Popper problem of demarcation science pseudoscience Falsifiability A

Popper的否證論 problem of demarcation: science與 pseudo-science如何劃分？ Falsifiability (可否證性) ： A hypothesis is scientific if and only if it has the potential to be refuted by some possible observation.

Popper的否證論 可以被否證的述句： It never rains on Wednesday. All substances expand when heated. Heavy objects, such as brick when released near the surface of the earth, fall straight downwards if not impeded. When a ray of light is reflected from a plane mirror, the angle of incidence is equal to the angle of reflection. Unlike magnetic poles attract each other. An acid added to a base yields a salt plus water.

Popper的否證論 無法被否證的述句： Either it is raining or it is not raining. All points on a Euclidean circle are equidistant from the center. 牡羊座的人今天的幸運顏色是粉紅色。

Popper的否證論 Popper argues that there is no such thing as inductive confirmation. No scientific theory or law is made probable by evidence. Rather, science follows the method of conjectures and refutations.

Popper的否證論 Scientists propose bold conjectures and then devise severe tests to falsify them if, indeed, they are false. A theory that withstands such tests is not confirmed or made probable by its successful predictions. Instead, it is what Popper calls corroborated.

Popper的否證論 Corroborated theories should not be accepted as true or even probable, but nevertheless it is rational for us to rely on them at least until better theories come along. Eventually, by continually replacing falsified theories with ever bolder ones that have not yet been refuted, science progresses towards the truth.

Popper的否證論 Many people believe that scientific theories can be made more probable by evidence. But Popper denies. Consider a card randomly drawn from a standard deck of 52 cards. What is the probability that the card selected is the ten of hearts? Obviously, the answer is 1/52. There are 52 possibilities, each of which is equally likely and only one of which would render true the statement “This card is the ten of hearts. ”

Popper的否證論 Now consider a scientific theory that, like Newton’s theory of gravitation, is universal. The number of things to which Newton’s theory applies is, presumably, infinite. Imagine that we name each of these things by numbering them 1, 2, 3, . . . , n, …

Popper的否證論 There are infinitely many ways the world could be, each equally probable. 1 obeys Newton’s theory, but none of the others do. 1 and 2 obey Newton’s theory, but none of the others do. 1, 2, and 3 obey Newton’s theory, but none of the others do. …………. All bodies（1, 2, 3, . . . , n, …）obey Newton’s theory.

Popper的否證論 Since these possibilities are infinite in number, and each of them has the same probability, the probability of any one of them must be 0. But only one, the last one, represents the way the world would be if Newton’s theory were true. So the probability of Newton’s theory (and any other universal generalization) must be 0.

Popper的科學方法論 例三：Kepler的太陽系理論（three laws of planetary motion） 和Newton的理論。 Potential falsifiers of Kepler’s theory consist of sets of statements referring to planetary positions relative to the sun at specified times. Newton’s theory, a better theory that superseded Kepler’s, is more comprehensive. It consists of Newton’s laws of motion plus his laws of gravitation. Some of the potential falsifiers of Newton’s theory are sets of statements of planetary positions at specified times. But there are many others, including those referring to the behavior of falling bodies and pendulums, the correlation between the tides and the locations of the sun and moon, and so on. There are many more opportunities for falsifying Newton’s theory than for falsifying Kepler’s theory. And yet, Newton’s theory was able to resist attempted falsifications, thereby establishing its superiority over Kepler’s.

Popper的科學方法論 Despite insisting that we can never support or confirm scientific theories, Popper believed that science is a search for the true descriptions of the world. How can one search for truth if confirmation is impossible? This is an unusual kind of search. We might compare it to a certain kind of search for the Holy Grail, conducted by an imaginary medieval knight.

Popper的科學方法論 Suppose there are lots of grails around, but only one of them is holy. In fact, the number of nonholy grails is infinite or enormous, and you will never encounter them all in a lifetime.

Popper的科學方法論 All the grails glow, but only the Holy Grail glows forever. The others eventually stop glowing, but there is no telling when any particular nonholy grail will stop glowing. All you can do is pick up one grail and carry it around and see if it keeps on glowing. You are only able to carry one at a time. If the one you are carrying is the Holy Grail, it will never stop glowing. But you would never know if you currently had the Holy Grail, because the grail you are carrying might stop glowing at any moment. All you can do is reject grails that are clearly not holy (since they stop glowing at some point) and keep picking up a new one. You will eventually die (with no afterlife, in this scenario) without knowing whether you succeeded.

Popper的科學方法論 This is similar to Popper’s picture of science’s search for truth. All we can do is try out one theory after another. A theory that we have failed to falsify up till now might, in fact, be true. But if so, we will never know this or even have reason to increase our confidence.

Popper的科學方法論 當假設被否證後，科學家應該設法提出大膽 臆測的假設，而不應提出特置的假設（ad hoc hypothesis）。 A modification in a theory, such as the addition of an extra postulate or a change in some existing postulate, that has no testable consequences that were not already testable consequences of the unmodified theory will be called ad hoc modifications.

Popper的科學方法論 特置假設的例子之一： Having carefully observed the moon through his newly invented telescope, Galileo was able to report that the moon was not a smooth sphere but that its surface abounded in mountains and craters. His Aristotelian adversary had to admit that things did appear that way when he repeated the observations for himself. But the observations threatened a notion fundamental for many Aristotelians, namely, that all celestial bodies are perfect spheres. Galileo’s rival defended his theory in the face of the apparent falsification in a way that was blatantly ad hoc.

Popper的科學方法論 He suggested that there was an invisible substance on the moon, filling the craters and covering the mountains in such a way that the moon’s shape was perfectly spherical. When Galileo inquired how the presence of the invisible substance might be detected, the reply was that there was no way in which it could be detected. There is no doubt, then, that the modified theory led to no new testable consequences and would be quite unacceptable to a falsificationist.

Popper的科學方法論 特置假設的例子之二： Prior to Lavoisier, the phlogiston theory was the standard theory of combustion. According to that theory, phlogiston is emitted from substances when they are burnt. This theory was threatened when it was discovered that many substances gain weight after combustion. One way of overcoming the apparent falsification was to suggest that phlogiston has negative weight. If this hypothesis could be tested only by weighing substances before and after combustion, then it was ad hoc. It led to no new tests.

Popper的科學方法論 Popper: “I can therefore gladly admit that falsificationists like myself much prefer an attempt to solve an interesting problem by a bold conjecture, even (and especially) if it soon turns out to be false, to any recital of a sequence of irrelevant truisms. We prefer this because we believe that this is the way in which we can learn from our mistakes; and that in finding that our conjecture was false we shall have learnt much about the truth, and we shall have got nearer to the truth. ” (Conjectures and Refutations, p. 231. )