In the vein of verificationism and related to problems of falsifiability as per Karl Popper, I ask the following:

Let's say hypothesis X is proposed in order to account for a certain set of observable facts. Let's say that if X is true, then lots of logical implications can be derived from X. However, if only a very tiny fraction (say, 0.1 %) of those logical implications can be empirically tested, can X be regarded a scientific hypothesis? What if only 1% of its logical implications can be empirically tested? What about only 5%? What is the threshold that discriminates between unscientific and scientific hypotheses?

Is there a misapplication of reason in my question in regards to various methods of scientific theory generally, and if so, what is it?

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    Percentage of the number of implications it not very meaningful, it depends on how one counts what is a distinct implication, and the vast majority of them are trivial by any count, so the percentage of testable implications will always be tiny. General relativity initially did not have many confirmations, only perihelion of Mercury and deflection of light. What matters more to the scientific status is how theory stands up to expansion of testing over time and integration with other established theories. – Conifold Oct 28 '20 at 3:31
  • There are attempts at measuring the "closeness to the truth", through the degree of truthlikeness, or verisimilitude – Mauro ALLEGRANZA Oct 28 '20 at 8:03
  • @Conifold - for instance, is the multiverse hypothesis scientific? – Spirit Realm Investigator Oct 28 '20 at 8:16
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    Sure, as a hypothesis, but its scientific prospects are dim unless there is evidence of non-linear corrections to standard QM that would allow interaction across decohered branches. – Conifold Oct 28 '20 at 13:05
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    Abiogenesis is plainly testable: the ultimate confirmation would be producing a living organism from non-living organic matter. It hasn't been done yet, but at least there is no theoretical prohibition on testability as in the case of the multiverse (causal isolation of decohered branches). The obstacles are merely pragmatic, requisite conditions are hard to reproduce and the supposed process requires a long time to conclude. – Conifold Oct 29 '20 at 20:17

When an academic researcher works on a scientific theory, they will do formal experimentation that is (effectively) proof of concept. They don't need to do much: an example or two that shows the theory works in principle is usually more than sufficient for the academic community.

The real tests of a theory occur outside academia in pragmatic, technological uses. People apply the theory to make things happen, and each successful application increases our confidence in the theory. For instance, Einstein's theory of relativity may only have been tested formally a few times, with difficult and esoteric research. But pragmatically, technology like GPS systems are improved by accounting for relativity, so every time we use a mapping application on our smart phone we are implicitly confirming that Einstein's theory is correct.

Further, researchers often find the grounds for revising or replacing theories when they try to do practical things and find the theory fails them. E.g.:

  • Someone wants to make a better widget
  • 'widget theory' says that tweaking the widget just so should make it better
  • tweaking the widget just so actually makes the widget worse

That problem will send academics go back to the drawing board to figure out what's wrong with 'widget theory' and how it can be improved.

The upshot is that the meat of a theory's credibility comes from day-to-day usage in technology more than academic research. We don't need a scientist in a lab coat to tell us that the wheel makes moving loads easier. We might need a scientist to figure out the wheel in the first place, and scientists might tease out non-obvious properties of a wheel (like the gyroscope effect), but anyone that has to move a load of bricks knows just how useful wheels are.

  • But, from a philosophical perspective, it doesn't matter whether it's done in an official human institution called "academia" or in any other social environment, right? If a given human activity has a component that consists of testing hypotheses following the "scientific method", then that component is still science, not technology. – Qfwfq Nov 17 '20 at 0:50

If even a single one of the implications of a theory is empirically testable, then the theory is scientific. Testing that one implication would amount to doing a scientific experiment.

That being said, the word "empirically testable" means that there must be another theory that predicts a different outcome for that experiment. Then doing the experiment is the scientific way of distinguishing between the two theories. If you don't come up with other theories that make contradictory predictions, then you have no way of knowing whether your experiment is useful.

Once you have empirically determined one theory to be better than the other, then all the implications of the preferred theory are more sound than those of the other theory (at least where the implications differ). This doesn't rule out other theories that agree with that one implication, but differ in others. Identifying those theories and doing further experiments is what keeps scientists in business.

This was a big issue for Quantum theory and Einstein's theories of relativity. Some of the implications of those theories were testable, while many others were not (at least not with the technology of the time). The ones that were testable were tested and the theories were given credence, despite having many other as-yet untestable implications. People today are still finding new implications of Einstein's theories that had not yet been tested and testing them.

