An epiphany around Induction vs Deduction

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.

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?

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.

Okay, to start with, let’s go back to those swans.

On your walk back from your riverside stroll (keeping work life aside else would have used on your way back from work) 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.

This is an example of inductive reasoning, or simply induction. 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, 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 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, 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. 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.