H-D 方法

先前談過 D-N 模型﹝deductive-nomological model﹞，今回再論 H-D 方法﹝hypothetico-deductive method，在網上找到的中文翻譯為「假說演繹法」﹞。H-D 方法旨在將發展科學理論的過程程序化，有說這方法早於十九世紀初經已出現。根據 H-D 方法，科學理論是依以下程序發展出來的：

1. 憑觀測及經驗訂出要解釋的事件；
2. 嘗試為解釋該事件構想出一個假說﹝hypothesis﹞；
3. 將假說套用到其他事件，透過演繹邏輯﹝deductive logic﹞得出預測﹝prediction﹞；
4. 將預測與實情作比較，若預測符合實情，假說便得以驗證﹝verified﹞，並可將其視為可接受的理論；若預測與實情不符，假說便遭否證﹝falsified﹞，那便需對假說作出修正，甚至乎重新構想另一個新的假說，再重複過程的第三及第四步，如是者直至假說得以驗證。

要注意假說一般是不可能透過邏輯構想出來的，正如 Karl Popper 在 The Logic of Scientific Discovery ﹝《科學發現的邏輯》﹞中提到：

[...T]here is no such thing as a logical method of having new ideas, or a logical reconstruction of this process. My view may be expressed by saying that every discovery contains 'an irrational element', or 'a creative intuition'[...] (p.8)

H-D 方法有不少疑難，它既不能讓人分辨某理論是「定律」﹝law﹞還是「全稱推廣」﹝universal generalization﹞，亦導致「 烏鴉悖論」﹝The Raven Paradox﹞；Stanford Encyclopedia of Philosophy【Laws of Nature】對前者說明得很詳細， William Bechtel 在 Philosophy of Science: An Overview for Congnitive Science 第二章將後者解釋得很清楚：

[...A] law statement of the form

For all x, if x is F, then x is G
is logically equivalent to the statement

For all x, if x is not G, then x is not F.
If F stands for raven and G for black, then the law "All ravens are black" (e.g., for all x, if x is a raven, then it is black) is logically equivalent to "All things that are not black are not ravens" (e.g. For all x, if x is not black, then it is not a raven). To test the first statement, the H-D model would lead us to examine ravens to see if they are black. The more black ravens we encounter, the greater support for the law (as long as we do not encounter raven that are not black). But the form to which it is logically equivalent only requires us to examine things that are not black and test the prediction that these things will not be ravens. Every nonblack object that you see that is not a raven will confirm that putative law. So you can sit in the room you are now in and test the law that all ravens are black by making sure all the nonblack objects in the room are not ravens. Something clearly seems to have gone wrong! (p.26-27)

此外，傳統的 H-D 方法在測試理論方面﹝過程的第四步﹞不夠全面。Karl Popper 在《科學發現的邏輯》第三節提出測試理論可循四個方向進行：

We may if we like distinguish four different lines along which the testing of a theory could be carried out. First there is the logical comparison of the conclusions among themselves, by which the internal consistency of the system is tested. Secondly, there is the investigation of the logical form of the theory, with the object of determining whether it has the character of an empirical or scientific theory, or whether it is, for example, tautological. Thirdly, there is the comparison with other theories, chiefly with the aim of determining whether the theory would constitute a scientific advance should it survive our various tests. And finally, there is the testing of the theory by way of empirical applications of the conclusions which can be derived from it. (p.9)

上述最後一個方向即傳統的 H-D 方法的第四步。

Karl Popper 強調縱然理論得到事實支持，亦只是暫時可信，難保日後可能會被推翻：

It should be noticed that a positive decision can only temporarily support the theory, for subsequent negative decisions may always overthrow it. (p.10)

正如他所言：

[...N]o matter how many instances of white swans we may have observed, this does not justify the conclusion that all swans are white. (p.4)

這便是「黑天鵝問題」﹝The Black Swan Problem﹞。Karl Popper 對「黑天鵝」的關注促使他主張科學家檢測理論應採「否證法」﹝falsification﹞ ── 即 modus tollens ── 以否定理論為目標尋找證據；而非「驗證法」﹝verification﹞ ── 即 modus ponens ── 以肯定理論為目標尋找證據。

其實，可追溯「最先」提出黑天鵝問題的不是 Karl Popper，更不是《黑天鵝》﹝The Black Swan﹞的作者 Nassim Nicholas Taleb﹝他提出的「黑天鵝事件」有別的定義﹞，而是懷疑實證主義者大衛‧休謨﹝David Hume，1711-1776﹞：

In his Treatise on Human Nature, the Scots philosopher David Hume posed the issue in the following way (as rephrased in the now famous black swan problem by John Stuart Mill): No amount of observations of a white swan can allow the inference that all swans are white, but the observation of a single black swan can refute that conclusion. (摘錄自Fooled by Randomness, p.117)

噢！講完烏鴉又講天鵝，難道哲學家都喜歡鳥？


參考資料：

• Wikipedia【Hypothetico-deductive model】
• The Logic of Scientific Discovery, Karl Popper, Routledge Classics 2002, ISBN 978-0-415-27844-7
• Stanford Encyclopedia of Philosophy【Laws of Nature】
• Philosophy of Science: An Overview for Congitive Science, William Bechtel
• Fooled by Randomness: The Hidden Role of Chance in Life and in the Markets, Nassim Nicholas Taleb, Penguin Books 2004, ISBN 978-0-141-03274-0
• The Black Swan: The Impact of the Highly Improbable, Nassim Nicholas Taleb, Penguin Books 2007, ISBN 978-0-141-03459-1