Are Hypotheses Naively Refutable?

Upfront apologies for this post. It’s a bit messy. That’s because I’m exploring ideas that I’m confused about and I’m seeking other’s thoughts to clarify my own thinking.

In a past post, I pointed out that Popper was not clear on if his theory of falsificationism was naïve falsificationism or if it was intended to be in a theory-to-theory comparison only. I believe this led to confusion about what Popper’s theory was really about. To this day most people think of Popper’s theory as being about naïve falsification. Even from respected scientists, you hear things like “scientists are always trying to disprove their theories” which is a statement as naïve as naïve falsification itself. Among many philosophers “Karl Popper’s philosophy” (by which they actually mean naïve falsificationism) is even considered refuted. [1]

I already noted, in the previous post, that naïve falsification is clearly false of our best scientific theories (or what Kuhn might call “paradigm theories”) and I gave examples of this. But it is less clear if this is false for early conjectures. Can at least early conjectures be refuted by single observations? Or do they also require a theory-to-theory comparison as well?

Consider again this quote from Popper:

In so far as scientific statements refer to the world of experience, they must be refutable; and, in so far as they are irrefutable, they do not refer to the world of experience.

Open Society Vol 2, p. 13

In my previous post, I took the phrase ‘scientific statements’ to refer to ‘scientific theories.’ But is this what Popper actually intended? One might here claim that Popper wasn’t talking about scientific theories but about scientific hypotheses.

In the popular account of the scientific method (which in the past I’ve claimed Popper refuted) there is this idea that a “scientific hypothesis” is an early conjecture that isn’t well-tested yet whereas a “scientific theory” is a well-tested conjecture. Under this use of terms (whether or not this is really in common usage among scientists) “theories” are the conjectures that survived attempts to criticize them long enough to become widely accepted but “hypotheses” are just initial early conjectures being researched and tested and no one is taking them too seriously yet.

I already mentioned if we’re talking about a well-tested and currently widely accepted scientific theory then a naïve refutation is impossible because:

  1. Any new theory must be compared to the old theory
  2. If we had an observation that contradicts the theory, the Duhem-Quine problem indicates we would have no way of knowing if the problem was the theory or our background knowledge. (As discussed in this post.)

But is that also true for early conjectures that aren’t well-tested yet? In other words, in the quote above, could we take the stance that Popper was just talking about early hypotheses? Let’s explore that idea further.

How Can We Refute Grass Cures Cancer?

I find this a tougher question. Let’s take a simple example. Suppose I have a theory that grass cures cancer. Deutsch points out that this is a bad explanation. But say I test my theory using rigorous randomly controlled trials and I find that grass does cause a 50% increase in cancer going into remission. Then this theory – even if it is a bad explanation – will probably seem a lot more interesting to us and a deeper explanation will be sought to explain the observation.

However, if the randomly controlled trials show no difference in the rate of cancer remissions we’d probably all consider the hypothesis refuted by observation. So is this an example of naïve falsificationism actually working?

If you answer ‘yes’ here, then consider again Deutsch’s statement:

In any experiment designed to test a scientific theory T, the prediction of the result expected under [Theory or Hypothesis] T also depends on other theories: background knowledge, including explanations of what the preparation of the experiment achieves, how the apparatus works, and the sources of error. Nothing about the unmet expectation dictates whether [Theory] T or any of those background-knowledge assumptions was at fault. Therefore there is no such thing as an experimental result logically contradicting [Theory] T…. an apparent failure of T’s prediction is merely a problem, so seeking an alternative to T is merely one possible approach to solving it.

David Deusch, “Logic of experimental tests”, p. 27)

Deutsch seems to leave no room in his statement for hypotheses to be naïvely refuted either. He’s literally saying there is no experiment you can come up with that logically refutes a hypothesis because of the Duhem-Quine thesis. So is Deutsch wrong? Or is Popper wrong? Is there a way to allow both to be correct?

I admit I am partial to Deutsch’s logic here, but not entirely convinced. Let me try to explain why.

