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A paradigm is a model or exemplar. The paradigm case is the typical or archetypal case. A paradigm shift is the movement from one paradigm to another.
One notion of a paradigm is that used in law, where a paradigm is a model case to be distinguished from penumbral or atypical cases. A law might make it a crime to use a gun while committing a crime. A case where a robber uses a loaded .357 magnum would be a paradigm case; a case where a robber uses a squirt gun would be considered penumbral. A court would have to decide whether the law meant to include the use of squirt guns as a crime, but there would be no need for interpretation of the law to decide whether using a loaded .357 magnum was within the legislature's intent. Paradigm in this sense has no correlative to paradigm shift.
A more common use of paradigm as model would be something like the paradigm of policing, which would include the basic assumptions, values, goals, beliefs, expectations, theories and knowledge that a community has about policing. Many models, like that of policing, have emerged over time in response to various changes in society and are not the result of a grand design or plan. A paradigm shift in policing might occur slowly over many years or it might occur abruptly as the result of a conscious analysis and evaluation of the current paradigm. An individual or a group might list the inadequacies, dangers, etc. of the current paradigm in light of relevant changes in society and present a new model for policing. If the new model is accepted by the community, then a paradigm shift occurs. The new paradigm would replace old assumptions, values, goals, beliefs, expectations, theories, and the like with its own.
T.S. Kuhn in his Structure of Scientific Revolutions (1962) used the term 'paradigm' to refer to the conceptual frameworks and/or worldviews of various scientific communities. For Kuhn, a scientific paradigm includes models—like the planetary model of atoms—and theories, concepts, knowledge, assumptions, and values. The concept of a scientific paradigm was essential to Kuhn's argument that the history of science is characterized by conceptual frameworks giving way to new ones during what he called scientific revolutions.
Kuhn believed that during periods of "normal science" scientists work within the same paradigm. Scientific communication and work proceeds relatively smoothly until anomalies occur or a new theory or model is proposed which requires understanding traditional scientific concepts in new ways, and which rejects old assumptions and replaces them with new ones.
A paradigm of a scientific revolution in Kuhn's sense would be the Copernican revolution. The old model of the Earth at the center of a god's creation was replaced with a model that put Earth as one of several planets orbiting our sun. Eventually, circular orbits, which represented perfection and a god's design for the heavens in the old worldview, would be reluctantly replaced by elliptical orbits. Galileo would find other "imperfections" in the heavens, such as craters on the moon.
For Kuhn, scientific revolutions occur during those periods where at least two paradigms co-exist, one traditional and at least one new. The paradigms are incommensurable, as are the concepts used to understand and explain basic facts and beliefs. The two groups live in different worlds. He called the movement from the old to a new paradigm a paradigm shift.
Whether Kuhn was right or wrong about the history of science—and he has plenty of critics—his notions of a paradigm and a paradigm shift have had enormous influence outside the history of science. In many ways, how Kuhn is understood and applied is analogous to how Darwin's conception of natural selection has been misunderstood and applied outside evolutionary biology. For a paradigm of this type of misapplication, see the Skeptic's Dictionary entry on neuro-linguistic programming.
What's Your Paradigm?
One of the more common applications of the terms paradigm and paradigm shift is to mean "traditional way of thinking" vs. "new way of thinking." Some New Age thinkers seem to think that paradigms can be created by individuals or groups who consciously set out to create them. They seem to mean by 'paradigm' nothing more than "a set of personal beliefs," e.g., Essays on Creating Sacred Relationships: The Next Step to a New Paradigm by Sondra Ray and Handbook for the New Paradigm from Benevelent Energies. Many of the New Age self-help promoters base their approaches on the notion that one's current paradigm is holding them back and what they need to do is create a new paradigm (set of beliefs, priorities, assumptions, values, goals, etc.) for themselves that will allow them to break through, etc., e.g., The Paradigm Conspiracy: How Our Systems of Government, Church, School, and Culture Violate Our Human Potential by Denise Breton and Christopher Largent.
Others seem to identify the term paradigm with theory, e.g., Lamarck's Signature: How Retrogenes Are Changing Darwin's Natural Selection Paradigm, by Edward J. Steele et al.
Some, like Joel Barker in his video "The Business of Paradigms," use paradigm and paradigm shift to explain how some people or companies fail and others succeed. The ones who succeed are those who can shift to a new paradigm; the ones who fail are those who remain hidebound and fixated on traditional ideas because they have proved successful in the past or because they can see no use for some new idea. The Swiss failed to patent or market the quartz watch, even though they invented it, because they couldn't shift paradigms. They couldn't shift paradigms because they couldn't see that there would be a market for another kind of watch besides the kind they'd been successfully making and selling for generations. The Japanese made all the money from the quartz watch because they didn't have an old paradigm that locked them into a way of thinking that precluded patenting and marketing quartz watches.
This model might be called retroactive clairvoyance because it sees always and only after the fact who failed to make a paradigm shift and who benefited by having foresight to take advantage of other people's creations. This model is useless for predicting what creations will prove profitable and useful. But it is excellent in hindsight. It infallibly sees that Xerox didn't do a paradigm shift and screwed up when it did not pursue ethernet or graphical user interface or the laser printer, and that IBM screwed up when it initially rejected the notion of the personal computer.
Barker has moved on and now claims to be able to recognize when paradigms will shift in the future and he will teach you to do so, too, in his new book Paradigms: The Business of Discovering the Future.
Probably the most serious misapplication of Kuhn's conception is the notion that everything that makes up a paradigm is relative and subjective, and therefore purely personal with no connection or test in reality. Some of those who think that creationism and evolution are competing paradigms or theories make this mistake. It may be true that all theories and beliefs are "subjective" to some extent, but this does not mean that they are all equally useful or probable, or even of the same type. The fact that red and all colors are "subjective" hasn't prevented the development of interior decorating, painting, clothing design, etc. Nobody hesitates to buy a red car on the grounds that red and all colors are purely subjective. Most of us can still tell the difference between red and blue even if we know that neither really exists except in our minds or in the subjective interaction of our senses with objects under certain conditions. And most of us know that there is no comparison and no competition between understanding red in terms of wavelength of light and understanding red as a symbol for love or passion or the belief that all things red are infused with divine love and worthy of veneration.