C.D. Broad, a 20th century British philosopher, once said, “Induction is the glory of science and the scandal of philosophy.” Induction, as we recall, is essentially reasoning from patterns. Given that something’s happened in the past, we think it will happen in the future. So, for instance, you believe that the sun will rise tomorrow because it’s risen in the past. If you lived on some planet where that wasn’t true, like a non-rotating planet, you would not have that same belief. Deduction, by contrast, is reasoning by definitions. Aristotle’s syllogisms are famous examples of these, but there are more complex examples, including much of math. For instance, no matter what planet you lived on, you’d still believe in the Pythagorean theorem.

Induction is the glory of science because it’s what most of science is based on. Our earliest science was a primitive sort of induction, in which our reasoning from patterns was careless. That’s how the Aztecs ended up believing that they needed to sacrifice people to keep the universe from collapsing, because they saw the pattern that they sacrificed people and the universe didn’t collapse, so assumed a necessary connection. Later on, philosophers like Francis Bacon helped us get more careful with reasoning from patterns, warning us about “idols” which can prevent us from properly reasoning. Science then split from philosophy and developed its own standards of proof, including double-blind studies and statistical analysis.

However, no matter how far science advances, it always relies on induction. Every prediction we make about the world relies on the idea that there are necessary connections. The law of gravity, for instance, supposes that every object obeys the law of gravity, and we assume that because that’s been true so far. However, we don’t have any proof. It’s entirely possible that beachballs, when painted neon yellow, do not obey the law of gravity. We assume they do because that would be a strange and inexplicable exception to our pattern of gravity. However, if tomorrow we find out that neon yellow beachballs do not obey the law of gravity, it’s the law that will have to change, not the beachballs.

Induction is the scandal of philosophy because, in the end, it’s impossible to prove outside of induction. Let’s go back through Hume’s critique so we have a good idea of why this is. Say you took a sip of tea, and burned your tongue. You say, “the tea burned my tongue”, or “the hot tea caused the burn on my tongue.”

Hume disagrees with you. He tells you that you only believe that because the two happened almost simultaneously, but there’s no necessary connection. You respond that every time you’ve taken a sip of hot tea, you’ve burned your tongue, therefore there is a necessary connection. He disagrees, and says that he doesn’t believe you can assume that.

You respond that everything works that way. You’ve formed all of your beliefs by patterns like hot tea burning your tongue, and this is why you’ve been able to avoid repeating other stupid mistakes, like that time you stuck a fork in the toaster. Hume responds like this: “So, you’re reasoning from the pattern that you’ve successfully formed beliefs in the past by reasoning from patterns? Sounds pretty circular to me.”

That’s the essential critique. Now, we can dress it up in fancy ways, and add words like probably, or statistically significant, and it seems that those methods work better than just guessing from patterns. We can even add theories and equations, which try to explain why certain patterns hold up better than others in predicting the future. But, in the end, the only proof of those methods being better is that they’ve been better in the past. In other words, we can only prove based on the pattern, or prove via induction.

Hume’s response to his own critique was that this is why philosophy should only be done for fun. Scientists, on the other hand, have mostly ignored Hume’s critique, and it’s very rarely taught in science classes, even when students learn the scientific method. Philosophers, of course, love it, and have taught it to their own students for centuries. But nobody ever really tried to solve it, or thought of it as something to be solved.

Until a philosopher came along: an Austrian Jew who escaped the Holocaust to become a philosophy professor in England. No, not Ludwig Wittgenstein, although that description fits him perfectly. It was Karl Popper, who, ironically, considered Wittgenstein his mortal enemy. Popper took the critique of induction very seriously, and was bothered that scientists had ignored it. After all, it seemed to attack the foundations of what they believed.

Now Popper was a big believer in science. During his lifetime, Freud and Einstein both rose to prominence. Both were taken equally seriously as innovators of a new sort of science; Freud as the innovator of psychoanalysis, and Einstein as an innovator in physics. But Popper thought this was unjustified. In Popper’s eyes, Freud’s theories were much less trustworthy than Einstein’s. The question was how he could prove that.

What Popper came up with was the theory of falsificationism. In short, a good scientific theory should result in unlikely predictions. The test of a scientific theory is if the predictions are confirmed or not. Einstein’s theories, for instance, were confirmed by the observations of Sir Arthur Eddington. This was especially nice because Einstein’s predictions weren’t just unlikely, but actually went against the predictions of the dominant theory in physics at the time, Newton’s physics.

Freud’s theories, by contrast, were not falsifiable. As Popper saw it, any action could be explained by Freud’s theories. If a man killed someone, Freud could explain it. If that same man then saved someone’s life, Freud could explain that. Therefore, no matter what a man did, Freud was never wrong, which meant his theories were not scientific. It’s important to note that Popper didn’t think they were necessarily useless, but he did think that meant they weren’t science.

Now, there are good parts and bad parts to Popper’s theory of science, here. The good part is that we avoid the problems of the Aztecs. If we focus on proving a theory false, instead of proving it right, we’d never end up in a situation where we think that human sacrifice is necessary to keep the universe from collapsing. Presumably, the first time we don’t sacrifice a human and the universe doesn’t collapse, we realize the fault in our theory (assuming we’re bold enough to do so).

We can also avoid a lot of the idols of Bacon. Many of them revolve around the fact that we often want certain hypotheses to be true, and we’re willing to twist the evidence to “prove” ourselves right. If we’re focusing on proving ourselves wrong, instead of proving ourselves right, we will hopefully avoid twisting the evidence or the experiment.

However, Popper’s original purpose was to avoid Hume’s critique of induction, and to that extent, he fails. Hume’s critique relies on never knowing if a connection is necessary, or just coincidence. However, if we try to prove a theory wrong, like Popper wants us to, we can never know if we really proved it wrong, or if an unknown factor made it look like it was wrong. For instance, we might drop a balloon, watch it float up, and think we disproved gravity, never realizing that we just didn’t know about buoyancy.

There’s also the problem of coming up with theories in the first place. There’s an infinite number of possible ways to explain anything, and Popper can cross some of them out, but they can’t tell us which ones to choose to test, given a limited time frame. For those we need something else, and it’s probably going to be a theory of induction.

Finally, not all of science can be tested so easily as Popper wants. Physics was an easy example for Popper to use, but it took a couple years for Einstein to be proven right by Arthur Eddington. If we had waited to called Darwin’s evolution science, then there’s no telling how long we would have had to wait. We needed to employ different methods of proof, involving the explanatory power of the theory and the number of assumptions needed. Popper never really considered this.

Popper provides us with a new and useful way of thinking about science, and makes a valiant and somewhat successful attempt to reunify science and philosophy. He doesn’t come up with the grand theory of science that he thinks he does, but he provides us with an excellent example of how science should be in certain circumstances.

Other philosophers, most notably Thomas Kuhn, talk about how science should be in other circumstances. More importantly, they describe how science is actually done, which is something that Popper neglects completely. Popper, much like Aristotle, assumed that the world comported itself to his theories, and saw no need to falsify this assumption.

What is the next leap forward in the philosophy of science? Well, to my mind, it has to something about integrating enormous amounts of data. I was trained in geosciences, and the current problem in that field is that there’s too much data and a million different ways to read it. It’s a problem that someone like Bacon would have loved to have, but it’s still a problem, and the field regularly gets roiled by competing data sets and drastically different conclusions. Who knows, perhaps the next philosopher of science will be you!