Popper agrees with the definition of accidental truth, but it emphasizes that such empirical science should obey a falsificationism. Falsificationism has at least two advantages. First, the expression of scientific theory is generally full-name judgment, while the object of experience is individual. Therefore, if the theory is proved by experience, it is impossible to exhaust the general theory. For example, no amount of white sheep can prove that all sheep are white, but only one black sheep can prove that the theory that all sheep are white is wrong. Therefore, the real meaning of experience is that it can falsify scientific theories. Second, falsificationism can avoid the defense and dogma of wrong theories. If we insist on positivism, once we have experience contrary to the theory, people will make special settings or restrictions to make the theory conform to the experience. But in fact, such a setting is often extremely unscientific. Falsificationism makes people believe that all science is just speculation and hypothesis, which will not be finally confirmed, but will be falsified at any time.

Falsificationism should adopt trial and error method. This means that people should boldly make assumptions and guesses, and then look for examples that do not meet this assumption. Modify the hypothesis according to the example, repeat this process constantly, or even completely deny the original hypothesis. There is no end to the revision and perfection of the theory by trial and error, and the result of trial and error can only be a better hypothesis, but it is not the best hypothesis. The best hypothesis is synonymous with the ultimate truth, which violates the scientific spirit.

Popper also wanted to integrate the conflict between rationalism and empiricism, but he also criticized rationalism and empiricism. Both rationalism and empiricism admit that knowledge comes from an unchangeable foundation. Rationalism holds that this foundation is a universal and inevitable principle, while empiricism holds that it is human experience. The core of Popper's philosophy of science is that all theories and principles can be falsified, and experience is the standard for testing knowledge, although it is not the source and foundation of knowledge. He called this view rational criticism.

So the division between science and non-science is clearly defined by Popper here, which is contrary to common sense. The essence of non-science is not whether it is correct, but whether it can't be falsified. So mathematics and logic are classified as unscientific. Similarly, psychoanalysis, astrology, physiognomy and "Marxism" after Marx are all unscientific. None of them can be falsified. Mathematics and logic are classified as non-science because they don't need to be tested by experience and are called inevitable truths by Hume. Science, like non-science, contains both truth and fallacy.