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I'm intrigued by the conventional portrayal of the scientific method involving binary testing of hypotheses: accepted or rejected. Is this binary framework an inherent part of scientific inquiry, or are there alternative approaches? I'm curious to learn about instances where hypotheses are assessed on a more nuanced scale and how this diversity contributes to scientific knowledge. Are there specific disciplines or theories that deviate from the binary norm, and what are the implications? Looking for insights, examples, and references that highlight the spectrum of hypothesis testing methodologies within the scientific community.

Basically my question: is (scientifically) acquiring knowledge fundamentally based on the binary testing of hypotheses?

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  • I would like to put forth the idea that any attempt at distilling science into a single simple thing is always going to fall short. There isn't one single scientific method, there are many methods. There are many scientific journals and ways for scientists to interact both with the scientific community, and with educational systems, and with the public. There is not one single thing science is or does.
    – TKoL
    Dec 11, 2023 at 16:37

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I mean the progression by testing of hypothesis is the major part of how science develops knowledge or whatever else it produces, but this neat binary model of accepting and rejecting is a lot more complicated in real life.

Like first of all you cannot really "accept" in the sense of knowing that you are correct, so it's usually much easier to distinguish between "incorrect" and not "incorrect yet".

Also proving that something is indeed incorrect is also not as easy as it sounds because ALL our measurements come with a margin of error and so it's not really a neat binary of right and wrong and more of a "likely" and "less likely".

Also the more complex the experiments and theories the more likely you could have just made a mistake, had a calculation error, used faulty equipment, had someone interfere with the experiment and whatnot. As any experimentalist will tell you it might take a lot more than one try to get things working. So if the theory says it can work people might tinker way longer to make it work before they reject the theory than just treat it as a binary.

Also even if data emerges that shows that the theory is giving the wrong predictions, there might still be time frame where the old theory is patched rather than discarded. Idk where it's range of application is reduced or where it's taken as a special case of a more general theory and so on. So failure might not lead to outright rejection if there is no competing theory to replace it.

I forgot the specifics but afaik there are also cases where Occam's razor kinda decided what theory to prefer, in that one model was easy an successful and so it became the theory, while it was later found out that the other model would have also worked just fine. So it's possible that a theory falls out of favor not because it's wrong but because it's shelved because another theory is easier to handle.

And last but not least while the pure theory doesn't always treat that as relevant, in practical application science is also a social discipline. So regardless of the scientific merit, what is being studied and advanced is not decided by a) those who provides the grants for people to dedicate their time to a problem and b) by what the next generation of students finds interesting enough to dedicate their time towards. So sometimes "the hype" can also decide what becomes the theory.

Now regardless of all these problems and distractions the ideal is still the scientific method and if it doesn't work it will sooner or later result in the theory falling out of favor, but in the practical reality, things are a lot more fuzzy and complicated.

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At heart is the notion of "conventional portrayal". The scientific method, as a monolithic and generalized epistemological strategy is an oversimplification of how science is practiced, but science is a complex psychological and sociological process and there are a number of characterizations of it that are quite valid but often not recognized by Latour, Feyerabend, Kuhn, and others who are often left out of the conventional portrayal.

You ask:

Basically my question: is (scientifically) acquiring knowledge fundamentally based on the binary testing of hypotheses?

The answer to that is no. The basic acquisition of knowledge is based on experience which is a complicated affair to even describe. Ryle in his The Concept of Mind talks about knowledge-how and knowledge-that. I would say that the preponderance of knowledge is fundamentally of the sort called knowledge-how. We learn how to speak, not the rules of grammar, as children. We learn how to do our jobs, indeed, with the aid of language, but usually not the myriad theories that explain our jobs. (Think of an automechanic who has never studied calculus based thermodynamics.) And where we do acquire knowledge-that, we are often unaware of the metaphysical basis of our craft.

Most practicing scientists have little to no engagement in the philosophy of science, just as most practicing mathematicians have little to no engagement in the philosophy of mathematics. And practicing scientists and others, who do engage in empirical design and implementation, sometimes try to answer questions in the yay-or-nay fashion, more often than not are looking for any form of language that will give insight and serve as an explanatory basis for the phenomena they study. Let's consider an example.

Charles Darwin and Alfred Rusel Wallace were preoccupied with the origin of species. But neither man set themselves up to say, either my theory is correct or my theory is incorrect. Consequently, the theories advanced were complex and descriptive, with Darwin publishing On the Origin of Species which ranged over quite a diverse array of contexts with all the complexity of full discourse in language. The acceptance of evolution is not based on a single A/B test, but rather consisted of a complex series of arguments each of which was based in part on descriptive science.

The theory of evolution is not preserved or rejected based on one or more binary experimental tests. Rather, it happened that a great deal of analysis and testing of all sorts ultimately supports, modifies, and extends the thesis. Thus, evolution is a strong theory because it integrates the various subdisciplines of biology, conjoins nicely with genetic theory and practice, manifests a high degree of consistent and rational claims, carries with it rhetorical force, and supports methodological naturalism, an important aspect in scientific methods.

Scientific theory is the forging of robust language that requires all manner of sophisticated activity and varies from science to science. Scientific theories are complicated epistemological processes that appeal to prior science, rhetorical strategies, to methodologies of rationalism and mathematics, that presume metaphysical theories, and that engage with a diverse set of experimental methods. Science is so varied and complex, it raises the demarcation problem, and yesterday's crackpot theory might become tomorrow's science, or today's science becomes tomorrow's pseudoscience.