  • "empirically testable means that there must be another theory that predicts a different outcome for that experiment" - In an experiment you don't test theories: you test individual propositions. In principle, you always have a different outcome at your disposal: it's the negation of the proposition. E.g. "temperature will be in interval [T-ε,T+ε]" vs "temperature will be outside of interval [T-ε,T+ε]". – Qfwfq Nov 17 '20 at 0:59

Popper is an excellent starting point for understanding what is or isn't science. His falsifiability criteria is basically a precondition, but even more important is that the practitioners of science need to have an attitude embracing falsifiability -- IE look for and accept falsifications of one's views.

For example, two relevant cases are Creationism and Intelligent Design. Both are testable claims about our world. Creationism is pretty easily refuted by the observed evolution of life, plus the timelines observable in geology and astronomy. Intelligent design makes testable predictions about design stability and commonality, and optimality, which also are refuted when one examines details of structures and evolution, and the part of randomness in life. What makes these NOT scientific hypotheses, is that their advocates do not embrace the scientific methodology in evaluating them.

You ask about quantifying degrees of predictive power -- Popper attempted to do this, over decades, but his effort to quantify either predictability or confidence through numerical processes failed. The alternative is a judgement call, as to whether a community is applying the scientific attitude to their research programme. The best explication of this process is from Imre Lakatos, summarized here: http://people.loyno.edu/~folse/Lakatos.html Lakatos too tried to quantify his criteria of progressive/regressive, but that quantification also was flawed. As with much in the world, we must rely upon a consensus of reasonable observers to judge the boundary of science/non-science.

You also asked questions about two areas of current scientific inquiry -- abiogenesis, and a multiverse. These two subjects reveal yet more about what is or isn't science.

Abiogenesis is clearly a scientific hypothesis, and it has been a scientific field of study for ~80 years. The hypothesis makes a number of predictions -- including that our world's history should have been fertile for chance processes to produce life, and that the chemical path to life is possible. The first of these predictions was dramatically confirmed in the Urey-Miller experiment. The second -- has a much rockier history. Most of the Abiogenesis research since Urey Miller has been discoveries of just how difficult that chemical pathway IS. Chirality, and poisoning with closely related compounds, basically prevent any build-up of proteins or RNA in natural processes. And for RNA in particular, the UV light that is needed to create one building block also destroys the growing strand. Plus lipid membranes are lethal to a developing metabolism inside, unless they are semi-permeable -- and basic lipid membranes are not semi-permeable. The best book I have seen on this is Dyson's Origins of Life. Dyson considers the RNA path too complex, and lipids too problematic to start, so hypothesizes that proteins metabolism in free environments evolved first, then was lipid-captured, then taken over by a basically parasitic RNA. This strikes me as an almost equally implausible sequence to RNA first.

Note the response of Abiogenesis community is to narrow over and over the environments that Abiogenesis can happen in. The RNA precursors need UV, but RNA cannot have any, but SOME energy source is needed to fuel the strand build-up, hence a deep undersea vent is proposed (the precursor can be formed on the surface, then fall to the vent). But to overcome chirality, a clay banks which bonds the proteins and RNA in only one direction is proposed. This is now a TINY FRACTION of the massive pool of oceans that Urey-Miller suggested were available --- the number of monkeys at typewriters is reduced by something like 10^10 or worse. This raises a throughput question for abiogenesis -- is there sufficient mass of reaction events, and time for life to have abiogenesised in the time it appears to have? Note that fully formed stromatiolite mats are found in rocks from 4.4 billion years ago -- IE multicellular colonies appeared within 300 million years of the oceans cooling.

When one looks at the logic of life complexity -- a single bacteria cells is about half as complex as an elephant. Evolution SINCE 4.4 billion years ago took 4.4 billion years to get to elephant-level of complexity from half that level. That the first half of the complexity development took place is 1/15th the time of the 2nd half -- despite the 2nd half basically having the entire biomass to work with, while the first half only had 1/10^10 of that biomass (the clay surfaces around the vents) -- basically abiogenesis research since Urey-Miller has accumulated a case that Abiogenesis is increasingly improbable.

When I have discussed this with materialists, they typically say that there is no other alternative, hence they have faith that abiogenesis will get there eventually. There are two other alternatives -- panspermia, and non-material causes. Panspermia has the same logic issues, but by putting it in TBD environments, it may not have the timeline constraints or volume constraints that Earthly abiogenesis has. Non-material causes can include an "organizing principle for the universe" which some materialists such as Christian De Duve and Stuart Kauffman hypothesize. Or it could be a spiritual intervention. The REJECTON out of hand of these sorts of alternatives, when Abiogenesis seems to be a regressive research programme, arguably is making the abiogenesis community increasingly iffy on being "scientific". It is held to as an article of faith among materialists.

