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I am not an expert in epistemology and I am currently searching for the name of a particular approach in physics (an historical one). Since Galileo, the role of the physicist is to simplify the physical systems (ie do not consider the temperature of a room, or the wind speed as relevant parameters to study the behaviour of a pendulum) in order to deduce the fundamental laws of Nature. In this approach, the observed phenomenon are seen as coming from simple but fundamental laws. And it works well.

But another historical approach was to try to explain things without fundamental laws, but only based on reproductibility and experience : in this approach the dynamic of a pendulum is not seen as a consequence of gravity and laws of motion but as an independent phenomenon. This approach is an approach of "models without laws". It was the traditional approach for very complex systems, like in medicine : for this "input", the experience tell me that I have this "output" (but I am not even searching for the underlying fundamental laws).

In a certain sense the first approach thinks in terms of laws, cause and consequences, and the second one thinks in terms of models and correlations.

So my question is : what are the correct terms of these approaches in epistemology ?

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The distinction that springs to mind is between mechanistic vs. empirical explanations. This is used in philosophy of science and I've come across it in philosophical debates concerning evidence based medicine and in law (others too), where there is some conflict over whether an empirical account is valid without a mechanistic account, and vice versa.

Mechanistic - understanding how things work in detail, and from principles, laws etc. In its extreme a reductionistic, microscopic account.

Empirical - does changing X result in Y. Not how it works, but does it work. In it's extreme a holistic, macroscopic account.

It also correlates quite well with the distinction between hard vs. soft science.

I'm not sure I would want to call these terms epistemological but they are used in modern discussion, and I feel they capture what you are describing.

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The classic distinction was between rationalism and empiricism. Descartes was the godfather of rationalism, while Hume was the godfather of empiricism.

From the Stanford Encyclopedia of Philosophy,

Rationalists generally develop their view in two ways. First, they argue that there are cases where the content of our concepts or knowledge outstrips the information that sense experience can provide. Second, they construct accounts of how reason in some form or other provides that additional information about the world. Empiricists present complementary lines of thought. First, they develop accounts of how experience provides the information that rationalists cite, insofar as we have it in the first place. (Empiricists will at times opt for skepticism as an alternative to rationalism: if experience cannot provide the concepts or knowledge the rationalists cite, then we don't have them.) Second, empiricists attack the rationalists' accounts of how reason is a source of concepts or knowledge.

So rationalists believe the model can provide insight beyond the data, while empiricists believe the data are the ultimate authority and the model can only approach the truth of the data.

These are two philosophical schools. In physics the competing theories are classical mechanics and quantum mechanics, respectively - and roughly. Quantum mechanics cannot be explained by classical mechanics, and so adopted a piecemeal approach out of necessity. There is also a professional distinction between theoretical and experimental physicists, who again roughly split along these lines.

As in philosophy, these physical schools are currently not reconciled, and are sometimes competitors for the truth, yet exist symbiotically. There is a consensus on a sort of "separation of powers" in physics, whereby theory is allowed to predict things for which there is no data as long as theory submits to the veto power of data.

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    As a physicist, I object to your exposition of classical and quantum mechanics. They are definitely not two competing theories. It is unambiguously true that quantum mechanics is the correct way to describe microscopic phenomena. If we ever should find a better theory, that will be not classical mechanics, but a new theory that reduces to quantum mechanics in an appropriate limit, just as quantum mechanics reduces to classical mechanics in an appropriate limit. Now some quantum interpretations (like DeBroglie-Bohm) have some "classical" features, but that doesn't make them classical mechanics.
    – celtschk
    May 1, 2014 at 20:46
  • I was under the understanding that at the microscopic level they are indeed competing theories, and that quantum mechanics has mostly won the day. Classical mechanics relies on the infinitesimal, while quantum mechanics does not. I am not arguing that there are some scientists who doubt QM and hold close to CM, but that CM fell short in explaining certain phenomena and QM filled the breach. Is the Standard Model not an attempt to bridge the two theories? This point may turn on the words "competing" and "compatible".
    – Jack C
    May 2, 2014 at 16:47
  • Classical mechanics indeed couldn't explain the microscopic phenomena, and that is why quantum mechanics was developed, but they are not competing theories, but one that works there and one that doesn't. You might be confusing classical mechanics with the more general term "classical theory" which encompasses all theories which are somewhat "like classical mechanics". For example, General Relativity is a classical theory (but certainly is not classical mechanics), but it isn't used for microscopic phenomena. The standard model, on the other hand, is a purely quantum theory.
    – celtschk
    May 2, 2014 at 18:37
  • Anyway, there's nowhere a classical theory competing with quantum mechanics. There are quantum interpretations like DeBroglie-Bohm which are in some sense classical, but reproduce quantum mechanics (at the cost of violating other principles, like no action on a distance, thus being at odds with relativity).
    – celtschk
    May 2, 2014 at 18:42
  • If we're going to talk about "godfathers," then I think you should go back to Locke; Hume seems more like the youngster of the British Empiricists to me!
    – senderle
    May 3, 2014 at 17:29
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The two approaches described in the question correspond closely but not perfectly to those set out by Carl Hempel in his classic "Two Models of Scientific Explanation". One he calls "Deductive-nomological", the other "Probabalistic". However he differs from the questioner in that he assumes that covering laws are invoked in both cases. A lot seems to depend on whether laws are considered to include generalisations and correlations, or to specify something more fundamental and compelling.

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