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Thus, C has more content than both P and E – it has more content than P by being more universal, and it has more content than E by being more precise.

Popper claimed that modifications that increase a theory’s falsifiability contribute to the progress of science. The intuition behind this claim seems to be this: If we protect a theory from falsifications by modifying it in a nonfalsifiable way, scientific development comes to a stand still. Yes, the current theory has been protected from falsification, but at the expense of stagnation. It’s like going into the corner and pouting. Here’s a sports analogy. Suppose you have been beaten at your favorite sport. Sure, you can look for excuses – the referee was unfair, there was too much wind, the ball was rigged, etc. And since these things seem to be always happening, you won’t play anymore. But if that’s your reaction, you clearly won’t make progress. Maybe the better strategy is trying to improve your game and then compete as hard and as often as you can, which of course increases your opportunities of being beaten. If you then stay unbeaten in ever tougher competition, it seems like you’ve made progress, certainly more than you could have made by frowning in the corner and not playing again. Of course, even if you stay unbeaten for a long time doesn’t mean that you are a perfect player; there might still be better ones out there. But you have earned your right to play on for a while, to be kept on the team, as it were. And what goes for sports, Popper thinks, goes for theories. If we expose them to severe competition with other theories through tests, the ones that keep on winning earn their keep.

      As mentioned earlier, Popper’s technical term for staying unfalsified through severe tests is being corroborated. The corroboration of a theory does not provide a reason for believing it to be true, or even probable to any degree. Rather, it means that it has survived varied and severe tests, where severity is a function of the number of potential falsifiers for a theory. Assigning corroboration is simply saying that the theory is consistent with a set of statements that are currently accepted as basic. Thus, the degree of corroboration of a theory can change with changes in bodies of accepted basic statements. It is therefore clearly not a sort of truth value, because the truth of a statement is not in this way relative to what other statements are accepted.

      3.3.2 Basic Statements

What statements are accepted as basic at a given time? In contrast to the positivists, who thought they have found epistemically privileged statements in so-called protocol sentences, which allegedly describe the experiential bedrock for all of our theorizing, Popper thought that what statements are accepted as basic depends on the experimental context and can change over time. He did provide a list of considerations that should be involved in any decision process about basic statements. First, they must be easy to test. In Prout’s time, finding the atomic weights was thought to be easy. Second, they must be relevant to the theory undergoing testing. When Prout claimed that the weights of all elements are whole multiples of the weight of hydrogen, it was clear that a relevant basic statement is one about the weight of some element other than hydrogen. Third, we must keep in mind that their acceptance is provisional, and should the need arise, they too can be tested relative to other statements that are then accepted as basic for that purpose. The statement about chlorine was accepted as basic when it was used in an attempt to falsify Prout’s claim. But the experimental methodology eventually became the subject of testing itself when it was determined that the available procedures for purifying substances were imperfect. Testing the standard purification procedures required other statements to be accepted as basic. Thus, on Popper’s considered view, the process of falsification is a far cry from simply finding out that nature is in conflict with a hypothesis. Instead, it is embedded in a context of continuing criticism, where in principle nothing is exempt from criticism. There is no epistemic bedrock.

      3.3.3 Moving and Burning

      Popper’s conception of empirical science as a process of continual criticism of bold empirical conjectures has been attractive to many working scientists. But is his model of how science grows through criticism borne out by historical evidence? Let’s look at the Polish astronomer Nikolaus Copernicus’ reaction to the problem of stellar parallax and the British chemist Joseph Priestley’s introduction of negative weight.

Suppose you are in a driving car, approaching a city. You happen to look at two tall buildings far ahead on the right side of the road. One of them seems to be almost attached to the other, that’s how close they look to you. However, once your car is driving right past them, you notice that the two buildings are actually dozens of yards apart; of course, as the car continues on its way and you look back, the buildings seem to be closer together again. Something very similar should happen, if heliocentrism is true. As the earth moves around the sun, stars that look to be very close to each other at one point during the year should look to be much farther apart at a later point, at a time when the earth is moving “right past them.” This apparent change in the distance between the stars, as observed from the moving earth, is the phenomenon called “stellar parallax.” The problem was, for Copernicus and his contemporaries, that no stellar parallax had ever been observed! Thus, the opponents of heliocentrism argued that the earth can’t be moving through space and around the sun. To them, the absence of an observable stellar parallax clearly falsified heliocentrism.

      In response, Copernicus resorted to the move we discussed earlier: Blame some auxiliary hypothesis! He simply proposed that the absence of an observable stellar parallax is due to the fact that the stars are much further away from us than we thought. If so, then the distance travelled by the earth would be negligible in terms of observing parallax. During his time, most estimates of the size of the universe put the stars, which were thought to be located at the outer edge of the universe, at a distance of about six times that between the earth and the moon (they were off by about one quintillion-fold). In such a small universe, one would expect to observe a stellar parallax. In effect, Copernicus pointed out that to infer that we should observe stellar parallax, two claims need to be true: that the earth moves around the sun and that the universe is sufficiently small. Thus, he was able to blame the assumptions about the size of the universe for the failure to observe stellar parallax. Heliocentrism had not been falsified.

      There is another infamous case in which an important scientist tried to save a theory from counterexample, but in which the attempted “rescue mission” led to a rather curious claim. We are thinking of Joseph Priestley, a lifelong defender of the so-called phlogiston theory of combustion. According to this theory, when things burn, they release a very subtle substance, called “phlogiston.” The more phlogiston a material contains, the easier it burns. Given the importance of combustion for chemical experiments, phlogiston was a central concept in early chemistry. In the 1780s, the French chemist Antoine-Laurent de Lavoisier conducted experiments in which he burned mercury. Upon measuring the weight of the residue, he realized that it was heavier than the sample of mercury he started with. This was extremely puzzling: If combustion involves the release of a substance, why should the resulting “ashes” be heavier than the material before it was burned? This fact seemed to conclusively refute the phlogiston theory.

Priestley, however, had an “ingenious” idea to save the theory. Phlogiston, so he claimed, has negative weight. Thus, since phlogiston is released during combustion, the residue will be heavier than the original sample. Of course, since most things that we ordinarily burn, such as wood, also contain water, their ashes will be, all things considered, lighter than what we put into the fireplace, because the water evaporates. Obviously, Priestley made the same move as Copernicus. In order to observe weight loss during combustion, when adjusted for the loss of other components, two things have to be true: phlogiston is released during combustion and phlogiston has positive weight. Thus, he was able to blame the assumption about the weight of phlogiston for the failure to observe weight loss. The phlogiston theory had not been falsified.

      3.3.4 Lucky Modifications

      We quite deliberately phrased the ending of Copernicus’ successful rescue of heliocentrism and the ending of Priestley’s attempted rescue of the phlogiston theory almost identically, only replacing some of the words, in order to bring out how eerily similar the two episodes

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