Karl Popper 2010春台大哲學系科學哲學第四講

科學理論的檢驗 科學理論必須經過測試才能接受，然而在進行理論的測試時，究竟是在驗證（confirm）它（confirmation）還是否證（falsify）它？ 當理論通過測試時，意謂著它受到證據的支持而成立嗎？ 為使科學能夠建立，勢必得進行假設的測試，但它非得仰賴假設的驗證不可嗎？ 或者，為使科學得以建立，固然得進行假設的測試，但無須仰賴假設的驗證，而只須訴諸假設的否證即可？

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 冒著出錯之風險的假設才是科學性的假設，沒有冒任何出錯之風險的假設不算科學假設。 pseudo-science的例子之一：Marx的歷史理論。 之二：Freud的精神分析理論。 之三：Adler的individual psychology。

Popper的否證論 為Popper而言，confirmation is a myth—科學中所謂的測試，都是嘗試以觀察來否決理論，而不是以觀察來支持理論的成立。 觀察測試能夠顯示理論為假，但無法顯示理論為真，也無法顯示理論很有可能為真。即使理論的成功預測或說明再怎麼多，也絲毫沒有被觀察證據給支持，一點也沒有。

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 何以Popper認為再多的觀察都無法支持理論的為真或很有可能為真呢？ Popper與Hume一樣都質疑歸納推論的可靠：一個理論過去在說明以及預測上的優異表現並不做為它將來在說明以及預測上也仍然會成功的保障。一個理論過去在說明以及預測上的優異表現並非是使得我們相信它將來在說明以及預測上也仍然會成功的好理由。

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的否證論 Popper雖然質疑歸納推論的可靠，但並不因此認為科學的進行便流於非理性。相反，無須歸納法，也能顯示科學理論的測試與淘汰接受的過程是合乎理性的。

Popper的科學方法論 科學理論的發現與科學理論的證成：前者無邏輯可言，後者有邏輯可循。 (1)大膽臆測（可否證性愈高的假設愈好，冒愈大的出錯風險的假設愈好）：說得愈多，預測得愈準確，應用範圍愈廣。 例一：“Mars moves in an ellipse around the sun.” vs. “All planets move in ellipses around their sun.” 例二：“Planets move in ellipses around the sun.” vs. “Planets move in closed loops around the sun.”

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 (2)從大膽臆測的假設演繹出可觀察測試的結果來。 (3)實驗測試理論所預測的結果是否為真： (i)如果預測失敗，則理論遭到否證，被淘汰； (ii)如果預測成功，則理論未被否證。但這並不表示理論為真，或很有可能為真，或理論比測試之前更可能為真。

Popper的科學方法論 (4)從大膽臆測的假設演繹出另一個可觀察的結果來。 (5)再次進行否證的嘗試，直到理論果真被否決為止。 倘若理論經過相當多嚴格的測試，但始終沒有被否證。我們便說理論是至今尚未被否證的理論，如此而已。

Popper的科學方法論 我們應該繼續不斷進行否證理論的嘗試，卻不應該由於理論已經通過種種測試而增強我們相信理論為真的信心。 不管理論過去的表現是多麼優異，我們對於理論應該採取批判的態度，不應守舊。

Popper的科學方法論 雖然Popper認為科學理論無法被證據給支持而成立，但科學仍舊是以真實地描述世界作為逐漸逼近的終極目標。 如此的科學研究活動，可以尋找聖杯作為譬喻。

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 科學進展的過程就是理論的大膽臆測與力求否證的過程。 科學的進展過程是藉著嘗試錯誤（trial and error），從錯誤中學習的方式來進行的。每一次的理論否證，都是科學的一次進展。科學是在不斷的理論提出、否證、提出、否證…當中才得以進展，而不斷逼近真理的。

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.)

問題 以falsifiability作為科學與非科學之間的劃界判準是否恰當？科學理論一定可被否證，而非科學理論一定無法被否證嗎？可被否證的理論一定是科學理論嗎？不可被否證的理論一定不是科學理論嗎？

問題 Popper對falsifiability一詞的界定足夠清楚嗎？

問題 一旦拒絕承認歸納法的可靠性之後，如何交代rational prediction這一回事？當面對兩個都尚未被否證的假設T1與T2，其中T1已經通過很多嚴格的測試（well-corroborated），都沒有被否證。T2是剛被設想出來，尚未予以測試，從而也尚未被否證的假設。當要用來預測某現象或是用來建造某個重大工程時，選擇哪一個理論來做預測會比較合理呢？

問題 什麼時候科學會取得重大的進展呢？當大膽臆測的假設被否證嗎？