We previously discussed Popper’s own views on why there is an asymmetry between refutations and verifications. But this didn’t really answer my question entirely. If, as Deutsch claims, refutations only happen within theory-to-theory comparisons why can’t we count every refutation as support for the remaining theories?
But it should be obvious that it literally makes no difference if we want to call the Eddington expedition a refutation of Newton or support for General Relativity. In fact, we can easily just think of ‘support’ as scientifically defined as “a test that causes a problem for its competitor but is explained by the new theory” which just makes ‘support’ a euphemism for refutation — and vice versa. For many years this problem bothered me and I just assumed either Deutsch or Popper must be wrong.
This problem can be resolved by introducing an idea that I got from a Facebook conversation with Popper scholar Danny Frederick.
Initially, I started arguing with Frederick over whether or not a refutation required a second rival theory or not. I was following Deutsch’s interpretation where you can’t refute a theory without a rival as Deutsch states in his Logic of Experimental Tests:
When we, via arguments or experiments, find an apparent flaw, conflict or inadequacy in our theories, that constitutes a scientific problem and the theories are problematic (but not necessarily refuted yet…)” (p. 7)
In this view a scientific theory is refuted if it is not a good explanation but has a rival that is a good explanation with the same (or more) explicanda. So another consequence is that in the absence of a good rival explanation, an explanatory theory cannot be refuted by experiment: at most it can be made problematic. If only one good explanation is known, and an experimental result makes it problematic, that can motivate a research programme to replace it (or to replace some other theory). But so can a theoretical problem, a philosophical problem, a hunch, a wish – anything.” (p. 8)
“But in any case, the existence of a problem with a theory has little import besides, as I said, informing research programmes – unless both the new and the old explicanda are well explained by a rival theory. In that case the problem becomes grounds for considering the problematic theory tentatively refuted.” (p. 10)
Frederick was quite insistent that I was incorrect and even went so far as to claim I was probably mangling Deutsch’s view (though Frederick openly admitted he’d never read the Logic of Experimental Tests nor any of Deutsch’s books.) Frederick continued to insist that you did not need a rival theory to ‘refute’ a theory and instead insisted that a second theory was only necessary when you ‘rejected’ a theory long after you ‘refuted’ it.
At some point in the conversation, I suddenly realized that Deutsch’s view and Danny’s view were actually identical, but that they were using different words to describe the concepts in question. Here is the mapping between the two men:
|Frederick’s Interpretation||Deutsch’s Interpretation|
|When you discover that an experiment doesn’t come out as a theory predicts, this is a ‘refutation‘ though it is understood not to be a refutation of the theory proper but a refutation of a combination of the theory and the background knowledge.||When you discover that an experiment doesn’t come out as a theory predicts, this is not a ‘refutation’ of the theory but is instead merely a ‘problem‘ for the theory because you don’t yet know if it’s a problem with the theory proper or the background knowledge.|
|When you have a new rival theory that explains the above-mentioned refutation you can now tentatively ‘reject‘ the old theory.||When you have a new rival theory that explains the above-mentioned ‘problem’ you can now tentatively ‘refute‘ the old theory.|
It just isn’t hard to see that what Deutsch calls a ‘problem’ is what Frederick calls a ‘refutation’ and what Deutsch calls a ‘refutation’ is what Frederick calls a ‘rejection’! Yet I just could not convince Frederick that this was the case! He was insistent that I was just misunderstanding Popper’s epistemology because he could not be persuaded that Popper’s view of what a ‘refutation’ was was anything but a single experiment that went against the prediction of the theory.
That is when it finally struck me: the word ‘refutation’ is not likely to have a single definition. It’s a word that existed before Popper that Popper was using to explain a concept. So it makes sense that different people would use the term in different ways and may not be entirely consistent with each other.
Consider Popper’s argument that the word ‘confirmation’ comes to us with existing connotations that cause people to misunderstand Popper’s meaning.  What if the word ‘refutation’ does as well? It really shouldn’t be surprising at all that Frederick understood the word ‘refutation’ as not requiring a rival theory and Deutsch understood it as requiring a rival theory–for each was using the word ‘refutation’ to represent a different concept! And both concepts could arguably be thought of as a kind of ‘refutation.’
