Popper's standard for science is: only falsification, not proof. In other words, any scientific theory can only be proved to be untenable, but can not be proved to be established. For example, all swans found by human beings are white, so it is regarded as a scientific proposition (and a scientific hypothesis) to declare that swans are white. No matter how many white swans are found later, this proposition cannot be proved absolutely correct (confirmed), but as long as a black swan is found, this proposition will be falsified. This is the standard that Popper thinks that science can only be falsified but not proved.
Why is this happening? Because scientific propositions are full-name judgments and belong to universal knowledge, the empirical basis of scientific understanding is carried out on a single object, and no scientist can conduct "full-name experiments" unless he is God. So all scientific theories are hypotheses, which may be falsified at any time, but they can never be proved. Although another philosopher, Carnap (logical positivism), put forward the scientific standard of verifiability, it is not contradictory with Popper, because Carnap's "verification" is logical self-consistency within experience and does not involve the ultimate truth.
By this standard, mathematics and logic are not science, because they are tools of falsification, and they cannot be falsified by themselves. Human beings must believe that logic and mathematics are reliable, otherwise they cannot prove any knowledge. Hume called mathematics and philosophy "inevitable truths", which means that human beings must believe in their reliability, and they are self-evident. Metaphysics and theology also think about the hypothesis that mathematics and logic are untenable, but it is meaningless to scientifically judge such thinking because it is transcendental and cannot be falsified.
Popper believes that although mathematics and logic are not science, their status may be higher than science itself, because they are the "authorities" that issue scientific licenses to knowledge, that is, the ways and methods for human beings to obtain science. There are two basic conditions for a proposition to be regarded as knowledge: first, it conforms to experience, and second, it conforms to logic and mathematical deduction. Therefore, if mathematics and logic are not "self-evident" truths, the building of human knowledge will have no foundation.
In the history of western civilization, there are not a few people who deny the authority of God, but few people who deny logic and mathematics because they are too basic. Unfortunately, however, China people challenged mathematics and logic. There are several obvious means: 1, to popularize the Olympic mathematics in primary and secondary schools, that is, to establish a brain teaser "anti-mathematics" thinking mode outside traditional mathematics to prevent children from forming mathematical thinking; 2. It is very simple to know that there is no systematic logic course in universities, but it is "forced" to offer logic courses in law and other majors; 3. Strengthen memorizing arithmetic instead of geometry in basic mathematics education, because geometry is more inclined to pure logical deduction; 4. A large number of abacus mental arithmetic, an "algorithm course" of non-mathematical thinking. In other words, it is absolutely incomprehensible that such a huge nation should weaken mathematics and logic in basic education.
Although logic and mathematics are not science in themselves, they are the mother of science. Without the knowledge of mathematics and logic, China people generally lack the ability to understand and create science, showing a kind of ignorance. It can be said that this kind of education is a kind of destruction of people's natural rationality and an anti-intellectual education, and the consequences are unimaginable. Now China people's scientific chaos has shown this incredible self-harm.