What’s in it for me? Dive into a classic of twentieth-century scientific philosophy.
Picture this. It’s a lovely morning in your small hometown, and you’ve decided to go for a short stroll along the river. As you’re walking along, soaking up the warm summer sun, a beautiful white swan comes swimming around the nearest bend.
And oh, look! Just behind it is yet another white swan!
And then another!
You, being a ponderous, scientific sort, notice a common theme. All of these swans are white. And because these are the first swans you’ve ever seen, it’s easy to formulate a little theory: all swans must be white.
Then, almost right on cue, a fourth swan turns up. Lo and behold, it’s also white. Well, that just proves it! This theory is quickly becoming fact.
But . . . hold on. How do you know a fifth swan won’t turn up that’s black? Or pink? It’s impossible to discount that possibility – however unlikely it is.
Oh, dear! And here you thought you were just going on a calm, uncomplicated walk in the sunshine. Yet unwittingly, now surrounded by this concerningly large number of swans, you’ve stumbled across one of the trickiest questions in twentieth-century philosophy.
How can we ever truly prove a theory to be correct?
Luckily, this Blink to Karl Popper’s philosophical classic, The Logic of Scientific Discovery, aims to solve this very question.
Be it white swans or any other hypotheses you’ve been brewing on the side, you’re about to find out why your theories might not be as airtight as you once thought.
Scientists should use deduction not induction, and aim to falsify – not prove – their theories.
Okay, to start with, let’s go back to those swans.
On your walk back from your riverside stroll, you get to thinking. How are you going to explain your new findings that all swans are white to the world?
It shouldn’t be too hard. The evidence is on your side. You took a limited and specific data set – four swans, in fact, practically a flock – and you drew a reasonable theory from it. Every swan you’ve seen has been white. So, therefore, it’s only natural, to theorize that all swans are white.
It’s airtight, surely even Popper would be on your side.
This is an example of inductive reasoning, or simply induction, and Popper opposes it strongly. The problem is that we’re using singular statements, like “This swan is white,” to prove universal statements, like “All swans are white.” Logically speaking, Popper argues this approach simply isn’t valid. It’s always possible that a black swan – or a pink one, or a yellow one – might have come swimming around that corner. That applies if you’ve seen four swans, or 40, or all the swans you can imagine. A black swan could always appear.
Here’s a question, though: What would happen if a black swan actually did turn up?
Well, that would disprove the theory that all swans were white. So there’s an asymmetry to the logic here: specific statements can’t prove universal ones, but they can disprove them.
That’s an important point when it comes to Popper’s preferred scientific method – known as deduction.
Rather than starting with specifics, deduction starts with universals and examines the relationships between them to see what other logical conclusions can be drawn. You might say, for instance, that all birds can fly, and also that swans are birds – and hence, you can deduce that swans can also fly.
That’s logically valid, Popper says, but that doesn’t mean it’s necessarily true. Rather, a good scientist would be constantly on the lookout for anything that goes against their hypothesis.
They’d be looking to falsify their own theories. For instance, if they found out about a nonflying bird like a penguin. That specific case falsifies the general statement that all birds can fly.
That shouldn’t be a disappointing result for a scientist: in fact, it should be exciting. It’s an intriguing new piece of information that will cause them to formulate a better, more accurate theory. Instead of “All birds can fly,” maybe it’s “All birds have wings.” And then, they’ll be looking everywhere for a bird with no wings to try and then falsify that statement.
In this way, falsifiability is a big deal for Popper. It’s even what he calls the criterion of demarcation: the simple fact that distinguishes science from nonscience. A statement is only scientifically valid, he says, if it can potentially be falsified. Otherwise, you’re not dealing with science at all, but rather with something much vaguer: metaphysics.
Deciding which theories to accept isn’t strictly logical.
There’s absolutely nothing wrong with saying “All swans are white” in the first place. The mistake is to think this is true simply because you’ve seen a few white swans on your local river. Instead, you have to accept that your statement that “All swans are white” is only a guess.
But, even then, we’re not out of the woods yet. That can still be picked apart by Popper. Because in order to still have that theory, guess or not, you have to think about how you even came up with that in the first place. How did you get the idea to suggest that all swans were white?
