But What If You Verify a Theory That Can Only Be Verified?

In a previous post, I mentioned a partial resolution to Penrose’s challenge to Popper’s falsifiability. But in footnote 3 I mentioned that there was still a problem to resolve with Penrose’s challenge:

…let’s say you really did find a superpartner particle, thus verifying Supersymmetry and String theory by an experimental test. Why would this not be considered an ’empirical theory’ then? And why would that be a problem for regular physics (absent supersymmetry) since it makes no specific predictions that superpartners do not exist? So finding a superpartner does not ‘refute’ regular physics, it only ‘verifies’ Supersymmetry and String theory. Is this a counterexample to Popper’s epistemology?

I have asked numerous FBook Rats this question and I’ve yet to receive a satisfying answer. (One of my favorite answers was the simple declaration that ‘Supersymmetry is wrong’ as if that somehow resolved my question.) So my perception is that Popperians do not really understand how to resolve this problem using Popper’s epistemology.

This is actually a reoccurring perceived problem with Popper’s epistemology that Popper never fully addresses.

First, let’s understand why this feels like a problem to others: it is because it really feels to people like you can ‘test’ a theory that is based on an existential statement. And, in fact, you can! So they are correct in their assumption.

Consider again the theory “Bigfoot exists.” People will tend to see this as an ’empirical theory’ because you can, at least in principle, find Bigfoot. This would ‘test’ the theory. Further, it even ‘verifies’ the theory seemingly counter to Popper’s whole epistemology. So people will tend to see this as an example of how Popper is wrong about empirical theories requiring refutation rather than verification.

This problem is resolved if you realize that Popper’s epistemology isn’t really about any kind of empirical outcome but instead about forming a realistic program for how to test a theory. (As discussed in this post.) Is there really any doubt that there is no meaningful way to set up a program to test for the existence of Bigfoot that would adequately intersubjective settle the question for a community scientists? The obvious problem is that no matter how much you test, if you fail to find Bigfoot you can always claim that you just haven’t found him yet. [1]

But What if You Do Verify a Theory that is Only Verifiable?

But let’s say you did find Bigfoot–maybe just by chance. While there was no official empirical program for testing, it is at least an empirical outcome. There is now a basic statement to the effect of “Bigfoot exists at the zoo where we are keeping him.” How can this possibly not be an empirical outcome to the “verifiable only” theory of “Bigfoot exists”? Because of this, many have struggled with Popper’s insistence that theories that only assert existential statements (like “Bigfoot exists”) should be considered non-empirical.

A better real-life example of this is Penrose’s examples of supersymmetry and monopoles. These are theories that currently can’t have a program for testing because they can only be verified–a point that Popper and Penrose actually agree upon. But once you’ve actually found a superpartner or monopole, at that point it becomes a basic statement and is now an ’empirical observation’ to be contended with.

But under Popper’s epistemology, how does that change the status of the rival theories? Which in this case would be regular physics without Supersymmetry vs physics (particularly String theory) with Supersymmetry. The issue here is that regular physics doesn’t predict the absence of superpartners but String theory (at least with Supersymmetry included) does predict the existence of superpartners though only as a purely existential statement. While you can’t actually set up a program for testing supersymmetry you can at least potentially find superpartners which would then ‘confirm’ Supersymmetry’s prediction as correct. And if you did, scientists would overwhelmingly see that as ‘confirming’ the theory of Supersymmetry and would be seen as ‘support’ for String theory. Are these scientists just wrong? Are they misunderstanding the nature of science?

I’d argue that they are not wrong. I think it’s somewhat intuitively obvious that if we did at some point find a superpartner that this would be a positive testable outcome for the theory that predicted it and would ‘weaken’ the competing theory despite it never having made a prediction that superpartners do not exist.

Here we seem to have an example of a purely verifiable test with no refutation at all for the competing theory. Does this count as a refuting case for Popper’s epistemology? I suspect many would claim it is but many have told me otherwise. Further, I was unable to find an answer to this challenge within Popper’s own writings. (If someone knows where he addresses this problem, let me know.)

How Deutsch Resolves The Problem

I believe that the correct answer to this question is simply that once we have such a basic statement (i.e. we observe a superpartner) we should consider regular physics the inferior theory because it was implicitly refuted due to a lack of explanation to explain a new regularity (i.e. the existence of superpartners.) But this is, I admit, not the most satisfying answer so I don’t blame anyone for not buying it right away.

But as it turns out, this is exactly the answer Deutsch gives! Here are the relevant quotes that you probably read and missed from his Logical of Experimental Tests: (See this post here)

Refuting Theories By Their Failure to Explain: “Suppose for simplicity that two mutually inconsistent theories, D and E, are good explanations of a certain class of explicanda, including all known results of relevant experiments, with the only problematic thing about either of them being the other’s existence. Suppose also that in regard to a particular proposed experiment, E makes only the everything-possible-happens prediction (my discussion will also hold if it is a something-possible-happens prediction) for results a1 , a2 ,…, while D predicts a particular result a1 . If the experiment is performed and the result a2 is observed, then D (or more precisely, the combination of D and the background knowledge) becomes problematic, while neither E nor its combination with the same background knowledge is problematic any longer (provided that the explanation via experimental error would be bad – Section 6 below).

