6

If we make predictions with a new theory, but cannot verify its internal mechanisms and causal processes, but find that the predictions turn out to be accurate every single time, is this enough evidence for the theory? Let's assume that the predictions being correct by chance/the null hypothesis are possible but just extremely improbable otherwise.

9
  • 4
    There is no "just from", "internal mechanisms and causal processes" are part of what the theory predicts. If they are untestable that puts a question mark over the theory even if its other predictions are successful. For example, Bohmian mechanics postulates "Bohmian particles" to explain quantum effects by classical mechanisms. Its observable predictions are equivalent to those of quantum mechanics, so "accurate every single time". But since nobody observed "internal mechanisms" with "Bohmian particles" it is not "proven". The same criticism is made of multiverse and string theories.
    – Conifold
    Jun 15, 2023 at 0:21
  • There's a very-well known 3.5 century-old "theory" that says yes to the OP's yes-no question.
    – Hudjefa
    Jun 15, 2023 at 1:57
  • 3
    Usually, a new theory will be considered a "better alternative" wrt a previous one when it explains all known facts already explained by the previous theory AND explain some "puzzling" known facts (facts that the previous theory does not explain) AND predicts some unknown facts. Contra: string theory. Jun 15, 2023 at 5:35
  • 3
    "Can a new theory be proven...". No theories are ever proven, since they can always be replaced by better theories. Having said that, well-substantiated theories are colloquially "proven". Also, "wrong" theories can still be right: hermiene.net/essays-trans/relativity_of_wrong.html
    – RonJohn
    Jun 15, 2023 at 8:28
  • 1
    @AgentSmith Newton's Laws? If not, then what are you referring to? If so, then, as mentioned they are Laws, not theories. What's the difference? Laws are "just math that works", but provide no explanation.
    – RonJohn
    Jun 17, 2023 at 18:07

4 Answers 4

6

The ideal standard against which all induction can be evaluated is Solomonoff's theory of inductive inference. This is Bayesian inference with a minimum description length prior.

In Solomonoff's theory, we are first given some observations. We suppose that the observations were generated by some computer program, but we want to know which program generated them.

To do this, we start with a prior distribution over all computer programs, that weights a program exponentially less likely, the longer the program happens to be. Then we rule out the computer programs that do not exactly match all the observations. The posterior distribution assigns nonzero probability to the remaining computer programs (the ones that do exactly match all the observations), with posterior probability exponentially decreasing with program length. This means the shortest program that exactly matches all the data will be assigned the highest probability.

Back to your question. If your theory is accurate every single time, is that enough to prove it?

  • No. It must also be short and simple, without shorter competing theories. If there is a shorter theory that is also accurate every single time, the shorter theory will be more likely.
  • It also depends on how many observations you test it against. You can never really know when you've done enough testing, although you may decide to stop when the posterior probability of the theory is high enough, such as greater than 95%.
  • In practice, it also depends on whether you are testing it against new observations or only fitting it to old data. That a model fits old data is weaker evidence than that the model predicts new data. This is because we imperfect humans use the fact that a model "came to our attention" as a proxy for the model having a high prior probability. This proxy is much closer to the truth if the model came to our attention before having seen the data the model is supposed to predict.
3
  • "It must also be short and simple". Do you consider QED "short and simple"? Jun 15, 2023 at 8:20
  • 8
    @MauroALLEGRANZA Name me a shorter, simpler theory than QED that makes exactly the same predictions as QED. You can't. (Or if you could, there's a Nobel prize in your future!) So, yeah, QED is short and simple compared to known competing theories.
    – causative
    Jun 15, 2023 at 10:59
  • Yes. just to note that if a theory is more complex but makes precisely the same predictions, that does not make it wrong as such, but it does make it less explanatory because it has a higher Kolmogorov complexity than the other. It is a better theory because it explains more facts with a smaller theory (or the same facts with a smaller theory, or more facts with the same amount of theory).
    – Ben
    Jun 15, 2023 at 16:30
5

It depends on what you what the theory to do.

Generally scientific theories aren't accepted just because of their predictive power, but for their explanatory power too. This is actually a very complicated question with a lot of disagreements among philosophers of science.

Consider, for example, you went to pre-Newtonian England and said something like "there are these dragons at the center of all planets and stars that pull everything closer to them at rate proportional to this equation : GM/r^2" You would be able to correctly predict the orbits of planets and so forth, but you would also draw some substantial criticism and probably would be ultimately rejected.

So predictive power is not just the sole justification for a theory, it needs to fit in with existing scientific understanding at some level, at least in theory.

Obviously there is a caveat to the need to fit in with existing understanding, (demonstrated by the advent of relativity and QM). It is important to note that the issue isn't entirely to do with QM and relativity being unintuitive or something like that; for example, Newtonian mechanics is a good theory to use when you are calculating the motion of 2 balls or something simple like that, but suppose now you are trying to calculate the motion of an air molecule with the same approach, it would be borderline impossible. Fluid mechanics is a much better theory to use when calculating something like this, does that mean Newton was wrong? Obviously not, because Newtonian mechanics works fine at the appropriate scale.

