2013年1月10日星期四

D-N 模型

Karl Popper 曾提及他認為存在同樣適用於描述自然科學與社會科學發展的統一方法。索羅斯﹝George Soros﹞不同意,他認為人的感知會影響事態,並破壞 "deductive-nomological model" 之中預測與解釋的對稱性,繼而否定統一方法的存在。

似乎索羅斯是拋錯書包。事實上,從《歷史定論主義的窮困》﹝The Poverty of Historicism﹞第 29 節﹝121 頁﹞可知 Karl Popper 所指的統一方法並非 "deductive-nomological model" ,而是 "hypothetical-deductive method":
[...]The methods always consist in offering deductive causal explanations, and in testing them (by way of predictions). This has sometimes been called the hypothetical-deductive method, or more often the method of hypothesis[...]
在此先談 "deductive-nomological model",日後有時間再論 "hypothetical-deductive method"。

"Deductive-nomological model" 簡稱 "D-N model", 亦稱為 "covering law model",中文有的譯作「演繹‧法則模型」。為簡便,以下將其稱為 D-N 模型。

D-N 模型旨在將解釋事件的科學方法邏輯化,根據 D-N 模型,解釋某事件便是以已知的事實作為「前題」﹝premises﹞,並透過演繹邏輯﹝deductive logic﹞推理出事件,而那些前題便是事件的解釋。D-N 模型要求所有前題均能夠被實証﹝empirically testable﹞,且必須真確,而當中至少一項是定律﹝law﹞。例如要解釋「釘子會生鏽」──
前題一:釘子是用鐵造的﹝事實 C﹞
前題二:鐵會生鏽﹝定律 L﹞
結論:釘子會生鏽﹝事件 E﹞
D-N 模型還有以下特點:

  1. 解釋與預測是對稱的 ── 若事件還未發生﹝或未知﹞,得到的結論便是個「預測」,箇中引用的前題在事後便可用來解釋事件,故能預測便等於能解釋,反之亦然;
  2. 漠視因果關係 ── 沒要求定律描述的是從因到果的過程。
另一方面,D-N 模型亦存在兩大疑難,分別是「不對稱疑難」﹝the problem of asymmetry﹞及「不相關疑難」﹝the problem of irrelevance﹞。某程度上這兩大疑難的出現皆因 D-N 模型漠視了因果關係。

「不對稱疑難」
試考慮一支垂直的旗杆,若知道旗杆高度﹝前題一﹞及太陽仰角﹝前題二﹞便可根據光行直線﹝前題三﹞及三角幾何﹝前題四﹞預測旗杆影子的長度﹝事件﹞,前題一、二是已知的事實,前題三、四是已知的定律;事件既可根據這些前題透過演繹邏輯預測出來,這些前題亦可視為對事件的解釋。倘若將影子長度視為前題一,而前題二、三、四不變,那麼預測出的事件便是旗杆高度;但是,將影子長度﹝加上其他前題﹞說成是對旗杆高度的解釋就怎樣都說不通!那旗杆有多高是人為既定的嘛!

「不相關疑難」
根據「吃了避孕藥的人不會懷孕」﹝前題一﹞、「強仔是人」﹝前題二﹞及「強仔吃了避孕藥」﹝前題三﹞,透過演繹法便可預測強仔不會懷孕;強仔固然不會懷孕,但這些前題其實與強仔不會懷孕沒有關係,亦不是強仔不會懷孕的正確解釋。強仔是男人才是他不會懷孕的真正原因嘛!