That was when it really struck me that I had been reading Popper with the assumption that ‘refutations’ only could take place in a theory-to-theory comparison when in reality Popper may have often meant the word ‘refutation’ more like how Danny Frederick used the term: as ‘refuting’ a combination of the theory plus the background knowledge. I saw no reason why this wasn’t an equally valid way to understand the term ‘refutation.’ Was perhaps my concerns with several passages of Popper actually all due to me unintentionally bringing an implicit theory of refutations that Popper didn’t intend? Could this realization that ‘refutation’ has more than one valid meaning clear up the problems I had with Popper’s writing? (As discussed here and here.)
In the end, the two men were actually agreeing with each other they just couldn’t agree on which linguistic terms to use. But there was nothing deeper than a linguistic difference going on. Many of my previous concerns with the problems of refutation started to melt away.
How Did Popper Use the Term “Refutation”?
But this led me to a very interesting question: how did Popper use the term ‘refutation’? Did he use it more like Frederick? Or more like Deutsch? Was he even consistent in his usage or did he sometimes use it both ways and not notice that he was actually subtly equivocating between two different concepts–one at the time we first have a prediction go awry and one at the time when we have a rival theory to explain why that prediction went awry?
To resolve this question, let’s look at actual quotes from Popper where he uses the term refutation or falsification. 
Popper’s Use of The Term ‘Refutation‘
The first place I want you to look at is this entire post where Popper explains why he believes refutation is important to science and verification is not. You probably weren’t thinking of it at the time, but there is no way to make sense of Popper’s view of refutations here without accepting that he is not (at least here) talking about refutations as happening at the time we create a rival theory to explain why the prediction went wrong. This follows from Popper’s view that refutations are more important than verifications due to the logic of how empirical tests work. Popper is here using the term ‘refutation’ for any basic statement that conflicts with a prediction. Consider this quote again:
As to falsification, special rules must be introduced which will determine under what conditions a system is to be regarded as falsified. We say that a theory is falsified only if we have accepted basic statements which contradict it. This condition is necessary, but not sufficient; for we have seen that non-reproducible single occurrences are of no significance to science. Thus a few stray basic statements contradiction a theory will hardly induce us to reject it as falsified. We shall take it as falsified only if we discover a reproducible effect which refutes the theory.LoSD, p. 66
There is not even an implication of a rival theory in this quote. Popper is clearly talking about acceptance of the basic statement that creates a contradiction to what the theory predicted. That moment in time would normally be long before we conjecture the rival theory so here ‘refutation’ matches with Frederick’s reading rather than Deutsch’s and is equivalent to what Deutsch refers to as a ‘problem’. In fact, we can easily read this statement using the Deutsch terminology by replacing it every occurrence of ‘refutation’ or ‘falsification’ with a reference to a ‘problem’ instead:
As to [a problem], special rules must be introduced which will determine under what conditions a system is to be regarded as [having a problem]. We say that a theory [has a problem] only if we have accepted basic statements which contradict it. This condition is necessary, but not sufficient; for we have seen that non-reproducible single occurrences are of no significance to science. Thus a few stray basic statements contradiction a theory will hardly induce us to [consider it as having a problem that needs to be resolved]. We shall take [a basic statement] as [a problem] only if we discover a reproducible effect which [creates a problem for] the theory.
It seems to me that this new form is conceptually identical to the original even though we’re now talking about ‘problems’ instead of ‘falsifications’ or ‘refutations’. Other than a linguistic change, nothing else changed. But by comparison, it seems impossible to read this same statement as being about refutations taking place at the time you finally get a rival theory. If a refutation requires a rival theory, then we’re quite late in the process. It seems entirely out of place for Popper to be explaining why we need a special rule of reproducibility to count a basic statement as a falsification if Popper has in mind that this only happens once we have a rival theory. So to read this passage properly, you need to have Frederick’s understanding of refutation/falsification in mind.
But this makes sense since to Popper a refutation or verification is a logical matter. The moment you have a failed prediction you have a logical contradiction that must be resolved. That’s what a ‘problem’ actually is.
Popper is explicitly claiming that the only reason he feels ‘refutations’ are better than ‘verifications’ is that a theory can only be empirical if a test can fail to match a prediction. But the happens the moment you have a failed prediction, not when you finally conjecture a good rival theory. So Popper’s entire argument of the asymmetry between refutation and verification requires us to equate Popper’s use of the term ‘refutation’ with Frederick’s view of refutation–as happening the moment you have a prediction go wrong.