Here are some papers which explain the issue and give some solutions that you might be interested in :

https://repository.brynmawr.edu/cgi/viewcontent.cgi?article=1016&context=philosophy_pubs

http://www.strevens.org/research/expln/Idealization.pdf

12
  • 2
    Continuing with the history of astronomy, Kepler's ad-hoc phenomenological laws were good predictors, and continued to hold up with the discovery of the outer planets (though by then Newton had explained why the laws work.) They are not completely precise, however, and Newton's theory could account for most of the error as gravitational interactions between the planets - but not Mercury's precession...
    – A Raybould
    Jun 15, 2023 at 2:32
  • 1
    Still in astronomy: the Ptolemaic system with it's epicycles was pretty accurate, but Kepler "won" back then because of Occam's Razor.
    – RonJohn
    Jun 15, 2023 at 8:39
  • 2
    @MauroALLEGRANZA Pretty much every scientist ever uses Occam's Razor all the time (whether they call it by that name or not). There's an entire section on Wikipedia on the topic, which even includes a quote by Einstein expressing the same sentiment. You're going to have a hard time building a coherent and sensible model of reality when you add a bunch of unnecessary claims to your explanations.
    – NotThatGuy
    Jun 15, 2023 at 9:24
  • 2
    @MauroALLEGRANZA the Ptolemaic system wasn't just circles. It was circles circling circles circling other circles that were circling circles. Epicycles were very, very complicated. Three simple laws using area and ellipses made things stupendously simpler than epicycles.
    – RonJohn
    Jun 15, 2023 at 11:49
  • 1
    @NotThatGuy The point of mentioning dragons is that we prefer theories that explain why something happens. Darwin's theory of evolution and Mendel's discovery of dominant and recessive traits are nice, but we didn't feel fully satisfied until the mechanism of DNA was discovered to explain it.
    – Barmar
    Jun 15, 2023 at 13:46
3

There is a very simple argument that should convince you that the answer should be no. Suppose you have two or more mutually incompatible theories that make the same accurate predictions- they cannot all be true, so the predictions alone must therefore be insufficient to determine the correctness of any individual theory.

3
  • Hi. Thank you for this answer. Would you please consider expanding on the meanings of "incompatible" and "true"? In particular, how does your argument apply to the two theories "light is a wave" and "light is a particle" - are these two theories incompatible? Is any of them not true? I've actually never had a notion of what "true" could mean for a theory, other than "it predicts stuff correctly"
    – Stef
    Jun 15, 2023 at 15:53
  • @Stef by incompatible I mean that they make conflicting claims about the causes of the results. By true, I mean that their claims about the nature of the causes have been verified in some way. For example, there are conflicting interpretations of quantum mechanics which we can't currently decide between experimentally, but they can't all be right. I will comment separately, when I get more time, about the nature of light, as that question does not have such a simple answer. Jun 15, 2023 at 16:17
  • @Stef Ptolemy's geocentric epicycles and Kelplerian heliocentrism both made accurate (for the era) predictions of planet's orbits. They were, though, mutually exclusive.
    – RonJohn
    Jun 16, 2023 at 5:26
1

I think this question comes from a slight misconception about what constitutes a "theory", and what it means to "prove" it.

A theory's usefulness is in its ability to predict things about the world. A new theory is generally tested by seeing what it predicts about some scenario and finding a place where its predictions differ from some other theory, and then finding a way to observe what happens in reality to compare how well it matches up to the predictions. If observation differs from prediction, the theory is clearly wrong somehow.

If a new theory matches all observed behaviours exactly as well as an existing theory, its only merit is if it can shed new light on the possible causes or mechanisms that give rise to those observed behaviours.

If you have two possible mechanisms that could cause an observed behaviour, by definition you can't declare either to be correct, because the existence of an alternative explanation casts doubt. Whether that is a reasonable doubt depends on how reasonable each theory is, at which point we turn to things like Occam's Razor to decide whether theory A is more probable than theory B - but we can't say that either is "proven".

If your new theory makes accurate prediction about observations that we previously had no theory to explain, then that certainly lends credence to it, but we have to look at what it says about the causes. If your proposed explanation is provably the only thing in existence that could possibly be causing the observed behaviour, then yes, we can probably call that proof, but that's unlikely.

Far more likely is that your theory has two separate parts: a set of rules and logic that predicts the behaviours, and a set of unverifiable speculation about the causes and mechanisms. In this case, we can generally come up with some other set of unverifiable speculations to replace yours with, at which point we're back to the previous paragraph. If the speculative parts can be trimmed out of the theory with no loss of predictive power, then it's less a theory and more a description of observed behaviours. Look at Kepler's laws of planetary motion, which describe with reasonable accuracy the observed behaviour of celestial bodies, but say absolutely nothing about why celestial bodies behave that way.

At this point, "proof" means something slightly different, if it means anything at all - it's perhaps more accurate to say that you can "demonstrate your theory's accuracy" rather than that you can "prove" it.

That's not to say that there's no merit to that speculation. It might be that you were examining a particular field of science and realised that you could use it to construct an explanation for some phenomenon, and even though you couldn't verify the inner workings, you could still see some related effects to provide some evidence for it.

A lot of scientific discoveries started out with someone speculating that some process might be the cause of a phenomenon, and the scientific community spending years (or decades, or longer) coming up with some way to test the previously untestable and finally verify those internal mechanisms. We have theories about what might be happening inside a planet's core, or in the centre of stars, or in the instant of a supernova, but observing those things directly is very difficult so we can't verify with complete certainty that our theories are correct. At this point Occam's Razor comes back into play, or else we get into Bayesian epistemology and a really thorny discussion on what it means to "prove" something, or even to "know" something.

You must log in to answer this question.