What is a paradigm?


The original sense of “paradigm” is “exemplar” and Kuhn’s “paradigm” signifies such a textbook theory or an experiment method as students imitate as an exemplar in their scientific education. Normal science engages scientists in puzzle-solving based on a paradigm, which is more economically rational than the frequent revolutions. Even in scientific revolutions new paradigms succeed to the old ones continuously. What changes drastically in a revolution is not the paradigm itself but the balance of power between paradigms. Like political revolutions, scientific revolutions are the struggle for existence and paradigms do not shift to copy the reality better.


1 : What does “paradigm” originally mean?

Paradigm is a term that Kuhn[1] adopted in The Structure of Scientific Revolutions published in 1962 and it is used today as a buzzword meaning an intellectual framework out of the context of natural science. Masterman[2] pointed out that Kuhn’s paradigm has 21 senses[3] in the International Colloquium in the Philosophy of Science held in 1965. Kuhn proposed a new term “disciplinary matrix” whose elements are symbolic generalizations, beliefs in particular models, values, exemplars and so on in the postscript in 1969[4], trying to avoid the confusion owing to the ambiguity. Considering these developments, I want to put 21 senses into order.

The word paradigm stems from a Greek word “παράδειγμα (paradeigma)” meaning a pattern or model of the thing to be executed[5] and this noun derived from the verb “παραδείκνυμι (paradeiknumi)” composed of “παρά (beside, beyond)” and “δείκνυμι (to show, to point out)”, thus meaning to exhibit side by side[6]. For example, if you show a painter a model beside him or her, the model is a paradeigma for his or her painting.

The Greek word paradeigma was succeeded to by the Latin word paradigma bearing a special sense “systematic arrangement of all the inflected forms of a word” while the general sense of “pattern, example, model…” was in the charge of the Latin (later English) word exemplar. The special sense is not far from the original one. A teacher of Latin shows students a sample verb conjugation table such as “amo, amas, amat …" as an exemplar beside them and makes them apply it to another verb, reciting “laudo, laudas, laudat …" and thus master Latin verbs. It would illustrate that the Latin word paradigma still holds the original Greek sense.

Paradigms in scientific education fulfill a similar function to those in grammatical education. A teacher of math does a sample exercise in the eye of students and makes them solve similar problems and master the solution. A teacher of physics exhibits the exemplary treatment of experiment tools and students imitate it after the exemplar. Kuhn was a physicist and must have learned math and physics in such a way. Kuhn said the term ‘paradigm’ would be entirely appropriate, both philologically and autobiographically[7] for the fourth element of the disciplinary matrix, “exemplar”. By it I mean, initially, the concrete problem-solutions that students encounter from the start of their scientific education, whether in laboratories, on examinations, or at the ends of chapters in science texts[8].

According to Kuhn, however, there is a big difference between scientific and grammatical paradigms. A grammatical paradigm is an object for replication, but a scientific paradigm is not. Instead, like an accepted judicial decision in the common law, it is an object for further articulation and specification under new or more stringent conditions[9]. The common law is the ancient law of England which is enforced by the past judgments and decrees of the courts. They should be respected as exemplars but no case is exactly the same as the past one and therefore further articulation and specification are necessary. The application of scientific laws also needs similar articulation and specification and Kuhn named them “puzzle-solving”.

The other elements of the disciplinary matrix are derivatives from puzzle-solving based on the exemplar. That is to say, symbolic generalizations are expressions shared by group members, such as a formula like F=ma or a proposition like “action equals reaction”, beliefs in particular models are what Masterman called “metaphysical paradigms” and what we usually consider paradigms to be, and lastly values are concerned with internal and external consistency in considering sources of crisis and factors in theory choice[10], which determines the margin of permissible error. These expressions, beliefs and values specific to scientists are shared by them, because they were educated to accept the same paradigm as their exemplar.

Kuhn’s theory of paradigms is concerned only with natural sciences, because unlike other creative fields both undergraduate and graduate students acquire the substance of their fields from books written especially for students [11]. This difference is, however, not important, because history of textbook is far shorter than history of paradigms. His theory is applicable to knowledge systems in general and also to legal systems, as is known by his simile. In fact the paradigm (exemplar) of his theory of paradigms seems to be the legal or political systems.