There is an implicit second theory here. We are really comparing these two theories:

Theory 1: Grasses cures cancer

Theory 2: Grass does not cure cancer

While neither of these is truly a good explanation, the theory “Grass cures cancer” is at least a very high-level explanation asserting simple causation. In fact, it is possible to make this explanation of causation mathematically rigorous. But the assertion “grass does not cure cancer” is also a rough explanation in that it asserts a lack of causation. This assertion can also be made mathematically rigorous using the same technique. So in this case it seems fairly clear that Deutsch is correct, we have two ‘hypotheses’ that are competing and we consider ‘grass cures cancer’ refuted by experiment because we have an equally good (or rather bad) explanation to jump to.

But this seems almost like a cheat to me. Really, the only reason why this turned out to be a theory-to-theory comparison is that the original theory (“grass cures cancer”) was a really bad explanation to begin with, so i’s negation is no worse of an explanation than it was. But Deutsch has pointed out that a good explanation’s negation usually is not an explanation at all. So I think one could argue here that really just the example is a bad example.

The Negation of an Explanation is Not (Always) an Explanation

But this then gives us an idea on how to construct an example of a naïve falsification! We simply need to start with a hypothesis that is also an explanatory explanation (though possibly false) that has no competitors and then refute it by experiment. If we can do that, then we have an example of naïve refutation.

This makes the theory that “all refutations require a 2nd theory” a testable theory. If we can’t come up with even a single counter-example of it, then we’ll accept it as our best theory.

Let’s consider David Deutsch’s own example of how the negation of an explanation is not always an explanation.

However, if T is an explanatory theory (e.g. ‘the sun is powered by nuclear fusion’), then its negation ~T (‘the sun is not powered by nuclear fusion’) is not an explanation at all.

Link

How Do We Refute “The Sun Is Not Nuclear Fusion”

So how might we go about testing that the sun is powered by nuclear fusion?

As this Quora post explains, there are numerous ways we’ve tested the theory that the sun is nuclear fusion. One of the first ways we did was we showed that the sun emitted radiation. A later observation dealt with using emitted neutrinos that were consistent with the idea that the sun was full of hydrogen.

But now we have a problem: if the statement “the sun is not powered by nuclear fusion” is not an explanation, what does it mean to ‘refute’ it by observations like this?

In fact, this is actually even a bigger problem, isn’t it? The two experiments I just mentioned (that the sun emits radiation and neutrinos) aren’t really experiments meant to refute that the sun is powered by nuclear fusion but rather they are meant to verify that it was. And this, suprisingly, makes a sort of sense. If you have only one theory to work with, all you can really do is figure out some sort of prediction that it makes and then see if the prediction holds. Failure of that prediction would not refute the theory per se (due to Duhem-Quine) because it may just be that we haven’t set up the experiment well yet. But finding the prediction to be correct does seem to confirm the theory.

But this can’t be right, can it? Popper’s theory is that there is an asymmetry between verification and refutation — you can refute things but you can’t verify them, right? But here we see that isn’t the case, right?

That is unless you accept that there are actually two competing theories here after all:

Theory 1: The Sun Is Burning Using Regular Chemical Processes

Theory 2: The Sun is Burning Using Nuclear Fusion

But when stated this way, we’re right back to the idea that Deutch was right and that we do need two theories to do a falsification.

When Did we Refute Theory 1?

But this still leaves a bit of a problem, doesn’t it? The real truth is that it’s easy to refute Theory 1 without even referencing nuclear fusion. The very fact that the sun has been burning for so long and hasn’t gone out yet is an observation at odds with the idea that the sun works by regular chemical means. So Theory 1 was effectively ‘refuted’ before we even knew about nuclear fusion. In fact, it was one of the reasons why sought a theory of nuclear fusion.

So really, at one point, we have only a single theory:

Theory 1: The Sun Is Burning Using Regular Chemical Processes

And one day that theory got “refuted” when people realized that the sun is burning far too long than chemical theory allows it to. Only then did they start to seek a new theory.

So is this then an example of naïve falsification? It does sort of seem like that to me.

