The Application of Inductive Reasoning in Physics to "Waiting for the Rabbit"

Macao Post issued a set of four stamps of "Idiom Story" with the title of household idioms, the fourth of which is "waiting for the hare".

The idiom "waiting for a hare" says that in the ancient Song Dynasty, a farmer saw a sprinting hare hit a tree and died because his neck was broken. He therefore believed that it was a great good thing to get something for nothing. At this point, he put down his hoe, did not do farm work, and waited under the tree, hoping to get the rabbit killed again. Can he get it again? The answer is well known. But why is this result? Now we can get the correct answer through inductive reasoning in physics.

The inductive reasoning formula in physics is:

If X1 is A, X2 is A, X3 is A, Xn is A, X1, X2, X3... Xn is part of the object of class X, then all X are A. Where n is the number of inductive cases.

However, this inductive reasoning is logically flawed, such as "waiting for the hare". This is a simple inductive reasoning: because there is a rabbit hitting a tree today, there will be a rabbit hitting a tree tomorrow, and there will be a rabbit the day after tomorrow. The number of cases it induces is equal to 1. So "waiting for the hare" is actually inductive reasoning with the number of inductive cases n equal to 1.

With such a big loophole in inductive reasoning, can we think that inductive reasoning cannot solve the problem? The answer is also negative. The physics and other achievements obtained by learning inductive reasoning are reliable. How to explain this contradiction?

The physical method of inductive reasoning adopts Galileo's scientific methodology. First, accurate experiment, summarizing the experimental rules; Second, put forward a hypothesis to quantitatively explain the experimental laws; Third, according to the hypothesis, use mathematical and logical reasoning to obtain theories or predictions; Fourth, carry out objective, repeatable, accurate and quantitative experimental tests on the inference; Fifth, revise theories and hypotheses; Sixth, experiment tests hypothesis and theory. Galileo's scientific methodology is to demonstrate experiments and theories over and over again with accurate quantitative, objective and repeatable methods, reducing the loopholes of inductive reasoning and metaphysics to the limit.

Now let's discuss the reasoning of waiting for the hare. There are two key processes in the reasoning process of waiting for the hare, which do not conform to Galileo's scientific methodology. First, its reasoning defect is n=1. According to Galileo's method, this should be arbitrary and must be objective and repeatable; Second, it is not accurately quantified. The so-called quantity is obtained by mathematical operation.

At this point, we can clearly know why the inductive reasoning of waiting for the hare is correct, but it does not exist in fact.