Analogical reasoning by extension is not inference (anumāna)

In the secular world there is an analogy: for things of the same kind, proving one of them, or a portion of them, proves that all of the same kind are so—there is no need to prove every single one. This is the rule of the secular world, and the Buddha-dharma applies in the same way. The sampling surveys conducted in human investigations examine a portion and thereby prove the whole of the same kind. Does this belong to inference? No, it is not inference.

When I engage in contemplative practice (vipaśyanā-caryā) on my own five aggregates (pañcaskandha) and prove that my five aggregates are suffering, empty, impermanent, and non-self, I can conclude that the five aggregates of others are also so, and that the five aggregates of all sentient beings are so. Is this inference? No, it is not inference. For example, if I investigate Chan and attain enlightenment, realizing the eighth consciousness within my own body, I then know that the eighth consciousness of others is also so, and that the eighth consciousness of all sentient beings is so. Is this inference? No, it is not inference. In geometry, arithmetic, and all academic experiments and reasoning, this method of proof is frequently used: extrapolating from this to that. When writing articles to analyze matters and principles, the phrase "extrapolating from this to that" is always used, indicating that what follows is the same as this and need not be proven or derived again—this is the conclusion for the same category. Is this inference? No, it is not inference.

In proving the correctness of any conclusion of a matter or principle, sometimes one does not proceed from direct perception/valid direct cognition, but rather from erroneous cognition/non-valid cognition, deliberating and examining, and finally arriving at a conclusion of direct perception/valid direct cognition. Erroneous cognition/non-valid cognition also has many great uses. For a person with a sufficiently capable mind, if their wild imaginings are reasonable, then they are not wild imaginings—they are called a sharp mind.

For a person whose mind is not sharp, no matter how much data of direct perception/valid direct cognition you give them, they simply cannot arrive at a truthful, correct conclusion of direct perception/valid direct cognition. There are far too many such people. Having experienced countless sufferings, they still do not know suffering; their inner thoughts are numb—this is in fact foolishness. Foolish people make up more than ninety percent. Having experienced countless setbacks, they do not know to turn back and still bore into dead ends—a single-minded stupidity. Suffering, emptiness, impermanence, and non-self are plainly matters of direct perception/valid direct cognition, with so much data of direct perception/valid direct cognition to prove them, yet everyone simply cannot see clearly. They still study the Buddha-dharma, deliberate and engage in contemplative practice (vipaśyanā-caryā), and still cannot carry out the contemplative practice—this is called foolishness. The five desires and six sense objects are plainly impermanent, arising, ceasing, and changing; they cannot be grasped or clung to. The true facts have already been manifested in direct perception/valid direct cognition, plainly visible, yet countless people simply cannot understand, cannot control themselves, and still go on stubbornly grasping and clinging, unwilling to loosen their grip a little and rest a while—pitiable and foolish.