2 : Why is scientific revolution anomalous?

Paradigms of sciences cannot remain the same eternally. Scientists sometimes discard an old paradigm and accept a new one. Kuhn called it a scientific revolution. The word “revolution” usually indicates an overthrow of a governing political system by the governed. He adopted this term because scientific revolutions are similar to political revolutions.

Political revolutions are inaugurated by a growing sense, often restricted to a segment of the political community, that existing institutions have ceased adequately to meet the problems posed by an environment that they have in part created. In much the same way, 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.[12]

The process that Kuhn regards as a scientific revolution is different from what Popper[13] regards as the progress of science, namely the process of conjectures and refutation. Kuhn thinks of such a process not as anomalous revolution but as normal puzzle-solving.

Sir Karl has erred by transferring selected characteristics of everyday research to the occasional revolutionary episodes in which scientific advance is most obvious and by thereafter ignoring the everyday enterprise entirely. In particular, he has sought to solve the problem of theory choice during revolutions by logical criteria that are applicable in full only when a theory can already be presupposed.[14]

Popper, while admitting the distinction between normal science and extraordinary science, says, Kuhn is mistaken when he suggests that what he calls 'normal’ science is normal[15]. According to him, puzzle-solving is what engineers do and scientists should not be satisfied with it, so the 'normal’ scientist, as Kuhn describes him, is a person one ought to be sorry for[16]. He, then, insists that if what Kuhn calls normal science should become normal, it will be a danger to science and, indeed, to our civilization[17].

Unlike Popper, Kuhn is an ex-physicist and knows what scientists actually do. They usually engage in puzzle-solving and do not want to initiate any revolutions. Scientific revolutions take place when science faces a danger and they do not think of it as “a danger to science” that no revolutions break out.

In fact, the man engaged in puzzle-solving very often resists substantive novelty, and he does so for good reason. To him it is a change in the rules of the game and any change of rules is intrinsically subversive.[18]

Kuhn disagrees with Popper on the idea that even a single counterevidence refutes the ruling theory and brings about a revolution. Scientists do not want frequent revolutions for an economical reason. Suppose the conditions C1, C2, C3 … Cn result in a contradiction R∧¬R. To avoid this contradiction, you must deny either of C1, C2, C3 … Cn.

(C1∧C2∧C3∧…∧Cn ⇒ R∧¬R) ⇒ (¬C1∨¬C2∨¬C3∨…∨¬Cn)

When there are many candidates, the first to choose is the condition that can be modified at the least cost. Just as investors give priority to the most cost-effective investment, scientists prefer the most cost-effective modification. Typically they first doubt the experiment process when they encounter unexpected results. For example, OPERA researchers observed muon neutrinos traveling faster than light in September 2011 [19][20]. SF fans, hoping the realization of a time-machine, got excited at the news, but the researchers were careful in examining the measurement, because accepting the result would force them to modify the special theory of relativity thoroughly. Their doubt was right. They later found that a link from a GPS receiver to the OPERA master clock was loose and a clock on an electronic board ticked 10 MHz frequency faster than it was expected. In July 2012, OPERA researchers concluded that the speed of neutrinos is consistent with the speed of light[21].

Even after they found no errors in measurement, scientists try to minimize modification of the ruling theory. They abandon their paradigms completely and accomplish a scientific revolution as rarely as the governed people overthrow the government and accomplish a political revolution. To continue Kuhn’s parallelism between science and politics, the government, when they face some problems, first change the application of laws and then, if they find it not enough, modify them legally. The revolution is the last resort that can never be legal. It might solve the problems thoroughly, but might bring about long-term anarchism. Because of its high risk it cannot be the normal method to solve problems.