As such, science does not proceed merely by a string of formulaic scientific experiments and directly arrive at truth (whatever that may be).

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  • The knowledge -how vs -that is a good one. When teaching computer programming I want to impart the theory, which would allow learners to then generalize and use any language or system. But I got a lot of pushback from other educators in another forum (ahem) and I didn't understand why. I also realize that reducing Database Normalization to 4 sentences is probably too terse. (But it's all there! So simple!)
    – Scott Rowe
    Dec 9, 2023 at 15:48
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    @ScottRowe When I took an advanced DB class, they had us actually doing relational algebra, which I found to be fun. My classmates thought it was wholly irrelevant! :D
    – J D
    Dec 9, 2023 at 16:02
  • When you said that the answer to if binary testing is the only way of scientifically acquiring knowledge is no, I wonder if you answered 'acquiring knowledge' in general or specifically scientifically. Since the scientific method destillated is basically binary testing of hypotheses right? Dec 10, 2023 at 7:46
  • @bananenheld The scientific method, mijn vriend, is not the traversal of a binary tree, no. Most tests are not simple yes/no questions. Scientific theories are complex linguistic artifacts, and therefore, science proceeds by modeling the universe in language and as the language is modified, a little here, a little there, theories go stronger. There is not scientific-method by pregnancy test.
    – J D
    Dec 10, 2023 at 15:40
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  1. I agree that testing is a fundamental part of the scientific method.

    A famous example in history of science is Bell’s theorem. Bell developed a criterion to decide by experiments on the quantum scale between a local theory with hidden variables and quantum theory, a theory without.

    A certain quantity S should always lie between -2 and +2 for local hidden variable theories. Quantum theory, however, predicts that S should be greater than 2.

    Four corresponding experiments were performed in the 1970s. Three of them testified against local hidden variable theories, and in agreement with quantum theory. The fourth experiment did precisely the opposite, testifying against quantum theory and supporting local hidden variable theories, see Andrew Whitaker: Einstein, Bohr and the Quantum Dilemma. First edition 1996, Ch. 7 Experimental philosophy.

    I do not know the current state, possibly the 2. edition of the book from 2006 has an update.

  2. But before one can make the experimental test one needs the theories which can be put to test. Hence the first step is to develop a scientific theory. In general, this step is the more fundamental and the more challenging one.

    In the case under question this step is to develop quantum mechanics and the experimental apparatus to make observation on the quantum level.

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  • You have a theory, this leads to a hypothesis. Then you do experiments to check if that hypothesis can be falsified. If it can't, then you can say it is not false. That is all right? Dec 9, 2023 at 20:26
  • @bananenheld My sequence is similar: There is an open scientific question, you develop a theory, which has the status of a hypothesis. You do experiments which confirm or refute the hypothesis. In case the hypothesis is refuted you improve your theory and repeat the whole loop: "We err upwards." (Gerhart Vollmer)
    – Jo Wehler
    Dec 9, 2023 at 20:37
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  1. As said in other answers, an experiment can easily prove a theory wrong, but it can't prove a theory right.

All you can do is proving the compatibility of the experiment with the proposed theory. The acceptance of a new theory is a slow social process building slowly with the accumulation of non-contradictory experiments. A famous exemple is Einstein relativity theory who rejected the newtonian approach of time and space that everyone took for granted for centuries. Acceptance of Einstein's views took decades.

Actually, science is a corpus of knowledge that is designed to tackle the complexity of the world by simplifying it with the help of concepts and rules according to a context and set of objectives.

Newtonian Mechanics is adequate to describe most of macroscopic events in our human environment, inadequate for some rare examples (stars behind the sun are visible through the impact of gravity on light) and totally inadequate at the atomic level.

So at the core, you do deal more often in science with the definition of the scope of the validity of the theory, than with a binary acceptance. (specifically true in economy)

  1. Apart from that, science is not reducible to experimentations. You combine facts from experimentations and the use of logic to build on the laws you have established earlier. Which brings in the question of the actionability of logic.

First, we have to mention, the debate about the principle of excluded middle, that was vibrant in the beginning of the XXth century. Can we say that given a logical proposition, we either have it true or not true ?

For example what about the situation: Epimenide said he was lying. Is Epimenide word true or not true?

Or

"If you take out a grain of sand from a heap, it's still a heap"

Some very talented mathematicians, called 'intuitionnists", stood to the ground that something is not true until you have made an explicit demonstration of it (which excludes the demonstration of falsehood of the negation)

This led to much thinking of what is a valid proposition, what is a demonstration, and the need to define precisely the concepts from a set of grounding principles.

But then, we can summon Gödel incompleteness theorem. (1931) This theorem states that no axiomatic theory can be complete. Or in other words, that there are "true statements" that can't be demonstrated by the use of logic on foundation premises. Differently again, that there are some truth that can't be established by the use of what most people consider being the essence of rigorous scientific approach. So basically, in simple terms, it has been demonstrated that science can't demonstrate everything.

Intrinsically, a proposition is ternary : demonstrable as true, demonstrable as false, not demonstrable.

  1. Additionally, in the 90's, the trend was to model knowledge with "fuzzy logic", with the building of so-called expert systems that would attribute a likelihood to rules, and would calculate the likelihood of deductions. It eventually failed mainly because of the complexity of maintaining the knowledge base, but also because of computational complexity.

It could be seen as the closest implementation of a nuance scale for describing the world you suggested in your question.

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