Logic of Experimental Tests, p. 13

Let’s stop here and put this into plain English. We have two theories, E (regular physics which makes no prediction at all about superpartners) and D (String theory with supersymmetry which does predict superpartners.) You then find a superpartner and that is now a basic statement (an intersubjectively agreed-upon observation). E is now problematic and D is not. Why?

…that is an apparent regularity in nature. Again by criterion (i) [i.e. “(i) it seems not to account for its explicanda”], E then becomes a bad explanation while D becomes the only known good explanation for all known results of experiments. That is to say, E is refuted (provided, again, that experimental error is a bad explanation). Although E has never made a false prediction, it cannot account for the new explicandum (i.e. the repeated results a1 ) that its rival D explains.” (p. 12)

Thus it is possible for an explanatory theory to be refuted by experimental results that are consistent with its predictions.

Logic of Experimental Tests, p. 13. Emphasis mine.

The existence of a superpartner that can be verified intersubjectively would ‘support’ String theory precisely because it is now a regularity that the rival theory can’t explain. Of course, the reason it ‘supports’ string theory is because regular physics’ inability to explain the regularity ‘refutes’ that theory.

Or, in other words, it is possible to implicitly refute a theory once you are in a theory-to-theory comparison with a rival. Or so Deutsch is claiming. Yet it seems to me that is the only reasonable answer here. If we did find a superpartner, scientists would be right to see that as corroboration for String theory and would consider the rival theory now problematic because it failed to explain the existence of superpartners.

In other words, even in a case where we do have a so-called ‘only verifiable’ theory (due to making only purely existential predictions), so long as it’s in a theory-to-theory comparison, it can still act as a Popperian style refutations for the competing theory. This explains why Penrose’s challenge to Popper is not ultimately valid. ‘Science’ (in the Popperian sense) is about realistic programs for testing which can only be logical ‘refutations.’ And even in a somewhat unrealistic example like Penrose’s example–where we really are verifying a theory via experiment–it still acts as a tacit refutation to the competing theory.

A completely fair question here is how many times has this happened in the history of science where a theory was ‘verified’ via a purely existential prediction? I am not aware of even one example. If you are, please put it in the comments. I suspect that in real life, for all practical purposes, Popper is just correct: you can’t really empirically test a theory unless there are some universal (and thus irrefutable) predictions involved to help make the tests reasonable. I think this explains why Popper’s ‘convention’ of discounting purely existential predictions from being empirical makes valid sense.

Consider also Popper’s example of a purely existential theory that the use of Latin couples can summon the devil. (As discussed in this post.) It just is not practical to count purely existential theories as empirical. This is why, by convention, Popper counts only theories that can have realistic programs for testing them as empirical. Otherwise, there would be an infinity of such clearly non-scientific theories that would then have to be counted as empirical. So as a practical matter, we will never be able to count theories with purely existential predictions as empirical. However, should we find such a prediction to be true, at that point we would count it as ‘refuting’ the competing theory at that point where the observation was made and it became a basic statement? So this poses no real problem for Popper’s epistemology. [2]

Notes

[1] I anticipate an objection here that nothing can be ‘settled’ in Popper’s epistemology. But that’s just falling back into the Absolute Verification Fallacy. There is nothing wrong with using the word ‘settled’ in a less absolute sense like I’m doing here. In fact, this is an important part of Popper’s epistemology. To him, basic statements are observations that some community has–at least tentatively for now–‘settled’ upon as a valid observation. This is why he refers to it as ‘intersubjective’ testing rather than ‘objective’ testing. Popper explains it this way:

…the objectivity of scientific statements lies in the fact that they can be inter-subjectively tested. …We do not take even our own observations quite seriously, or accept them as scientific observations, until we have repeated and tested them. Only be such repetitions can we convince ourselves that we are not dealing with a mere isolated ‘coincidence’ but with events which, on account of their regularity and reproducibility , are in principle inter-subjectively testable. [i.e. others within the community will be able to reproduce the results.]

LoSC, p. 22-23. Emphasis Popper’s

See this post, for a full discussion on the meaning and importance of ‘intersubjective’ testing and why a community must agree upon what basic statements are correct. See also footnote 2 in this post.

[2] This example, however unrealistic, is still a possible outcome that needs to be addressed. This example is therefore a good example of why we should not fear the language of verification and support. Popper’s epistemology does not claim verification and support are in all circumstances impossible. Instead, his epistemology puts limits on when verification or support can take place and what the implications are, especially that they never imply we proved a theory as certain or even as a justified true belief.

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