Other Examples of Popper Following Fredericks’ Understanding of Refutation
Here is another quote from Popper that seems to match Frederick’s view:
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
The ‘world of experience’ is not what you get when you have two rival theories. It’s the moment you have an observation that is a problem that doesn’t match expectations. So here, again, we find Popper using the term ‘refutation’ consistent with Frederick’s view rather than Deutsch’s.
But here is one that is less clear. This first part seems to match Frederick’s understanding of the falsification:
Can the claim that an explanatory universal theory is true be justified by ‘empirical reasons’; that is, by assuming the truth of certain test statements or observation statements (which, it may be said, are ‘based on experience’)?
My answer to the problem is…: No, we cannot; no number of true test statements would justify the claim that an explanatory universal theory is true.
Can the claim that an explanatory universal theory is true or that it is false be justified by ‘empirical reasons’; that is, can the assumption of the truth of test statements justify either the claim that a universal theory is true or the claim that it is false? [Note: the only difference from the above question is that he is now adding the words “or that it is false.”]
To this problem, my answer is positive: Yes, the assumption of the truth of test statements sometimes allows us to justify the claim that an explanatory universal theory is false.Objective Knowledge, P. 7
Maybe it’s not obvious at first that this is another match to Danny’s view of ‘falsification’ so let me make clear why it is. Popper is here saying that no number of test statements can justify a theory as true, but that you can justify a theory as ‘true or false’ (specifically false) via test statements.  So he is clearly here saying you can falsify a theory with only test statements. There is no mention of a rival theory being necessary.
Also, consider this quote here that clearly equates testability, refutation, and falsification:
Testability is therefore the same as refutability, or falsifiability.Conjecture and Refutations, p. 266
So all tests of a theory are potential attempts to refute or falsify that theory. This clearly can’t be squared with Deutsch’s view that refutation solely takes place when you have come up with a new rival theory and before that point it’s not a refutation, it’s just a problem. Popper is saying unequivocally that all tests are identical to attempts to refute/falsify a theory. This is again clearly the Frederick interpretation.
But It’s Not As Clear Cut As We Might Like
But Popper refuses to make this an easy win for Frederick because he goes right on to say a paragraph later:
This reply becomes very important if we reflect on the problem situation in which we are faced with several explanatory theories which compete qua solutions of the same problem of explanation…OBJECTIVE KNOWLEDGE, P. 7
So though Popper is here initially equating falsification with Frederick’s view, Deutsch’s view is not far from his mind at all. In fact, he doesn’t seem to strongly differentiate between the two views at all in this quote here:
Our task [in determining the truth of a mathematical theory] is the testing, the critical examination, of two (or more) rival theories. We solve it by trying to refute them–either the one or the other–until we come to a decision.Conjecture and Refutation, p. 267
This sounds a lot like Deutsch’s interpretation. You might here complain that Popper is specifically talking about mathematical theories rather than scientific and empirical theories. But the next paragraph goes on to say:
If we now look at the empirical sciences, we find that we follow, as a rule, fundamentally the same procedure. Once again we test our theories we examine them critically, we try to refute them. The only important difference is that now we can also make use of empirical arguments in our critical discussion.Conjecture and Refutation, p. 267
But is this clearly the Deutsch view? It actually isn’t. Why, because you can easily read this utilizing the Frederick view without any problem at all. I’ll prove this again by using the ‘substitution method’ where I replace all occurrences of the word ‘refutation’ with Deutsch’s terminology of a ‘problem.’
Our task [in determining the truth of a mathematical theory] is the testing, the critical examination, of two (or more) rival theories. We solve it by trying to [find problems with] them–either the one or the other–until we come to a decision. … If we now look at the empirical sciences, we find that we follow, as a rule, fundamentally the same procedure. Once again we test our theories we examine them critically, we try to [find problems with] them. The only important difference is that now we can also make use of empirical arguments in our critical discussion.
So while this may seem closer to the Deutsch use of terms, it actually isn’t at all inconsistent with the Frederick use. This is because the statement does not require us to read a refutation as requiring a rival theory, it merely points out that you can have them once you have a rival theory.