Scientific revolutions are different from political revolutions in that the revolutionists of a new paradigm do not murder the rulers of the old paradigm. Still the new paradigm cannot persuade the followers of the old paradigm in a rational way. Kuhn, quoting[22] Max Plank[23]’s remark that a new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it[24] emphasizes the incommensurability between paradigms. The incommensurability is originally a term of Euclidean geometry, but Kuhn uses it as a term meaning the inability to communicate with other paradigms’ followers, because they use the same term signifying different objects. I will take up the incommensurability later.

3 : Does tradition suppress innovation?

Let me examine how original Kuhn’s theory of paradigms is in the history of the Western philosophy. Kuhn agrees with Popper on that scientists do not observe objects as they are. As for this idea Kuhn was influenced not by Popper, the Austro-British philosopher, but by Hanson[25], an American philosopher, who criticized the naïve empiricism prevalent in America at that time and insisted that observation is theory-laden. In his book, Patterns of Discovery published in 1958, he distinguished “seeing-as” from “seeing-that”, using gestalt-psychological examples such as Necker cube[26]. Kuhn, quoting this book, says that the switch of gestalt is a useful elementary prototype for what occurs in full-scale paradigm shift[27]. After the paradigm shift you see the same thing as something different in a figurative sense.

It has been a common sense in Germany since Kant[28] that observation is theory-laden. So, there is nothing new about Hanson’s philosophy. You might think that Kuhn’s theory of paradigms is different from Kant’s transcendental idealism in that paradigms shift with the times and scientific propositions are not synthetic judgments a priori, but as a pioneer of historical relativism Marx[29] is the predecessor. Marx thought that a worldview of a time is an ideology skewed by the interest of the ruling class and evaluated the role of the proletarian revolution.

There are some similarities between Kuhn’s theory of revolutions and Marx’s, but unlike Marx Kuhn did not think much of revolutions. In this point his idea of paradigms expressed in The Structure of Scientific Revolutions is similar to Gadamer[30]’s idea of tradition expressed two years before in Truth and Method and Habermas[31]’s criticism on Gadamer’s conservative hermeneutics is similar to Popper’s criticism on Kuhn’s theory of paradigms. Gadamer thought of such a criticism as too transcendent over language[32] and so did Kuhn. In fact it was because Popper followed his philosophical paradigm blindly that he could in a transcendent way criticize the scientists following a paradigm blindly.

Kuhn had also emphasized the importance of a firm commitment to the scientific tradition in The Essential Tension published a year before Truth and Method.

This central role of an elaborate and often esoteric tradition is what I have principally had in mind when speaking of the essential tension in scientific research. I do not doubt that the scientist must be, at least potentially, an innovator, that he must possess mental flexibility, and that he must be prepared to recognize troubles where they exist. That much of the popular stereotype is surely correct, and it is important accordingly to search for indices of the corresponding personality characteristics. But what is no part of our stereotype and what appears to need careful integration with it is the other face of this same coin.[33]

Following tradition and transcending it constitute two faces of the same coin and you cannot transcend tradition without following it. Kuhn named the relation of the two faces, conservation and innovation of tradition, “the essential tension".

As Kuhn admits, his idea is different from the popular stereotype of innovation. Liberal educationists would oppose to cramming and encourage pupils to think by themselves but reducing the curriculum for traditional knowledge and giving them time to think by themselves makes them less creative. Those who do not know tradition are not only unable to create new value that transcends the traditional value but also unable even to know whether a new paradigm is better than the traditional one or not. They will remain below tradition without knowing it.

You might be afraid that, if we are enslaved by tradition, all we can do is improve it at best, which is far less valuable than complete innovation. Innovation, however, is not always valuable and in reality valuable innovation emerges from imitation of tradition. For example, we regard the evolution of humans as epoch-making innovation, but human chromosome is only 1.44% different from the counterpart of chimps, although that difference is important, because it brings about 83% differences at the amino acid sequence level[34]. Judging from it, humans and chimps succeed to a common ancestor whose genetic paradigm is not so different from ours and apparent differences result from puzzle-solving to adapt to the environment. To parody the Edison’s famous cliché, valuable innovation is one percent originality, ninety-nine percent banality.