That might sound like a trivial question, but it’s not. Remember that Popper rejects induction very firmly: the existence of a few white swans isn’t enough to justify the general statement. So there isn’t actually any logical basis at all for coming up with a theory like your swan theory – or, for that matter, even more legitimate scientific theories like gravity, or relativity! It’s basically guesswork.
For Popper, coming up with a theory relies on a small but vital leap of faith, an act of imagination. He calls it psychologism – and it’s something logic simply can’t account for. And as such, it’s essentially outside the scope of what he discusses in his work: Popper’s concern is with the logical processes that you subject a theory to – in other words, all the stuff that happens after you’ve come up with a theory. But he happily accepts this moment of imagination as a crucial first step. We just have to remember that that’s all it is.
A slightly illogical leap of faith is also involved when it comes to deciding which theories to accept as true. We can’t use only our own experiences to decide what to accept, because that would be inductivism – instead, we simply have to make a decision.
It’s a bit like how a jury works in court. A jury is asked to determine what happened in a particular case. All it has to go on is the available evidence about the case, and a pre-existing set of rules – the law. A jury’s verdict is accepted as fact – but of course, if more evidence had come to light, they might have reached a different verdict. Is a jury’s verdict the actual truth? It’s probably more accurate to describe it as close as we can possibly get to it.
So, even though science aims for objectivity, it’s essentially like a jury’s verdict. It doesn’t really deal in absolutes – it just makes the best guesses it can, based on the evidence available.
Probability statements are of limited use to science.
For this next section, we’re going to deal with probability. Because when addressing the idea of statements being either true or false, it’s crucial to also factor in the role that probability might play in our reasoning.
Take a six-sided die, for example. Say you want to roll a six. Your probability of throwing a six is one in six. So, let’s pretend we roll a die 600 times? You’d likely end up with approximately 100 sixes – but would it be exactly that? Likely not. You might have, let’s say, 103 sixes rolled instead.
So should you revise your starting theory, and say that the probability of rolling a six is actually 103 out of 600? No, because our first statement was a numerical probability statement, calculated mathematically, rather than through experiment. Assuming the die is fair, the probability of throwing a six remains one in six. The previous 600 throws don’t affect that probability at all.
And what that means is crucial for Popper: probability statements are not falsifiable. Maybe if we could actually roll a die an infinite number of times, things would be different – but we can’t. We simply can’t truly put probability statements to the test.
What role do probabilities have in science, then? Popper, falsification fanboy that he is, says, not much. Most of the time, as they’re not falsifiable, they simply don’t have a role.
There are some occasions where probabilities really do have a role in theories – Brownian movement is one example, which is about how particles move in a fluid. That movement of liquid is somewhat random, so some deviations from average results are very much expected. But in a case like that, the variation becomes part of the theory itself – it’s hard-wired into the theory. So overall, a theory like that can, in fact, be falsified: it would be proved wrong if the results fell outside the window of acceptable outcomes. So, because it’s falsifiable, it then belongs in science.
Popper also makes another point about probability that throws a fascinating perspective on his views in general. What’s the difference, he asks, between predicting the orbits of the planets and predicting a throw of a die?
You’d probably respond that throwing the die is pure chance, whereas the planets move in a regular pattern. But Popper says that actually, the two scenarios are much more similar than you think.
Why? Because it’s all about initial conditions. We know the initial conditions in which the planets move very precisely through observations over many centuries. But precisely what movements go on inside someone’s fist as they shake a die? What are the exact properties of the surface they’re throwing onto? Throwing a die seems random, but only because we have such poor knowledge of the conditions. If we knew all that in detail, we’d be able to predict the outcome just as accurately as where Mars will be next Friday. And that would definitely help in a casino.
Popper disagreed with Heisenberg’s uncertainty principle.
There are some things, though, that we genuinely have no choice but to be uncertain about. At least, according to the physicist Werner Heisenberg.
