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I read from the Wikipedia site regarding the concept "paradigm" that:

The Oxford Dictionary of Philosophy attributes the following description of the term to Thomas Kuhn's The Structure of Scientific Revolutions:

Kuhn suggests that certain scientific works, such as Newton's Principia or John Dalton's New System of Chemical Philosophy (1808), provide an open-ended resource: a framework of concepts, results, and procedures within which subsequent work is structured. Normal science proceeds within such a framework or paradigm. A paradigm does not impose a rigid or mechanical approach, but can be taken more or less creatively and flexibly.

Now, if e.g. Newton's Principia does not impose a rigid approach, then what does this say about physics's rigor?

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    I think that you are not getting the gist of Kuhn's argument: Newtons' Principia was (maybe the most successful one) "paradigm" in modern science, exactly because it established "physics' rigor" for centuries. Jan 4 '20 at 19:59
  • @MauroALLEGRANZA But what then does it mean that: "A paradigm does not impose a rigid or mechanical approach, but can be taken more or less creatively and flexibly.?
    – mavavilj
    Jan 4 '20 at 20:09
  • "At the physical level of rigor" is often used by mathematicians to express "intuitive but not conclusive". "But "the physical level of rigor" is higher on certainty than the logical one, since reproducible experiments are more reliable than anybody’s, be it Hilbert’s, Einstein’s or Gödel’s, intuition" says Gromov, the most prominent living geometer.
    – Conifold
    Jan 5 '20 at 1:17
  • I'm not sure it says anything about rigour, but it does make clear that theories of the physical sciences are provisional. I see your point about paradigms not imposing a rigid approach. If not, then how is it a paradigm? It also seems odd to suggest that the paradigm of Materialism or Theism does not require a rigid approach and clearly very few believers take this view.
    – user20253
    Jan 5 '20 at 11:51
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Newton's Principia was a (maybe the most successful one) paradigm in modern science, exactly because it established "physics' rigor" for centuries.

See Thomas Kuhn's Concept of a Paradigm :

In normal science the key theories, instruments, values and metaphysical assumptions that comprise the disciplinary matrix are kept fixed, permitting the cumulative generation of puzzle-solutions [...] A particularly important part of Kuhn’s thesis in SSR focuses upon one specific component of the disciplinary matrix. This is the consensus on exemplary instances of scientific research. These exemplars of good science are what Kuhn refers to when he uses the term ‘paradigm’ in a narrower sense. [...] Such texts contain not only the key theories and laws, but also —and this is what makes them paradigms— the applications of those theories in the solution of important problems, along with the new experimental or mathematical techniques (such as the chemical balance in Traité élémentaire de chimie and the calculus in Principia Mathematica) employed in those applications.

Paradigms are collections of scientific laws and tools as well as collections of examples about how to apply laws and rules to "solve problems".

In this sense, they define the criteria of scientific rigor and, at the same time, they provide "an open-ended framework of concepts, results, and procedures within which subsequent work is structured", because they "show the way" to address new problems.

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  • But also, didn't Kuhn question somewhere in that same book that this "structurality"-assumption of normal science might hinder scientific progress. Because then one might see "only within a framework", and not, whether there's also something outside of it.
    – mavavilj
    Jan 5 '20 at 8:37
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Within Kuhn's philosophy of science, a paradigm is an exemplar of good work that others in the field copy. In essence, it works like this:

  1. Someone does a some specific analytical work on a problem in a given field.
  2. Other people working on the same or similar problems look at #1 and think: "Wow, that was impressive and successful. We should all do work like that."
  3. People start applying the tactics of #1 to their own work; start measuring the value of other people's work by the standards of #1; start training students to do work in the style of #1

When we get to stage #3, the research done in #1 has become the paradigm of how all work should be done in the field, enforced and imposed by the body of researchers working in that field. This doesn't mean that everyone is doing the same research; it means that everyone is applying the same standards to whatever research they happen to be doing.

With respect to Newton, consider the fact that Newton's primary contribution was the Calculus — a mathematical system for modeling the movement of bodies with mass — and part of the paradigm he established is that physics should be math-based. But note that math has progressed since Newton's day, and people use Newton's math and methods to research things Newton never did. Think about the entire field of thermodynamics, which is based on Newton's principles, but came into existence a hundred years or so after Newton's death.

Of course, this outward expansion of research eventually leads to the discover of anomalies in the original paradigm, which can lead to new paradigms. Einstein used sophisticate maths to expose and quantify flaws in Newton's theories under the effects of gravity; quantum physics took mathematical analysis in entirely new directions from Newton's clockwork physics. Such people are still within the original paradigm — they are 'doing physics' in the way that Newton 'did physics' — but they have expanded beyond that work to create new exemplars.

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Physics is rigorous because our measure is the real world whereas with mathematics, there is often no such check. This is the reason why good physicists talk about physical intuition, and not merely mathematical rigour; if one had to wait for mathematical rigour to arrive, one might never get any physics done (case in point - Hilbert spaces and QM)!

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