Is 1% originality insufficient? Then increase in the rate of originality, and it will also increase the risk. Although genetic mutation can be caused artificially by radiation or chemicals, the vast majority of the products are inferior to normal individuals in ability for survival. The higher the rate of mutation is, the higher the risk of extinction is. That is why the large-scale mutation is rare and the complete reconstruction of genes is impossible. Neurath[35] said that Like sailors we are, who must rebuild their ship upon the open sea, never able to dismantle it in dry dock or to reconstruct it there from the best materials[36] and our genetic paradigm is, like Neurath’s ship, allowed only to repeat partial refits so as to avoid extinction (sinking).

Coming back to paradigms of knowledge, we are apt to think that intellectual innovation must be completely original, but the complete originality cannot be understood by anybody and is destined to disappear. Suppose I am struck with a completely original idea and speak it in a completely original language. I will be sure to be isolated in a psychiatric ward. To be understood I must follow the traditional language paradigm and to be evaluated I must accept the value of the traditional paradigm and explain mine in terms of it. Kuhn’s assertion, new theories and, to an increasing extent, novel discoveries in the mature sciences are not born de novo. On the contrary, they emerge from old theories and within a matrix of old beliefs about the phenomena that the world does and does not contain[37] holds true of not only the mature sciences but also intellectual paradigms in general.

Kuhn’s theory is based on a traditional paradigm of philosophy, although it has some novelties in applying it to the history of science. His theory is self-consistent, because it is under “the essential tension” in his sense. On the other hand, Popper said that a paradigm follower is a person one ought to be sorry for, although he engaged himself in puzzle-solving throughout his life, based on the paradigm of Kant’s critical philosophy. Popper must have seemed contradictory to Kuhn.

4 : Do revolutions interrupt tradition?

Kuhn says, The normal-scientific tradition that emerges from a scientific revolution is not only incompatible but often actually incommensurable with that which has gone before[38]. Do revolutions interrupt tradition and create a new paradigm incommensurable with the old paradigm?

The most drastic scientific revolution took place in Europe between the end of the Renaissance era and the late 18th century. The word “the scientific revolution” usually signifies this single historical event. The paradigm shift at this time is so great that Aristotle[39]’s Physics is certainly incommensurable with Galileo[40]’s Le Meccaniche, Kepler[41]’s The Harmony of the World, Newton[42]’s Principia and so on.

It is, however, not true that the modern paradigm of physics and astronomy suddenly emerged from the incommensurable paradigm of Aristotle. The modern physical sciences should be regarded as the successor to Archimedes[43]’s geometrical approach to nature and there is no discontinuity in the tradition that stems from Ancient Greece. Galileo devoted deep study to Archimedes’ works translated into Latin in those days. Copernicus and Kepler learned heliocentric astronomy from Archimedes’ The Sand Reckoner. The origin of Newton’s or Leibniz’s infinitesimal calculus can be traced to Archimedes’ method of exhaustion.

Some might object that Archimedes’ physics was confined to statics (buoyancy, torque etc.) and he mentioned little of kinetics, but applying Archimedes’ geometrical approach to kinetics is a matter of puzzle-solving. The drastic change of the scientific revolution consists not in that Aristotle’s paradigm gave birth to an incommensurable mutant paradigm but in that a branch paradigm of Archimedes took the place of the mainstream paradigm of Aristotle, which withdrew from physics and astronomy to philosophy.

The nature of the paradigm shift is more apparent in the case of genetic paradigms. Dinosaurs except birds became extinct at the close of the Mesozoic Era and thereafter mammals flourished instead. It was not because dinosaurs suddenly gave birth to mammals but because a branch paradigm of mammals took the place of the mainstream paradigm of dinosaurs. What changed drastically was not the genetic paradigm itself but the balance of power between paradigms. The same thing is true of political revolutions. They break out not because the rulers radically change their policies but because an underground power replaces the ruling power.

5 : Do paradigms make progress?

Admitting paradigm shifts are changes in the balance of power between paradigms, the incommensurability between paradigms arouses another doubt as to whether the shifts contribute to progress of science. Progress is an advance toward higher value. So long as a paradigm provides a fixed criterion for evaluation, we can recognize progress in puzzle-solving. The question is whether there are any criteria on the meta-level that enable us to estimate a paradigm shift to be progress. Kuhn is suspicious about progress on the meta-level.