But I’m not sure I see Deutsch as entirely wrong here. This isn’t as clear-cut a case as I’m making it sound. For one thing, the words ‘regular chemical processes’ is a meaningless statement outside a world where we know about nuclear fusion.

I’m actually retroactively defining what Theory 1 was now that we know about nuclear fusion!

Prior to the discovery of nuclear fusion, we simply had a troubling observation about the sun and no idea how to resolve the problem. So if you prefer to see things that way, Deutsch is correct that we didn’t really refute Theory 1 until Theory 2 came along.

Did We Verify The Sun is Using Nuclear Fusion?

But wait! There’s more! We still have a problem!

If the discovery of Nuclear Fusion allowed us to both define and refute Theory 1, then what was the purpose of going on to verify that the sun was nuclear fusion? If we had a problem — the sun burns too long — and we resolve the problem by theorizing the existence of nuclear fusion, doesn’t that immediately make Theory 2 the best (and only!) theory to explain why the sun burns so long?

It certainly seems so to me. Yet I am glad they went on to strengthen the theory by verifying that this was correct by doing the experiments mentioned in the Quora post. But doesn’t Popper’s (and Deutsch’s) theory state that there is no such thing as verification? So what is going on here?

Conclusions

I have no conclusions. Instead, I’ve laid out a critical test for the theory that all refutations require theory-to-theory comparison. I’ve created a template for how to test that theory. See if you can come up with an example of a conjecture that is at once testable but also has no competing theory due to its negation being a non-explanation. And it has no competing theory due to being only an early hypothesis. I will offer my own best example in a future post. But I admit this seems to be a fairly difficult challenge, but perhaps not an impossible one.

Footnotes

[1] As a side note, this guy explicitly states that induction requires a background theory. I note this because Popperians tend to strawman Induction by claiming it, in all forms, eschews the concept of background theories. Apparently, that is not always true today. But it shouldn’t surprise us that Inductivists have borrowed from the Popperian playbook given that what we call Induction today seems to usually just be crypto-Popperian epistemology.

2 Replies to “Are Hypotheses Naively Refutable?”

  1. A rival theory doesn’t need to have the same reach as the theory it tries to refute. It can be a much simpler theory, for example: The sun does not emit neutrinos.

    I struggle to get a grip on the “hard to vary” criteria, but I think that when you have a theory that fulfills it you can easily create a rival theory by picking one of its claims and slightly change it. Then create a crucial test that selects between the two.

    Chemical fire is a hard to vary theory and that the sun was burning in this way could be refuted when the mass of the sun was known. The theory did not allow a variation that would include the sun. Having no theory for a phenomena is also a possibility.

    You ask why we should keep probing our single remaining theory. If I’m going to put my life and prosperity in the hands of a theory, I do want to check if the predictions it makes align with other theories I can compare it with before things get serious. I don’t need a second theory on par with the first to refute it. I can use a palette of small, isolated theories that perhaps only consist of a single empirical observation. The theory that claims universality will be refuted by all the non-universal theories that interfere with its reach. We know we must keep attacking our best theories and try to refute them before they fail in disaster. It is a matter of safety and survival.

    I can relate this difference in reach to when I troubleshoot system failures. We have observations A, B, and C and hope to find a theory that explains them all. Someone suggests a theory T that can explain A, but one of its predictions are (not C). T seems to be refuted unless we can go back to C and reevaluate it in light of the new theory T. We may have made a mistake with C. The search for a theory goes on until all observations can be explained.

    1. So I agree with you.

      But I guess the question is this. Does Popper’s epistemology say that you cannot, in any sense, verify a hypothesis? Many seem to read him that way. If that is so, then we should not feel like the experiments to confirm that the Sun is nuclear fusion are at all helpful. Yet I feel that they are very helpful.

      Of course, where I’m going with this is that I think people misunderstand Popper’s epistemology on how it looks at such experiments. And I agree with you that they in some sense strengthen the theory even though it was already a best (and only) theory for how the sun burns.

      “I don’t need a second theory on par with the first to refute it.” I think this is actually identical to Popper’s falsification criteria.

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