Multiverse is a similar area of concern for materialism and science. The multiverse used to be rejected out of hand, as untestable speculative piffle. THEN -- the realization took hold in the cosmology community that our universe is remarkably unlikely -- that it appears to be Fine Tuned for life. The probability calculations that one derives form the Standard Model suggest that there are multiple free variables (about 30) in our physics that can only support life within fractions of their range between 1/10^2 to 1/10^30. This is supporting evidence for our universe being a product of deliberate creation (note Creationism IS potentially a science hypothesis, depending on how one handles it). It is not GOOD evidence for intelligent/theistic creation, as our universe is poorly optimized for life, but still, it is somewhat related to what ID would predict. Non-theist Cosmologists cast about for some way to explain "apparent fine tuning", and realized that a very large Mutiverse would do the trick. An excellent discussion of this process is in Susskind's The Cosmic Landscape. I have a review here: https://www.amazon.com/gp/customer-reviews/R3JVQDAK1408BR/ref=cm_cr_getr_d_rvw_ttl?ie=UTF8&ASIN=0316013331

Most of Susskind's Cosmic Landscape is untestable in principle, which makes it highly relevant to your question. But it is not entirely untestable, as it has failed two tests, as noted in my review, which required kluges to fix. It also has NOT proven to be productive/useful for experimentalists, which is the basis for Smolin's critique. Sting/theory/multiverse/cosmic landscape therefore appears to be a regressive research programme, which once more materialists are holding on to, as there is no other better alternative which is compatible with materialism.

What you have hit upon, and seems to be a motivation for many of your questions on science, is that there IS a faith-view involved behind many scientists thinking.
That view is materialism. Materialism is generally not treated as a science hypothesis. If it were, then the Hard Problem of Consciousness, and the nature of both information and abstract objects, would constitute refuting test cases, while much of quantum mechanics would bring the coherence of the hypothesis into question. That faith-based assumption of materialism skews the reasoned response of many scientists to a variety of science fields, including both cosmology and abiogenesis.

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    Probability is meaningless if something already has happened. There, it suffices to show that there is one possible path. No matter how unlikely it may have been to come to pass, it obviously did since here we are, alive and kicking. This does not involve faith, but mere empirical experience. Your whole strand of argument is ideological, misinterprets probability, and does not have any positive base in empirical experience. The latter is the definition of faith. – Philip Klöcking Nov 12 '20 at 8:31
  • @PhilipKlöcking -- if you consider probability meaningless relative to something which appears to have happened, you would quickly be fired with cause from any failure investigation. More generally, as theory is underdetermined by facts, probability is the only method we have to sort between any science explanations. If you consider science, and explanations of events meaningless -- that is I suppose your prerogative, but it is not a perspective that most people consider useful or relevant. If you consider it important to offer to the questioner, I suggest you post a separate answer. – Dcleve Nov 12 '20 at 9:24
  • Probability is useful and at the centre of scientific inquiry when a hypothesis is tested with regards to future events, i.e. their predictive value, with either not rejecting the null hypothesis or rejecting it with (1-alpha) certainty. Using it as an "explanation" for past events, it is no scientific use of the term, it is a mere rhetorical means. But either way, hypotheses that are not testable are unscientific, hypotheses that are testable and built upon (reconcilable with) empirical data are guesswork until tested. Faith, by definition, lacks empirical data as a base. – Philip Klöcking Nov 12 '20 at 9:34
  • @PhilipKlöcking -- one cannot evaluate evidence, reach conclusions about experimental results, nor make the predictions you cite, unless one applies probability to explanations of past events. This is extremely obvious to anyone who has ever written a lab report, or even done any data analysis. And as I noted, it is the central activity in every failure investigation. While your assertions appear to be simply wrong to anyone who has done science, they also appear to be unrelated to the answer I posted. Is there a point to this tangent? – Dcleve Nov 12 '20 at 9:50
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    First off, this is statistics basics. (Probability) distributions are and should be used, but this is a very different beast from the probability of a given single event that as a matter of fact happened. This is relevant because your post is built on the fallacious arguments "the event is improbable so it lacks proper empirical base" and "faith-based beliefs are (roughly) equally probable and thus no less scientific" which in turn leads to the equally fallacious argument that "it all comes down to faith". But abiogenesis is reconcilable with empirical method, creationism not. – Philip Klöcking Nov 12 '20 at 10:23

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