Before the philosopher of science, Karl Popper, developed falsificationism as a possible method of science, at the turn of last century the French physicist and philosopher Pierre Duhem had already made an important discovery. Namely, that scientists never test hypotheses in isolation, but always with a set of other hypotheses, both main theoretical hypotheses and auxiliary ones. Consider for example Newton's Law of Gravity. We never test Newton's Law of Gravity by itself, but always in conjunction with a set of hypotheses. Some of those hypotheses are main theoretical hypotheses, for example, Newton's Three Laws of Motion. Others are auxiliary hypotheses, for example the hypothesis about the number of planets in the solar system, their masses, whether gravitational attraction among planets is weaker than the attraction between the sun and the planets, and so on. Now, suppose that from this set of hypotheses we go on and deduce a piece of evidence, and suppose that we look for this piece of evidence in nature, but we can't find it. How should we interpret this negative result? Well clearly something has gone wrong with one of our hypotheses. But we don't know which among all those possible hypotheses is responsible for the negative piece of evidence. So, whenever we encounter a piece of negative evidence, we actually don't know whether the piece of negative evidence is evidence against one of the main theoretical hypotheses, say one of Newton's three laws of motion, as opposed to being an evidence against the auxiliary hypotheses, for example the number of planets in the solar system. This is what philosophers of science call the problem of undetermination of theory by evidence. Very often our experimental evidence is not enough, is not sufficient to determine the choice between tweaking or modifying one auxiliary hypothesis as opposed to replacing altogether a main theoretical hypothesis. And this is an important topic to which we will go back in the session on dark matter and dark energy in cosmology. But before we finish this introduction, I want to mention one more philosopher of science whose work has been hugely influential in the field. Thomas Kuhn's seminal 1962 book entitled 'The Structure of Scientific Revolutions' changed our way of thinking about science. Kuhn began his career as a physicist, and from physics he moved to history of science, where he had the chance to engage with outmoded lines of reasoning, for example, Ptolemaic astronomy. And by reflecting on these sort of signs, Kuhn came to the conclusion that probably science doesn't have a distinctive method, no matter whether it's inductive or deductive, and that probably also we need to rethink the notion of progress in science, and how science is meant to deliver true theories, theories that capture exactly the way the world ought to be. So, how did Kuhn change our image of science? Before Kuhn, philosophers of science had a certain picture of how science grows and unfolds based on a sequence of scientific theories each of which were supposed to build on its predecessor and improve on its predecessor by delivering a more accurate or more likely to be true image of nature. But according to Kuhn this picture is totally wrong. If we look at the history of science, if we look at the actual scientific evidence, we obtain a radically different image of how science grows and unfolds. According to Kuhn, science goes through periods of normal science, crisis, and scientific revolutions. In periods of normal science, scientists work within a scientific paradigm. This is the expression that Thomas Kuhn introduced in 1962. Kuhn didn't define exactly what a scientific paradigm is, but roughly a scientific paradigm includes the main scientific theory, the experimental and technological resources and those by the community at the time, as well as the system of values of the community. So, the kind of value like simplicity, mathematical elegance, parsimony and others that scientists deem valuable. During periods of normal science, according to Kuhn, a scientific community works on a well-defined textbook. For example in the case of Newtonian mechanics, as a scientific paradigm, the main textbook will be Newton's 'Principia'. And all the scientific activity consists in solving problems, a specific puzzle arising from this textbook tradition. So, despite what Popper said, according to Kuhn during periods of normal science there is no attempt to falsify or refute a scientific theory. So the accepted scientific paradigm undergoes a period of crisis only when a sufficiently large number of anomalies accumulates. During periods of crisis, a new paradigm may come to the fore, and the scientific community may decide to abandon the old paradigm and shift to the new one. This is what Kuhn called the paradigm shift. Kuhn, however, stressed how the paradigm shift, or the process of theory choice is not dictated by the superiority of the new paradigm over the old one. On the contrary, Kuhn claimed that the new paradigm should only be able to have a higher puzzle-solving power than the previous one. So, the new paradigm should be able to solve the anomalies, solve the puzzle that the previous paradigm wasn't able to solve. So, in this way, Kuhn redefined the whole idea of how science progresses, not in terms of scientific theory being true or more likely to be true, but in terms of their capacity for solving puzzles and problems. This shift of focus from Popper Falsificationism to Kuhn puzzle solving has far reaching implications for the debate on the rationality of theory choice. Kuhn famously argued that some scientific paradigms are incommensurable. Incommensurable means they lack a common measure, common measure to assess and evaluate them, not to compare them. Kuhn was absolutely clear that we can compare paradigms. But it was also clear that we don't have a common measure for judging, assessing or evaluating whether one paradigm is better or superior than the other one. Different scientific paradigms use very different theories, very different concepts, but also different experimental, technological resources and system of values. So that, whenever we have a paradigm shift, we experience something similar to what psychologists call Gestalt switches. Like those we're all familiar with as in the case of a famous bistable images, such as the duck-rabbit. We will go back to Duhem, the problem of underdetermination of theory by evidence, Kuhn and the rationality of theory choice, in our session on dark matter and dark energy, where we discuss whether current cosmology is undergoing a possible paradigm shift. We very much look forward to seeing you all in the next class. Thank you.