In the sciences there need not be progress of another sort. We may, to be more precise, have to relinquish the notion, explicit or implicit, that changes of paradigm carry scientists and those who learn from them closer and closer to the truth.[44]

Rejecting the correspondence theory of truth, Kuhn does not regard accumulation of observed facts as progress of science. I agree with him on that point, but it does not follow that there are no criteria for judging whether science makes progress or not. Although criteria for evaluation seem variable with the times, the most fundamental criterion has never changed since the emergence of life on Earth approximately 3.5 billion years ago and will never change. That is to say, the ultimate purpose of all the living systems is to increase the probability of their existence and seemingly variable evaluation is concerned only with the value of means to it. Natural selection has selected genetic paradigms on this criterion and scientific paradigms have also been selected through power struggle for existence. As the paradigm (exemplar) of Kuhn’s theory of paradigms is the political paradigm, this power theory of truth would be acceptable to him. In fact he said, in the sciences might makes right, a formulation which would again not be entirely wrong if it did not suppress the nature of the process and of the authority by which the choice between paradigms is made[45].

When those who know little of science are asked whether science has been making progress, most of them answer yes. It is not because they feel convincing the gestalt-switch of worldview brought about by scientific revolutions, but because they feel science has contributed to extending our life span and increasing freedom of means. So, we can say truth is evaluated as “power of survival” and confirmed by “survival of power”. Of course those with a mistaken idea sometimes happen to survive, but if it is accidental, such a fortune does not increase the probability of their existence. The decision by majority of scientists have often resulted in erroneous theories, but to recognize them as erroneous the current decision by majority of scientists is necessary. In this sense, the propositions “in the sciences might makes right” and “knowledge is power” are true.

