4-5. The Nature of Scientific Revolution

とりわけ、ある時は既存のparadigmの崩壊breakdownと見なす人たちの絶望にもかかわらずcrisisに導いたanomalyをnormal scienceが究極的に扱い得る事を示す事がある。またある時は、其の問題は革新的アプローチすらも全て拒否する。
このような時は、其の問題は札付きで、もっと進歩した道具を持った将来の世代に期待して放置される。そしてまたある時は、新しいparadigm候補が現れて、続いて其の受容をめぐる闘争が起こる。その結果としてcrisisにあるparadigmから新しいものへ移る移り行き＝新しいnormal scienceの伝統の出現があれば、これをscientific revolutionと呼ぶ。
これは古いparadigmの整備と拡張で得られる累積的過程とは遙に隔たっている。scientific revolutionとは、古いparadigmが新しいものによって、完全に或いは部分的に、取って代わられるというepisodeであり、これはnon-cumulative developmentである。

既存のparadigmに取って代わろうかというparadigmは、既存のparadigmとはincommensurableなものである。anomalyに直面するのはparadigmの統合的な顕現である理論の外部にある証明不可能な大前提そのものであるから、危機的状態を解消するためにはこれとは別の大前提が必要とされる事になる。非論理的であるという事は、共有する地平を持たない事を意味し、これらの理論的前提同志は必然的にincommensurableなものとなる。
Scientific revolutionがrevolutionと呼ばれる所以を論じた箇所がある。抜粋してみよう。

...scientific revolutions are inaugurated by a growing sense, again often restricted to a narrow subdivision of the scientific community, that an existing paradigm has ceased to function adequately in the exploration of an aspect of nature to which that paradigm itself had previously led the way. In both political and scientific development, the sense of malfunction that can lead to crisis is prerequisite to revolution...

...the parallel has, however, a second and more profound aspect upon which the significance of the first depends. $\ldots$initially it is crisis alone that attenuates the role of political institutions as we have already seen it attenuate the role of paradigms. In increasing members individuals become increasingly estranged from political life and behave more and more eccentrically within it. Then, as the crisis deepens, many of these individuals commit themselves to some concrete proposal for the reconstruction of society in a new institutional framework. At the point the society is divided into competing campus or parties, one seeking to defend the old institutional constellation, the others seeking to institute some new one...

...Because they differ about the institutional matrix within which political change is to be achieved and evaluate, because they acknowledge no supra-institutional framework for the adjudication of revolutionary difference, the parties to a revolutionary conflict must finally resort to the techniques of persuasion, often including force. Though revolutions have had a vit al role in the evolution of political institutions, that role depend upon their being partially extrapolitical or extrainstitutional event.

paradigmは、其の具体的表現である理論を通じて研究活動の構成要素となる。この際にparadigmは科学者に自然がどういうもので、また同時にどういうものでないかを知らせる機能を持つ。従ってcompeting paradigms間の選択の基準は論理による事ができない。
異なるparadigmを受け入れる科学者は異なる世界に住んでいるのだから、異なるparadigmに由来する命題Aと命題Bとは、「AはＢと矛盾する」という表現しかできない。つまりＡはＢであるとかないとかいうことは問題として不適切なのである。paradigms間の闘争はnormal scienceの外部にある基準によってのみ決着し、paradigms間の闘争からrevolutionに至るのはこのnormal science以外の何かを研究活動に引き入れるからである。これはcriticalな現象である。

A profound change has taken place during the present century in the opinions physicists have held on the mathematical foundations of their subject. Previously they supposed that the principles of Newtonian mechanics would provide the basis for the description of the whole of physical phenomena and that all the theoretical physicist had a to do was suitably to develop and supply these principles. With the recognition that there is no logical reason why Newtonian and other classical principles should be valid outside the domains in which they have been experimentally verified has come the realization that departures from these principles are indeed necessary. Such departures find their expression through the introduction of new mathematical formalisms, new schemes of axioms and rules of manipulation, into the methods of theoretical physics.

Quantum mechanics provides a good example of new ideas. It requires the states of dynamical system and the dynamical variables to be interconnected in quite strange ways that are unintelligible from the classical standpoint. The states and dynamical variables have to be represented by mathematical quantities of different natures from those ordinarily used in physics. The new scheme becomes a precise physical theory when all the axioms and rules of manipulation governing the mathematical quantities are specified and when in addition certain laws are laid down connecting physical facts with the mathematical formalism, so that from any given physical conditions equations between the mathematical quantities may be inferred and vice versa. "

The Principles of Quantum Mechanics. P.15 By P. A. M. Dirac