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Even so I admit that the statement "All sciences use the same fundamental approach - the scientific method" may be true or false, it is not obvious to me whether it is actually true or false.

I looked up both "science" and "scientific method" in wikipedia (I'm not a native speaker). I learned that "scientific method" is a well defined concept, even so it went through some refinements and changes in its history. The meaning of the english word "science" is more problematic, but it should be possible to limit the question to individual disciplines that are unambiguously considered to belong to science.

My own takeaway from what I learned so far is that the above statement risks to delude the content of the concept "scientific method", because the english word "science" can have such a broad meaning.

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    You are aware, are you not, that mathematics degrees are often given as Bachelor of Arts, not Science? And that one has to fight for "Science-based Medicine", exemplified in sciencebasedmedicine.org/index.php/about-science-based-medicine This indicates to me that neither mathematics nor medicine are cleanly scientific; they are at best mixed. So your premise is questionable. – Rex Kerr Dec 19 '11 at 5:13
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    Is there a question buried in here somewhere? This appears to be a set of musings on the history of science and the scientific method. – Michael Dorfman Dec 19 '11 at 7:47
  • @MichaelDorfman You mean I should state the question more abstract and explicit, and move the "concrete" examples somewhere else? I will convert the "concrete" examples into an answer then, and try to clarify the question itself. – Thomas Klimpel Dec 19 '11 at 9:59
  • If you ask me, art is just unscientific science. – stoicfury Dec 20 '11 at 2:45
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    @stoicfury and that's why I wouldn't ask you. – Seamus Dec 20 '11 at 13:36
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"Science" is indeed a broad concept, and can be used loosely or more precisely.

Generally speaking, the natural sciences (physics, geology, biology, chemistry, etc.) are unambiguously based upon the scientific method. There's little room for dispute here, as I see it (unless we get into theoretical physics beyond the ability for experimentation).

The social sciences (psychology, anthropology, sociology, economics, etc.) attempt to adopt some of the principles of the scientific method, but are usually unable to follow it rigorously-- conducting experiments based upon controlled observation with reproducible results is notoriously difficult in behavioral fields.

Mathematics is generally not considered a science in the same way as the others, as the object of attention is intelligible, not sensible; the domain is based upon a set of abstractions, not on real-world objects which can be investigated.

Now, my question to you: why does this matter?

  • I tried to understand how I should read the mentioned statement, which is from an answer by stoicfury. I tried to explain why it seems questionable to me. What I learned now is that the classification of the "sciences" into "Naturwissenschaften" (natural sciences) and "Geisteswissenschaften" (humanities) was only common in German universities, and even there has been extended by "Sozialwissenschaften" (social sciences) and "Strukturwissenschaften" (formal sciences). This classification is still not identical to the one used in english speaking countries, but probably more similar than before. – Thomas Klimpel Dec 19 '11 at 17:41
  • It was important for me to clear my confusion about this statement, because it could imply that the "scientific method" is the only accepted way to acquire scientific knowledge. I think that the "scientific method" is a well accepted way to generate new knowledge, but not the only one. More importantly, I think that the "scientific method" has both its strengths and weaknesses. (It may be an attractive Pareto optimum, but it is not the only possible Pareto optimum.) – Thomas Klimpel Dec 19 '11 at 17:53
  • @Thomas Klimpel - If it's actually new knowledge (i.e. no-one has known it before) and you have some assurance that you haven't just gotten lucky, it is very hard to avoid something that is, implicitly at least, in all important aspects the scientific method. – Rex Kerr Dec 19 '11 at 19:53
  • @RexKerr I think that both mathematics and medicine are able to generate new knowledge (as are other "arts"). I admit that new knowledge in medicine often gets generated by the scientific method, especially if it's "genuinely" new knowledge. However, the important standard questions "can this therapy have dangerous adverse effects" and "has this therapy the intended therapeutic effect" are addressed by some "due diligence" procedure rather than the scientific method. But the procedure is not concerned with the "truth" of the new knowledge, but its "justifiability". – Thomas Klimpel Dec 20 '11 at 1:01
  • @ThomasKlimpel - Agreed on mathematics (and computer science extensions thereof). But to the extent that "due diligence" isn't using the scientific method at least informally, though, I'm not sure it works. There's not much to be diligent about except interpreting experiments or outcomes that can be viewed as (flawed) experiments. (Diligence also buys you some measure of legal protection, but that isn't because it generates knowledge.) – Rex Kerr Dec 20 '11 at 14:46
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Some sciences like mathematics and medicine are significantly older than the scientific method. This indicates to me that they may use a different fundamental approach than the scientific method.

In an effort to get a clearer picture, I took a look at the history of the scientific method:

Thales was the first to refuse to accept supernatural, religious or mythological explanations for natural phenomena, proclaiming that every event had a natural cause.

The first of these experimental scientific methods was developed in Iraq by the Muslim physicist and scientist, Ibn al-Haytham (Alhazen), who used experimentation and mathematics to obtain the results in his Book of Optics (1021).

In the On Demonstration section of The Book of Healing (1027), the Persian philosopher and scientist Avicenna (Ibn Sina) discussed philosophy of science and described an early scientific method of inquiry.

Probably mathematics became a science only after Thales, but it relied on the axiomatic method rather than the scientific method. Modern attempts to use formalism instead of the axiomatic method for the foundations of mathematics failed spectacularly. In a certain sense, mathematics is still one of the foundations of the scientific method. (Would there be circularity issues, if mathematics relied on the scientific method?)