This is the reality of Popper: he never did explain well what he meant by a ‘refutation.’ He sometimes uses the term as a proxy for any failed prediction and sometimes used it in the context of a theory-to-theory comparison. But I have so far found no examples where Popper clearly comes out (as Deutsch does) as requiring a rival theory to count as a refutation. This is why it seems to be always possible to read Popper in the Frederick language but isn’t always possible to read Popper using Deutsch’s language.
Did Popper See Falsification as Including Background Knowledge?
Another way to test between the Frederick and Deutsch interpretations of refutation/falsification is to test if Popper saw falsification as specific to a theory or as refuting a combination of the theory plus the background knowledge. If he did see refutations as including the background knowledge then we know Popper was utilizing the term more like Frederick. If he did not see it as including background knowledge, then we know he was using the term more like Deutsch. Consider, for example, this quote from Popper:
[A more serious objection to my epistemology is] closely connected with the problem of context, and the fact that my criterion of demarcation applies to systems of theories rather than to statements out of context. This objection may be put as follows. NO single hypothesis… is falsifiable, because every refutation of a conclusion may hit any single premise of the set of all premises used in deriving the refuted conclusion. The attribution of the falsity to some particular hypothesis that belongs to this set of premises is therefore risky…Realism and the Aim of Science, p. 187
This quote from Popper is clearly talking about how refutations apply to the theory plus the background theories. That is to say, the ‘system of theories.’ So Popper did see refutations/falsifications as applying to not only the theory we intended to test but also the background knowledge. This matches Frederick’s language.
In Nathan Oseroff’s excellent paper, “Addressing Three Popular Philosophic Myths about Karl Popper’s Demarcation Criteria” he gives another great example of how Popper say refutations/falsifications as logically applying to the whole system of theories rather than a single theory:
The most explicit quote is found in Replies to My Critics where Popper says:
[the problem of demarcation] can be considerably improved it one speaks of theoretical systems or systems of statements, as I did … even if we can apply it to systems of statements, it may be difficult if not impossible to say which particular statement, or which subsystem of a system of statements, has been exposed to a particular experimental test. Thus we may describe a system as scientific or empirically testable, while being most uncertain about its constituent parts. … if we falsify it, we falsify the whole system. (Popper 1974, p. 982)As quoted in Oseroff, p. 10
This is quite clearly a claim that falsification includes the background knowledge. So again, Popper is clearly using the term ‘falsification’ in the Frederick sense not in the Deutsch sense since Deutsh’s understanding of ‘refutation’ and thus ‘falsification’ does not falsify a combination of both the theory and the background knowledge due to the existence of a rival theory that explains what caused the falsification in the original theory.
Elsewhere, in Realism and the Aim of Science, Popper says:
… it is important to remember that [the criterion of demarcation] applies to theoretical systems rather than to statements picked out from the context of a theoretical system.Realism and the Aim of Science, p. 178
However, Oseroff admits that the reason why people often misunderstand this aspect of Popper is because of Popper himself.
Reading Popper’s The Logic of Scientific Discovery would be sufficient for many people to arrive at the conclusion that falsifiability applies only to individual theories. … To list a few examples in order, Popper says ‘… there is the investigation of the logic form of the theory, with the object of determining whether it has the character of an empirical or scientific theory …’ (LoSD 1959, p. 9); ‘… there is the testing of the theory …’ (LoSD 1959, p. 9); ‘… other statements …are deduced from the theory’ (LoSD 1959, p. 10); ‘…if the conclusions have been falsified, then their falsification also falsifies the theory from which they were logically deduced …’ (LoSD 1959, p. 10); ‘… no conclusive disproof of a theory can ever be produced’ (LoSD 1959, p. 28); (cf. LoSD 1959, 28, 29, 49, 55ff.). Similar examples can be found in, e.g., Popper (1962), Popper (1963), Popper (1974), and Popper (1983), each following the format of referring to a theory that is falsified by accepting an empirical statement that contradicts the theory.
Each of these statements fails to mention that falsification is of the theory plus the background knowledge. Thus it’s tempting to read them as closer to Deutsch’s interpretation. To resolve the contradiction Oseroff propose:
…this continued insistence and clarification that any use of the word ‘theory’ in relation to his falsifiability criterion be understood as an elliptical expression for ‘theoretical system’… [i.e. including the background knowledge.]Oseroff, p. 10
This explains the following quote that I previously reference as having a problem:
As to falsification, special rules must be introduced which will determine under what conditions a system is to be regarded as falsified. We say that a theory is falsified only if we have accepted basic statements which contradict it.
