies, when we use universal principles to solve specific concrete problems, we often use the form of hypothetical reasoning.\(3) The third form of deductive reasoning is disjunctive reasoning. In disjunctive reasoning, the major premise is a disjunctive judgment, while the minor premise and the conclusion are categorical judgments. In the process of using disjunctive reasoning, only if the two disjunctive components in the major premise are incompatible—that is, only under the condition of 'either this or that'—can one negate one disjunctive component and affirm the other. If the disjunctive judgment is compatible, not 'either this or that,' but a third possibility exists, a positive conclusion cannot be drawn.\(4) The fourth form of deductive reasoning is dilemma reasoning. This is a complex form that combines hypothetical and disjunctive reasoning. When examining complex problems, hypothetical-disjunctive reasoning is frequently used. B. Inductive reasoning is a form of thinking that generalizes a general principle from individual facts. The famous Goldbach conjecture was proposed using the form of inductive reasoning. In 1742, German mathematician Goldbach, based on examples such as the odd number 77=53+17+7 and 461=449+7+5=257+199+5, observed that many odd numbers can be obtained by adding three prime numbers, and thus he induced a rule: all odd numbers greater than 5 can be expressed as the sum of three prime numbers. He shared this conjecture with Euler, who affirmed his idea and additionally proposed that every even number greater than 4 can be expressed as the sum of two prime numbers. Later, these two propositions together became known as the Goldbach conjecture."However, this method of induction is incomplete; it cannot and is impossible to cite an infinite number of objects, and therefore has remained a conjecture for more than 200 years. This incomplete inductive reasoning, though its conclusions are not necessarily reliable, is an important pathway for discovering truth. After Copernicus proposed the heliocentric theory in the mid-16th century, theoretical thinking in science was mainly based on inductive reasoning until the 18th century when Kant proposed the nebular hypothesis, at which point deductive reasoning gradually developed. Einstein once said that methods suitable for the childhood of science, which are mainly inductive, are giving way to exploratory deductive methods. However, the form of inductive reasoning still plays an extremely important role in learning. Engels said: Induction and deduction, like analysis and synthesis, are necessarily interconnected. One should not sacrifice one and exalt the other; each should be used where it is appropriate, and to achieve this, one must pay attention to their interrelationship and mutual complementarity.
Analogical reasoning is a logical method and form of thinking based on the similarity or identity of certain attributes of two different objects to infer that other attributes may also be the same or similar. In creative studies, this form of thinking is called 'similarity thinking.' It is said that Hargreaves invented the spinning machine because he was inspired by an occasion when an old spinning wheel tipped over, and the spindle stood upright. The percussion method used by doctors was inspired by Austrian doctor Auenbrugger, who estimated the amount of wine in a barrel by tapping it. In China, Lu Ban invented the wooden saw after being inspired by getting his hand cut on straw, and so on. Many inventions in modern bionics are inspired by certain structures and functions of living organisms. Einstein said: In physics, progress is often made by drawing analogies after noticing that seemingly unrelated phenomena have points of consistency. Some common features are hidden behind outward differences. Being able to discover these common points and establish a new theory based on them is the essential creative work. In learning, by using analogical reasoning, we can more quickly grasp unknown knowledge. However, like incomplete induction in inductive reasoning, the objective basis and logical grounds for analogical reasoning are also insufficient, so it can only provide inspiration, and the conclusions drawn must still be verified through practice.After seeing these, I realize there is still a lot I need to learn.