6 : References

  1. Thomas Samuel Kuhn; July 18, 1922 – June 17, 1996; an American historian of science, philosopher of science
  2. Margaret Masterman; 4 May 1910 – 1 April 1986; a British linguist and philosopher
  3. The Nature of a Paradigm (author) Margaret Masterman (media) Criticism and the Growth of Knowledge: Proceedings of the International Colloquium in the Philosophy of Science (page) 65 (editors) Imre Lakatos, Alan Musgrave
  4. The Structure of Scientific Revolutions (page) 182-187 (author) Thomas Kuhn
  5. παράδειγμα (media) An Intermediate Greek-English Lexicon (author) Henry George Liddell, Robert Scott
  6. παραδείκνυμι (media) An Intermediate Greek-English Lexicon (author) Henry George Liddell, Robert Scott
  7. The Structure of Scientific Revolutions (page) 186 (author) Thomas Kuhn
  8. The Structure of Scientific Revolutions (page) 187 (author) Thomas Kuhn
  9. The Structure of Scientific Revolutions (page) 23 (author) Thomas Kuhn
  10. The Structure of Scientific Revolutions (page) 185 (author) Thomas Kuhn
  11. The Essential Tension: Tradition and Innovation in Scientific Research (page) 23 (author) Thomas Kuhn (media) The Essential Tension: Selected Studies in Scientific Tradition and Change
  12. The Structure of Scientific Revolutions (page) 92 (author) Thomas Kuhn
  13. Sir Karl Raimund Popper; 28 July 1902 – 17 September 1994; Austro-British philosopher
  14. Logic of Discovery or Psychology of Research($2) (author) Thomas Kuhn (media) [https://www.amazon.com/dp/0521096235/?tag=u-20 Criticism and the Growth of Knowledge: Proceedings of the International Colloquium in the Philosophy of Science (page) 19 (editors) Imre Lakatos, Alan Musgrave
  15. Normal Science and its Dangers (author) Karl Popper (media) Criticism and the Growth of Knowledge: Proceedings of the International Colloquium in the Philosophy of Science (page) 53 (editors) Imre Lakatos, Alan Musgrave
  16. Normal Science and its Dangers (author) Karl Popper (media) Criticism and the Growth of Knowledge: Proceedings of the International Colloquium in the Philosophy of Science (page) 52 (editors) Imre Lakatos, Alan Musgrave
  17. Normal Science and its Dangers (author) Karl Popper (media) Criticism and the Growth of Knowledge: Proceedings of the International Colloquium in the Philosophy of Science (page) 53 (editors) Imre Lakatos, Alan Musgrave
  18. The Function of Dogma in Scientific Research (author) Thomas Kuhn (media) Scientific Change: Symposium on the history of science held at Oxford 9–15 July 1961 (page) 364 (editors) A. C. Crombie
  19. Measurement of the neutrino velocity with the OPERA detector in the CNGS beam, V1 (media) arXiv (author) OPERA collaboration
  20. Oscillation Project with Emulsion-tRacking Apparatus
  21. Measurement of the neutrino velocity with the OPERA detector in the CNGS beam, V4 (media) arXiv (author) OPERA collaboration
  22. The Structure of Scientific Revolutions (page) 151 (author) Thomas Kuhn
  23. Max Karl Ernst Ludwig Planck; April 23, 1858 – October 4, 1947; a German theoretical physicist
  24. Scientific Autobiography and other papers (page) 33-34 (author) Max Planck
  25. Norwood Russell Hanson; 1924 – 1967; an American philosopher of science
  26. Patterns of Discovery: An Inquiry into the Conceptual Foundations of Science (page) 9 (author) Norwood Russell Hanson
  27. The Structure of Scientific Revolutions (page) 85 (author) Thomas Kuhn
  28. Immanuel Kant; 22 April 1724 – 12 February 1804; a German philosopher from Königsberg in Prussia
  29. Karl Heinrich Marx; 5 May 1818 – 14 March 1883; a German philosopher, economist
  30. Hans-Georg Gadamer; February 11, 1900 – March 13, 2002; a German philosopher
  31. Jürgen Habermas; June 18, 1929 – ; a German sociologist and a philosopher
  32. Rhetorik, Hermeneutik und Ideologiekritik (author) Hans-Georg Gadamer (media) Gesammelte Werke Bd.2: Hermeneutik II: Wahrheit und Methode – Ergänzungen, Register (page) 232-250
  33. The Essential Tension: Tradition and Innovation in Scientific Research (author) Thomas Kuhn (media) The Essential Tension: Selected Studies in Scientific Tradition and Change (page) 29
  34. DNA sequence and comparative analysis of chimpanzee chromosome 22 (media) Nature 429 (page) 382 (author) The International Chimpanzee Chromosome 22 Consortium
  35. Otto Neurath; December 10, 1882 – December 22, 1945; an Austrian philosopher of science
  36. “Wie Schiffer sind wir, die ihr Schiff auf offener See umbauen müssen, ohne es jemals in einem Dock zerlegen und aus besten Bestandteilen neu errichten zu können." Protokollsätze (author) Otto Neurath (media) Erkenntnis 1932/1933, Volume 3, Issue 1 (page) 206
  37. The Essential Tension: Tradition and Innovation in Scientific Research (author) Thomas Kuhn (media) The Essential Tension: Selected Studies in Scientific Tradition and Change (page) 27
  38. The Structure of Scientific Revolutions (page) 103 (author) Thomas Kuhn
  39. Ἀριστοτέλης, Aristotélēs; 384 BC – 322 BC; a Greek philosopher and polymath
  40. Galileo Galilei; 15 February 1564 – 8 January 1642; an Italian physicist
  41. Johannes Kepler; December 27, 1571 – November 15, 1630; a German mathematician, astronomer
  42. Sir Isaac Newton; 25 December 1642 – 20 March 1727; an English physicist, mathematician
  43. Archimedes of Syracuse; Greek: Ἀρχιμήδης; c. 287 BC – c. 212 BC; a Greek mathematician, physicist, engineer, inventor, and astronomer
  44. The Structure of Scientific Revolutions (page) 170 (author) Thomas Kuhn
  45. The Structure of Scientific Revolutions (page) 167 (author) Thomas Kuhn