Here Popper first refers to the falsification as applying to the ‘system’ (i.e. including background knowledge) and then goes on to refer to that system as ‘a theory’ that is then falsified at the time we accept a basic statement that contradictions it–not when we later find a rival theory. I do not see how to read this passage consistently unless we follow Oseroff’s suggestion that Popper used the word ‘theory’ in relation to his falsifiability criterion as an elliptical expression for ‘theoretical system.’ In any case, this is the passage that we above noticed wasn’t possible to read using the Deutsch understanding of what a refutation is (i.e. once you have a rival theory.)
Reading Popper Correctly
I had, for years, read Popper with the idea that a refutation required a rival theory and thus wasn’t possible with a single basic statement. This caused me to read Popper as saying some questionable things about refutations/falsifications. But once I realized these passages should instead be read as refutations/falsifications of the theory plus the background knowledge–the whole theoretical system–these passages no longer struck me as problematic. See for example this post that analyzes my writing that predates his paper. In that post, I still am holding on to the idea that ‘refutation’ requires a rival theory and quote myself saying that years before Deutsch’s paper and it’s causing me to not understand what Popper is really saying.
It’s tempting here to scratch this all up to Deutsch misunderstanding Popper, but in the post I demonstrate that my misunderstanding of Popper’s view of refutation/falsification (as including the background knowledge) predates Deutsch’s Logic of Experimental Tests by several years. So I managed to misunderstand Popper all on my own. But why did both Deutsch and I assume that a refutation required a rival theory?
The Connotations of the Terms Refutation and Falsification
At issue here is that the terms ‘refutation’ and ‘falsification’ both are words that come with a lot of baggage. To the vast majority of people, a ‘refutation’ or ‘falsification’ is not the moment you have some sort of problem with a theory but when you actually drop the theory in favor of another one. Both words, all on their own, strongly suggest this due to their simple connotations.
Refutation: The action of proving a statement or theory to be wrong or false.
Falsification: The action of falsifying information or a theory.From Google here and here
Neither of these words in common parlance includes the idea that we’re making a tentative decision much less against some combination of a theory plus its background knowledge. To put this bluntly, the terms ‘refutation’ and ‘falsification’ are a poor choice of words to convey the idea that Popper actually had in mind. It was entirely natural for Deutsch to instead equate a ‘refutation’ with when you have a rival theory so you can actually drop the old theory now. For that is what ‘refutation’ means to most people most of the time.
Put another way, Popper’s use of both refutation and falsification are both idiosyncratic uses inconsistent with most people’s intuitive understanding of those terms whereas Deutsch’s terms formalize the terms in a way far closer to how people normally use the terms but inconsistent with how Popper used the terms.
But Deutsch’s Usage is Somewhat Problematic Too
But even Deutsch’s usage is somewhat problematic. I think it could be argued that there no theory is ever truly refuted in the sense most people think of the term since most people see it as a sort of definitive thing whereas in Popper all refutations are always tentative. But that isn’t the biggest problem because the words refutation and falsification are normally seen as events. That’s why the above definitions are ‘actions’. But in real life, science never refutes or falsifies a theory as a single action or event.
What really happens is that scientists slowly start to give up on the old theory because it continues to collect problems that no one knows how to solve. But at the same time, the new rival theory not only solves the problems but all of the scientist’s peers are starting to embrace the new rival theory and are demonstrating how productive it is. One by one, sometimes over a very long period of time. people just stop using the old theory and start using the new theory. There may never be an event where the new theory becomes ‘accepted’ and the old theory ‘rejected.’ This is why Popper did not care much about when a theory finally became accepted: 
…the question of the acceptance of theories should, I propose, be demoted to the status of a minor problem. For science may be regarded as a growing system of problems, rather than a system of beliefs. And for a system of problems, the tentative acceptance of a theory or a conjecture means hardly more than it is considered worthy of further criticism.Myth of the Framework, p. 103
To put this more bluntly, what Deutsch calls a refutation–the dropping of one theory in favor of accepting a new one–has no real importance to Popper. Popper saw all the real action as the discovery of a new problem: i.e. the moment you have a counterexample to explain.