大部份文獻稱 D-N 模型是 Carl Hempel 與 Paul Oppenheim 提出的,有人更將 D-N 模型稱為 Hempel-Oppenheim 模型,原因是 Hempel 與 Oppenheim 於 1948 年發表過一篇題為 "Studies in the Logic of Explanation" 的文章,對上述解釋事件的科學方法作出了詳細分析,以下摘錄自該文章的引言:
To explain the phenomena in the world of our experience, to answer the question "why?" rather than only the question "what?", is one of the foremost objectives of all rational inquiry; and especially, scientific research in its various branches strives to go beyond a mere description of its subject matter by providing an explanation of the phenomena it investigates. While there is rather general agreement about this chief objective of science, there exists considerable difference of opinion as to the function and the essential characteristics of scientific explanation. In the present essay, an attempt will be made to shed some light on these issues by means of an elementary survey of the basic pattern of scientific explanation and a subsequent more rigorous analysis of the concept of law and of the logical structure of explanatory arguments.
事實上,Karl Popper 早在 1934 年已提出過類似 D-N 模型的構思,下文摘錄自《科學發現的邏輯》﹝The Logic of Scientific Discovery﹞第 12 節:
To give a causal explanation of an event means to deduce a statement which describes it, using as premises of the deduction one or more universal laws, together with certain singular statements, the initial conditions. […]We have thus two different kinds of statement, both of which are necessary ingredients of a complete causal explanation. They are (1) universal statement, i.e. hypotheses of the character of natural laws, and (2) singular statements, which apply to the specific event in question and which I shall call 'initial conditions'. It is from universal statements in conjunction with initial conditions that we deduce the singular statement. [...]We call this statement a specific or singular prediction.
注意 Popper 提的是 "causal explanation" 以及前題中的事實是 "initial conditions",顯示 Popper 著重因果關係對解釋事件的重要性。

Hempel 與 Oppenheim 在他們的文章中亦提過 "causal explanation";但他們提及的 "causal" 卻不是「前因後果」, 而是 "non-statistical",那只是說明 D-N 模型中的事件是決定性的﹝deterministic﹞:
The type of explanation which has been considered here so far is often referred to as causal explanation. If E describes a particular event, then the antecedent circumstances described in the sentences C1, C2, …, Ck may be said jointly to "cause" that event, in the sense that there are certain empirical regularities, expressed by the laws L1, L2, …, Lr, which imply that whenever conditions of the kind indicated by C1, C2, …, Ck occur, an event of the kind described in E will take place. Statements such as L1, L2,…, Lr, which assert general and unexceptional connections between specified characteristics of events, are customarily called causal, or deterministic, laws. They are to be distinguished from the so-called statistical laws which assert that in the long run, an explicitly stated percentage of all cases satisfying a given set of conditions are accompanied by an event of a certain specified kind.
邏輯實證主義﹝logical positivism﹞以邏輯及實證為本,而因果關係是無法證實的,D-N 模型對因果關係的漠視,充分反映 Hempel 與 Oppenheim 信奉的是大衛‧休謨﹝David Hume﹞式的懷疑實證主義﹝skeptical empiricism﹞──「病態般」的多疑。以下摘錄自 Samir Okasha 的 Philosophy of Science: A Very Short Introduction:
For Hempel subscribed to a philosophical doctrine known as empiricism, and empiricists are traditionally very suspicious of the concept of causality. Empiricism says that all our knowledge comes from experience. David Hume[…]was a leading empiricist, and he argued that it is impossible to experience causal relations. So he concluded that they don't exist – causality is a figment of our imagination! […]Most empiricists have not accepted this startling conclusion outright. But as a result of Hume's work, they have tended to regard causality as a concept to be treated with great caution. So to an empiricist, the idea of analysing the concept of explanation in terms of the concept of causality would seem perverse. If one's goal is to clarify the concept of scientific explanation, as Hempel's was, there is little point in using notions that are equally in need of clarification themselves. And for empiricists, causality is definitely in need of philosophical clarification. So the fact that the covering law model makes no mention of causality was not a mere oversight on Hempel's part.

參考資料
  • The Poverty of Historicism, Karl Popper, Routledge Classics 2002, ISBN 0-415-27846-5
  • The Alchemy of Finance: Reading the Mind of the Market, George Soros, John Wiley & Sons, ISBN 0-471-04206-4
  • The Logic of Scientific Discovery, Karl Popper, Routledge Classics 2002, ISBN 978-0-415-27844-7
  • Philosophy of Science: A Very Short Introduction, Samir Okasha, Oxford, ISBN: 978-0-19-280283-5
  • Studies in the Logic of Explanation, Philosopy of Science 15 (1948): 135-175, Hempel, Carl G. & Oppenheim, Paul