Paul Feyerabend was a philosopher of science who defended an anarchist view of science (in his book “Against Method”). That is, he opposed the idea that there should be methodologies imposed in science, because he considered that these are the expression of conservatism. One may not agree with all his conclusions (some think of him as defending relativistic views), but his arguments are worth considering. By looking at the Copernican revolution, Feyerabend makes a strong case that the methodologies proposed by philosophers (e.g. falsificationism) have failed both as a description of scientific activity and as a prescription of "good" scientific activity. That is, in the history of science, new theories that ultimately replace established theories are initially in contradiction with established scientific facts. If they had been judged by the standards of falsificationism for example, they would have been immediately falsified. Yet the Copernican view (the Earth revolves around the sun) ultimately prevailed on the Ptolemaic system (the Earth is at the center of the universe). Galileo firmly believed in heliocentrism not because of empirical reasons (it did not explain more data) but because it “made more sense”, that is, it seemed like a more elegant explanation of the apparent trajectories of planets. See e.g. the picture below (taken from Wikipedia) showing the motion of the Sun, the Earth and Mars in both systems:
It appears clearly in this picture that there is no more empirical content in the heliocentric view, but it seems more satisfactory. At the time though, heliocentrism could be easily disproved with simple arguments, such as the tower argument: when a stone falls from the top of a tower, it falls right beneath it, while it should be “left behind” if the Earth were moving. This is a solid empirical fact, easily reproducible, which falsifies heliocentrism. It might seem foolish to us today, but it does so only because we know that the Earth moves. If we look again at the picture above, we see two theories that both account for the apparent trajectories of planets, but the tower argument corroborates geocentrism while it falsifies heliocentrism. Therefore, so Feyerabend concludes, scientific methodologies that are still widely accepted today (falsificationism) would immediately discard heliocentrism. It follows that these are not only a poor description of how scientific theories are made, but they are also a dangerous prescription of scientific activity, for they would not allow the Copernican revolution to occur.
Feyerabend then goes on to argue that the development of new theories follow a counter-inductive process. This, I believe, is a very deep observation. When a new theory is introduced, it is initially contradictory with a number of established scientific facts, such as the tower argument. Therefore, the theory develops by making the scientific facts agree with the theory, for example by finding an explanation for the fact that the stone falls right beneath the point where it was dropped. Note that these explanations may take a lot of time to be made convincingly, and that they do not constitute the core of the theory. This stands in sharp contrast with induction, in which a theory is built so as to account for the known facts. Here it is the theory itself (e.g. a philosophical principle) that is considered true, while the facts are re-interpreted so as to agree with it.
I want to stress that these arguments do not support relativism, i.e., the idea that all scientific theories are equally valid, depending on the point of view. To make this point clearly, I will make an analogy with a notion that is familiar to physicists, energy landscape:
This is very schematic but perhaps it helps making the argument. In the picture above, I represent on the vertical axis the amount of disagreement between a theory (on the horizontal axis) and empirical facts. This disagreement could be seen as the “energy” that one wants to minimize. The standard inductive process consists in incrementally improving a theory so as to minimize this energy (a sort of “gradient descent”). This process may stabilize into an established theory (the “current theory” in the picture). However, it is very possible that a better theory, empirically speaking, cannot be developed by this process, because it requires a change in paradigm, something that cannot be obtained by incremental changes to the established theory. That is, there is an “energy barrier” between the two theories. Passing through this barrier requires an empirical regression, in which the newly introduced theory is initially worse than the current theory in accounting for the empirical facts.
This analogy illustrates the idea that it can be necessary to temporarily deviate from the empirical facts so as to ultimately explain more of them. This does not mean that empirical facts do not matter, but simply that explaining more and more empirical facts should not be elevated to the rank of “the good scientific methodology”. There are other scientific processes that are both valid as methodologies and necessary for scientific progress. I believe this is how the title of Feyerabend’s book, “Against Method”, should be understood.