In quantum mechanics, Heisenberg’s famous uncertainty principle is all about the limits of what we can know. At a subatomic level, the more accurately we know where a particle is, the less accurately we know its momentum. The most famous example of this is if we simply observe a particle at the subatomic level: this causes a small exchange of energy with the particle, which affects the way it behaves.
In other words, there really are hard limits on exactly what we can know. It’s not possible to continue getting more and more accurate in our measurements over time. It’s only ever a matter of approximation.
Given what you’ve already heard about Popper’s views on probability, it’s easy to see why he was uncomfortable with Heisenberg’s conclusions. Popper believed that scientists should be constantly modifying their theories to make them more and more accurate as they accumulate more information and knowledge – but Heisenberg says no, at a certain point that just isn’t possible.
To cut a long and complicated story short, Popper disagreed so adamantly with Heisenberg’s arguments, that in The Logic of Scientific Discovery he actually proposed an experiment designed to falsify Heisenberg’s uncertainty principle. But Popper’s efforts came in for criticism too, including from Albert Einstein. And, in later editions of his book, he modified his position on this.
It’s funny, really, when you stop to think about it – from one perspective, Popper and Heisenberg aren’t so far apart. What they have in common is an acceptance that it’s essentially impossible to know anything with 100 percent certainty. It’s just that, while for Heisenberg that puts a limit on what scientists can hope to achieve, Popper says scientists should never stop in their search for ever-greater accuracy.
Science isn’t about seeking truth – it’s about seeking ever greater accuracy.
For this last section, let’s zoom out a little, and think about what Popper’s ideas really mean. And let’s forget about swans this time – I think you’ve got the picture with those. So, here’s another scenario for you.
Let’s say, tomorrow morning, the sun doesn’t rise. It just stays dark all day. We’re assuming, for the purposes of this, that you don’t live in the Arctic circle where this is actually plausible – just imagine something happens that’s completely out of line with what you’d expect of the natural world.
Assuming all the scientists manage to find their way to the lab, what should they do?
It wouldn’t be enough simply to explain why, in this one instance, the sun hadn’t risen. The scientists would have to go right back to the drawing board and adjust all their existing theories about the way the world works in order to account for this one day’s peculiar events.
They’d need to find new scientific laws that explained not only the present but the past too – new laws that fit with all the evidence they had available.
That one day when the sun didn’t rise would be enough to falsify our current scientific theories. But remember, even once the scientists had made the necessary adjustments and come up with more accurate theories, every day that the sun either did or didn’t rise in accordance with those theories wouldn’t prove those theories to be true – because that would be inductive reasoning.
What those days would do is corroborate the theories – but that’s much weaker. It’s effectively just saying that there wouldn’t be any reason for the scientists to be concerned.
The moral of the story is that science is always uncertain and tentative. Science isn’t knowledge. It isn’t truth. It’s just as close as we can get to it. And when we encounter a result that falsifies what we think we already know, that’s something to get excited about – because it means we can come up with new theories that are ever so slightly better.
So what’s the aim of science, then? It isn’t to uncover absolute truth – because that’s impossible. And after all, it’s always possible that a black swan will come gliding down that river, or that the sun won’t rise tomorrow, and in that case, we’ll have to go back to the beginning and revise our theories from scratch.
The aim of science is simply to become ever more accurate: and to do it better each time.
Final summary
You’ve just listened to our blinks to The Logic of Scientific Discovery, by Karl Popper.
The key message in these blinks is that:
Scientists should aim to falsify their theories rather than verify them. In doing so, they can revise their theories and make them more accurate. It’s a mistake to think that science will ever uncover the absolute truth about how the world works. The aim should be to simply do a little bit better every time we learn something new.
To implement this into your daily life, here’s a quick piece of actionable advice to take with you:
Falsify your own opinions.
Popper’s focus is on dense and complex scientific topics like quantum mechanics – but really what he’s talking about is an attitude that can apply in far less academic situations too.
So next time you form an opinion about something – whether you’re scrolling through Twitter or listening to a podcast – don’t look for evidence that verifies your view, look for data that falsifies it. That way, rather than getting excited when you see yet another tweet that confirms what you already think, you’ll take an interest in something that challenges your views, and in doing so pushes you to find a better, more inclusive worldview.
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