The story for medicine is completely different from the story for mathematics. Its knowledge is never solid enough, and it has to constantly fight with many different distortions of its knowledge. There are quacksalver intentionally making false claims, economic constraints, and expectations by patients and society. The application of the scientific method is difficult due to measurement problems similar to those in quantum mechanics. The placebo effect is a well known example of this, but it is only the tip of the iceberg. Medicine has developed methods like blind studies and randomized controlled trials that go beyond the initial scientific method to mitigate these issues. It also actively seeks the help of other sciences, so that there are no reasons to doubt that medicine is indeed a science and has always been. But the Hippocratic oath might be more relevant for the foundations of medicine than the scientific method.

  • You still have not adequately supported the claim that medicine and mathematics are actually sciences, as opposed to having a scientific subset (e.g. clinical research). That Thales rejected supernatural explanations for natural phenomena says almost nothing about whether he treated geometry fundamentally differently from those who came before him. (Granted, there is precious little work remaining from earlier geometers.) – Rex Kerr Dec 19 '11 at 14:43
  • @RexKerr The fact that medicine and mathematics aren't considered as sciences in english speaking countries might actually explain my confusion that lead to this question in the first place. The statement "All sciences use the same fundamental approach - the scientific method" is from an answer by stoicfury. It confused me, but I noticed that it seemed to be an obvious truth for him. This "answer" was the initial question (before I reformulated it more abstractly), so that it would be clear why the statement seems questionable to me. – Thomas Klimpel Dec 19 '11 at 17:09
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Whereas mathematics proceeds by deductive inference, science characteristically proceeds by inference to the best explanation. The particular kind of inference that characterizes a truth-seeking pursuit is why a distinction between math and science is important.

If two explanatia for the same explanandum are equally probable then, by virtue of lex parsimoniae, the less ontologically superfluous of the two is the better explanation. An example can help to illustrate how science differs from math in that it infers to the best explanation rather than deduces.

Lightning is more/less likely in places with higher/lower atmospheric convection than others yet, regardless of whether or not Zeus makes any lightning at all, it is most likely that there is lightning today if Zeus makes lightning whenever he is mad and if Zeus is mad today. Yet, it is implausible that "Zeus makes lightning whenever he is mad and he is mad today" truly explains that there is lightning today, because it is highly improbable that Zeus is mad today (regardless of how likely it would be that that there is lightning today if Zeus makes lightning whenever he is mad and if he is mad today).

A no less plausible explanation for the lightning today (than an argumentum ad Jove) is that today's lightning was the making of unintelligent natural phenomena, which is plausible because it probably is a fact due to it being true a posteriori on many prior known occasions (whereas "Zeus makes lightning whenever he is mad and he is mad today" is not and has never been known a posteriori).

Moreover, "unintelligent natural phenomena" makes for a better explanation than an argumentum ad Jove because, by virtue of Ockham's Razor, although Zeus might make lightning daily by increasing atmospheric convection daily, to include Zeus in an explanation (of how a natural phenomena caused the lightning today) is unnecessary to explain, sufficiently, today's lightning, which necessarily requires some mention of natural phenomena but does not necessarily require any mention of Zeus. It would be excessive to appeal to Zeus; argumentum ad Jove is not as ontologically parsimonious.

On the topic of the social sciences, I think it's a mistake to think that the social sciences, in general, employ methodology inferior to that employed in natural sciences. Evolutionary biology, historically, has borrowed heavily from economics. "The ultimate subject matter of biology and economics is one, viz., the life process" (Daly 1968).

Toward the end of the Enlightenment-era, economics began to find a place for itself in the life sciences. Carolus Linnaeus described all life as an 'economy of nature' (Linnæo 1749) and Erasmus Darwin had written of an 'economy of vegetation' (E. Darwin 1791). Post-Enlightenment, the Linnaean imagery was adopted by Charles Robert Darwin, a grandson of Erasmus Darwin, who went so far as to employ the Malthusian population principle from classical political economics (see Malthus 1798) as the architecture for designing his theory of natural selection (see C. Darwin 1860). "Darwin has interested us in the history of nature's technology, i.e., in the formation of the organs [that] serve as instruments of production for sustaining life" (Marx 1887). Ronald A. Fisher, a protégé of political economist Leonard Darwin (who was a son of Charles R. Darwin), unified the Darwinian bioevolutionary theory of natural selection with the Mendelian genetics and, in doing so, he had employed a plethora economics concepts (see Fisher 1930). Fisher even considered the inheriting of household wealth by offspring from their parents to be an extension of a more generalized inheritance process stemming from the inheriting of genes by the offspring from the parents, which is a notion that foreshadowed the Dawkinsian theory of the extended phenotype (see Dawkins 1978). "In organisms of all kinds the young are launched upon their careers endowed with a certain amount of biological capital derived from their parents" (Fisher 1930). The adoption of economics by the life scientists had an influence on economists as well. The application of economics to the life sciences, in turn, resulted in a strong influence from the life sciences on economic theory (e.g. evolutionary and behavioral economics). In fact, Alfred Marshall considered economics to be "biology broadly interpreted" (Marshall 1922). With the influx of physics into the life sciences, recently culminating with the noteworthy work by Jeremy England (2013), it is only reasonable that the torch of progress in economic thought now has been passed on to econophysics.

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