So we find ourselves in a very strange situation: neither the Frederick interpretation of ‘refutation’ (and ‘falsification’) nor the Deutsch interpretation really works very well with the English word ‘refutation.’ The word is, at best, a poor fit to both when the first missed prediction happens and when the theory actually gets a rival to–very slowly–replace it as the old one becomes less interesting.
Refutation vs Confirmation
We already bumped into an identical problem with the word ‘confirmation.’ Popper initially talked about how testing a theory provided ‘degrees of confirmation’ and then later changed that to ‘degrees of corroboration’ due to people misunderstanding his terms. All I’m really saying here is that the word ‘refutation’ (as well as ‘falsification’) has a similar sort of problem. Indeed, in some sense, they have the very same problem that the word confirmation has. It implies invalid certainty: in this case both epistemic certainty as well as certainty as to which part of the system of theories is the real problem. So of course people misunderstand Popper’s views on refutation.
Do Others Misunderstand Popper Like This?
Of course, one might argue here that I (and apparently Deutsch) are outliers. Maybe we misunderstood Popper’s intent but most people do not. Of course, this might well be. It’s not like I’ve taken a survey of all the world’s views of Popper. But consider this Youtube video as an example.
David Deutsch tweeted this video as an example of how people ‘misunderstand’ Popper. Deutsch, referring to this video, said that the video contains things that “Popper didn’t say but people think he did.” Deutsch goes on to say that “There aren’t straw man arguments but sincere, vast, misunderstandings.” Deutsch voices his opinion that this is, “Caused, I think, by the fact that Popper’s achievement is bigger than most people conceive is possible, so they guess at what he must have meant and arrived at something silly. I did when I first read him.”
Deutsch later says, “If you hear ‘falsificationist’ you’re probably hearing a misunderstanding of Popper’s philosophy, even though Popper and Miller used the term.”
But this video’s misunderstanding of Popper is far simpler than Deutsch realizes. He merely points out that you can’t refute a theory with a single example because of all the implicit background knowledge required. In other words, he simply misunderstood the word ‘refutation’ as being about a single theory rather than a theory plus the background knowledge. This is a natural way to read the word but in this case it led him into a misunderstanding of Popper’s epistemology. So he turned to induction instead.
 See also this post here for further discussion about confirmation and corroboration actually being synonyms with slightly different connotations.
 I am not here making the claim that Popper always used ‘refutation’ and ‘falsification’ as identical synonyms. See “The distinction between falsification and refutation in the demarcation problem of Karl Popper” by Nicolae Sfetcu. However, there should be no doubt that Popper did often use them as more or less the same thing. For example: “…a set of singular observation statements (‘basic statements, as I called them) may at times falsify or refute a universal law” (Realism and the Aim of Science, P. 181) So in this post, I’m going to treat falsification and refutation as synonyms and analyze Popper’s use of both terms. I note that Frederick used the terms flexibly and interchangeably too as can be seen from my summary of Frederick’s view that he bought off on. I am unaware of anywhere that Deutsch attempts to make a distinction between the two words either.
See also this quote in the body of the post where Popper states he sees refutability and falsifiability as synonyms:
Testability is therefore the same as refutability, or falsifiability.Conjecture and Refutations, p. 266
 I note here Popper’s comfort with using the word ‘justify’ without immediately equating it with justificationism. Popper’s theory does allow one to ‘justify’ a theory as more correct than another and that is what he is saying here. This is one of the many ways in which Popper significantly differs from Twit Rats on use of language. There is nothing wrong with speaking of justifying something using Popper’s epistemology. It is specifically justificationism — that is to say, justifying with certainty or probability — that is false under Popper’s epistemology. The word ‘justify’ is just a word and not everyone uses the term to imply certainty or probability. More to the point, Popper did not.
 This happens in real life. The lightwave theory vs light particle theory contest originally was thought to be determined definitely in favor of lightwave theory because we had real empirical test cases that showed light to be a wave. Since at the time we thought waves and particles were mutually exclusive, light particle theory was widely believed to be a refuted theory. But then Einstein came up with the photoelectric effect that required light particle theory and was a problem for lightwave theory. At that point, we had two theories both of which had counterexamples to them. It required the invention of quantum mechanics to resolve the situation. So this shows why there just is no such thing as a single point in time where a theory truly becomes refuted. All theories are, in a sense, never refuted but simply no one has yet figured out a way to solve its existing problems so everyone jumped to its rival that didn’t have those problems.