In this blog post, I will explore what the nature of science is and where the beauty of science comes from based on the philosophy of Karl Popper and Thomas Kuhn.
It was a long time ago. As a freshman in high school, I was given the first situation in my life where I had to make a decision on my own. It was a question of choosing between the humanities and the sciences. My parents left the choice entirely up to me, telling me to choose what I liked without regret. Despite the tacit “maths is for the humanities” stereotype among people and the fact that all of my close friends had gone to the humanities, I eventually chose the sciences. This is because the natural sciences are the most beautiful of all disciplines.
More than the grand reasons that it contributed to the development of human civilization and changed our lives, I thought that the planets revolve gracefully around the Sun with the force of universal gravitation alone (although in reality, the force of universal gravitation does not affect them alone), that a stone thrown into the air moves along the trajectory of the quadratic function graph in mathematics, and that in a chemical reaction, molecules turn into products by random effective collisions.
As you can see, I argue that beauty is one of the properties of natural science. However, science has properties that are very different from the traditional beautiful disciplines—art, music, literature, etc. The aforementioned disciplines may be pursuing beauty from the very beginning. Natural science, which describes nature, has a different character from other disciplines.
“What is science?” This question was the subject of fierce debate among 20th-century philosophers of science. First, the Vienna School, which dominated the philosophy of science in the early 20th century, proposed a logical positivist view of science, which holds that science is formed by induction. In other words, scientific knowledge is generated and justified by induction through three steps: first, collecting unbiased data; second, generalizing the collected facts to obtain a hypothesis; and finally, testing the hypothesis with new observations and experiments. This view was a very plausible theory because it fit well with the image of ordinary research activities, which are about finding natural laws in objective facts. However, inductive reasoning always involves the expansion of content, so there is a serious problem that the conclusions are not guaranteed to be true just because the premises are true, and the feasibility of unbiased data collection has also caused a lot of controversy.
At this point, Karl Popper (1902-1994) argued that the principles of natural science cannot be perfectly proven, but only disproved, by presenting the possibility of disproval instead of proof. In other words, Popper defined scientific activities as follows.
1. Present a hypothesis that seems to explain the given problems well.
2. If empirical evidence is found to refute a hypothesis, the hypothesis is discarded immediately. Otherwise, the hypothesis is maintained. At this point, the hypothesis should not be claimed to have been proven. It can only be said that it has withstood several harsh empirical tests.
In other words, he argued that if the nature of science is refutable, then it is not science. From this, we can conclude that astrology, creationism, etc. can all be classified as pseudo-science, and that mathematics, which is a system constructed through perfect premises and deductive reasoning, is not science. However, even the refutationalism, which pursues perfect logic and describes the development of science in an extremely rational way, has also encountered difficulties. First, there is the fact that scientific theories that cannot be disproved actually exist. For example, it is impossible to disprove the existence of an object, such as “black holes exist” or “genes exist.” What is most fatal is that it is more difficult to disprove than one might think. For example, when judging the truth or falsehood of the proposition “All crows are black,” let’s say there was actually a gray crow. Does this immediately lead us to the conclusion that not all crows are black? To reach this conclusion, we must at least add the following premises: “Our color vision is accurate and we can distinguish colors accurately,” and “We have the ability to distinguish between crows and other birds.” In the case of scientific theories, the hypothesis required for refutation is more numerous and complex, so it is even more difficult to say that a theory is wrong based on the existence of a refutation.
As such, a gap emerged between the ideals of scientific theory and reality, which led to the emergence of Thomas Kuhn (1922-1994), who emphasized historical facts. He divided the process of scientific development into two processes: “normal science” and “scientific revolutions,” defining normal science as the expansion of academic applications within existing paradigms, while scientific revolutions are the replacement of paradigms themselves. What is noteworthy here is that the paradigm shift that occurs during a scientific revolution is different from the one that occurs through trial and error in the methodology of Popper’s argument—speculation and refutation—which leads to a more objective and rational direction. Kuhn argues that when a paradigm shifts, not only does our worldview change, but the world changes as well. The truth of nature is not something that has its original form like rubber clay, but something that changes depending on the interpretation of the observer, that is, scientists. Ultimately, this is concluded as the theory of impossibility of common denominators. The existence of common denominators is a prerequisite for two numbers or polynomials to be comparable to each other, and impossibility of common denominators literally means that theories in different paradigms cannot be compared to each other. Here, the scientific theory breaks Popper’s theory that it is developing into a cumulative, more fundamental, and better theory, and contains the claim that the superiority of one paradigm over another cannot be determined.
The biggest difference between Popper and Kuhn is the difference between ideal and reality. Popper is not interested in the actual history of scientific development, and has presented the ideal of science as to which science is more desirable. He presented the norms of rational and objective science, which are gradually approaching the truth through constant trial and error and the baptism of counterevidence. In contrast, Kuhn presents the reality of scientific development, arguing that it may seem irrational, but it has been working successfully, so it is difficult to find a more ideal methodology than the realistic working principle. Perhaps these two theories also have the impossibility of a commitment. In terms of presenting the nature of science, they can be seen as theories that cannot be ranked in terms of superiority or inferiority.
Where can the special nature of natural science be found among these theories? Is it the methodology of scientific development, or is it the existence of the paradigm that Kuhn claims? I think both of these arguments are correct. The use of a “scientific” methodology that is different from other disciplines, or the existence of such a paradigm, is all because there is a backing of nature behind science. Science is directly dealing with nature and attempting to understand it. Although it sometimes looks different, the existence of a universal and consistent nature is perhaps the most important factor that makes science special.
I believe that the beauty of science comes from the nature of science discussed above. The characteristics of generality, unity, and simplicity that nature possesses constitute the basic aesthetic properties of natural science. Or, according to Kuhn’s theory, these aesthetic properties are the values that scientists universally accept. He argued that scientists of the same era share these values, which leads to the formation of a paradigm, and that the replacement of a paradigm occurs when the weight of these values changes. Aesthetic qualities have not only attracted science, but also contributed greatly to the development of science. In fact, even when creating scientific theories, scientists approach and formulate hypotheses using a methodology that takes into account generality, unity, simplicity, and accuracy. A typical example is Dirac’s establishment of quantum electrodynamics by combining classical electromagnetism and quantum mechanics. He described the abstruse quantum mechanics mathematically in a guidebook called “The Mathematical Beauty.” In this process, Dirac emphasized the beauty of nature and studied it with the value of unity as a methodology. Simplicity was also a key guiding principle in the development of Aristotle’s dynamics into Newtonian dynamics.
As such, beauty is not only a property of science, but also a methodology for the development of science. Just as Popper regards the possibility of refutation as the methodology of science, I believe that the methodology of pursuing beauty has actually led to the development of science.
