Thoughts on Falsifiability and Popper

(Editorial: Please note that in this article on falsifiability, I use the phrases “science”, “sciences” and the like. Unless otherwise noted, I am talking about the “empirical” or “physical” sciences such as physics, chemistry and biology.

And not sciences such as mathematics and philosophy.

However, much of the same logic applies to those other sciences as well.

Also, I am not attacking the idea of falsifying a theory as such. I am discussing Popper’s philosophy of how falsification is the essence of science.)

Falsifiability is a problem to a “central problem” in the philosophy of science developed by Karl Popper. Popper was a philosopher of science and closely associated with the influential Vienna Circle.

According to Popper, the central problem in the philosophy of science is demarcation. The problem of demarcation is that of distinguishing between science and non-science.

In Popper’s own words:

The problem of finding a criterion which would enable us to distinguish between the empirical sciences on the one hand, and mathematics and logic as well as ‘metaphysical’ systems on the other, I call the problem of demarcation.

Karl Popper, The Logic of Scientific Discovery

In other words, the problem of demarcation is how to distinguish between science and what Popper considered to be non-scientific. Things such a metaphysics and logic.

Karl Popper proposed falsifiability as the solution to this problem.

It can be summed up as:

[S]tatements or systems of statements, in order to be ranked as scientific, must be capable of conflicting with possible, or conceivable observations.

Hansson, Sven Ove (2008). Zalta, Edward N. (ed.). “Science and Pseudo-Science”. The Stanford Encyclopedia of Philosophy (Fall 2008 ed.). 4.2 Falsificationism.

Popper accepted the Humean critique of induction and goes further.

We can briefly sum up Hume’s critique of induction with this quote:

From causes which appear similar we expect similar effects. This is the sum of all our experimental conclusions. Now it seems evident that, if this conclusion were formed by reason, it would be as perfect at first, and upon one instance, as after ever so long a course of experience. But the case is far otherwise. Nothing so like as eggs; yet no one, on account of this appearing similarity, expects the same taste and relish in all of them.

It is only after a long course of uniform experiments in any kind, that we attain a firm reliance and security with regard to a particular event. Now where is that process of reasoning which, from one instance, draws a conclusion, so different from that which it infers from a hundred instances that are nowise different from that single one? This question I propose as much for the sake of information, as with an intention of raising difficulties. I cannot find, I cannot imagine any such reasoning.

David Hume, An Enquiry Concerning Human Understanding, 4. Sceptical doubts concerning the operations of the understanding

Popper agreed with Hume that it is logically impossible to conclusively verify a universal proposition by reference to experience.

After all, in his view, it is easy to say that all swans are white. But you have no way to know this simply by observation.

All it would take, according to Popper, is a single counter-example to falsify the induction.

Of course, it would be baseless to assume that all swans are white and call that a valid induction. Why would we assume that? That is not how valid inductions works…

…The answer to this problem is: as implied by Hume, we certainly are not justified in reasoning from an instance to the truth of the corresponding law. But to this negative result a second result, equally negative, may be added: we are justified in reasoning from a counter-instance to the falsity of the corresponding universal law (that is, of any law of which it is a counter-instance). Or in other words, from a purely logical point of view, the acceptance of one counter-instance to ‘All swans are white’ implies the falsity of the law ‘All swans are white’ – that law, that is, whose counter-instance we accepted. Induction is logically invalid…

Karl Popper, The Logic of Scientific Discovery, Ch. 1 “A Survey of Some Fundamental Problems”, Section I: The Problem of Induction p. 27

He, therefore, rejects the validity of induction and insists that science does not use it. Instead, he argues that science consists of problem-solving.

But, in practice, as we shall see, this consists of producing theoretical bowling pins which you then spend your time trying to knock over.

Popper did not understand the importance of induction.

He seemed to equate induction with making an arbitrary generalization from observation and thus making unsupported universal statements.

It is therefore consistent that Popper insisted that you cannot prove a theory true by showing that it agrees with observation.

If you cannot make inductions in science, then you cannot generalize from experimental observation and form conclusions about the phenomena you are studying.

For instance, suppose you are Newton and you have the hypothesis that there is some force which attracts objects towards one another. How might you prove that this is the case?

You might observe the way Mars moves around the Sun. And the way the Moon moves around the Earth. And induce that they have similar behaviours which can be explained by the same inverse square law.

But, according to Popper science does not work by induction.

So, you are not meant to generalize from observations and form generalizations about instances/things you have not observed.

How then are you meant to show that your hypothesis about attractive forces is valid? If you cannot reason from the observed and generalize from observations to general principles, how do you validate your theories?

Well, this indeed means that you have no way to do so. So, yes, if Popper was right about science not using induction, then it would seem reasonable to believe that science cannot show anything to be true.

Induction is not how science works huh? Tell the classical physicists that then. Because Newton and others were masters of induction …

You can, however, according to Popper, disprove a theory by showing that it contradicts with observation. He believed that you can never prove a theory to be true since you might disprove it tomorrow!

So, if you take all this to its logical conclusion, then according to Popper you can never be sure that any given theory is right.

A conclusion Popper seems to have agreed with:

What we should do, I suggest, is to give up the idea of ultimate sources of knowledge, and admit that all knowledge is human; that it is mixed with our errors, our prejudices, our dreams, and our hopes; that all we can do is to grope for truth even though it be beyond our reach.

Karl, Popper, Conjectures and Refutations: The Growth of Scientific Knowledge

Indeed, according to Popper, the quest for any particular nugget of scientific truth is never-ending, further implying we can never hope to find it:

The game of science is, in principle, without end. He who decides one day that scientific statements do not call for any further test, and that they can be regarded as finally verified, retires from the game.

Karl Popper, The Logic of Scientific Discovery, 11 Methodological Rules as Conventions

So much for certainty in science then. Or knowing anything.

If we cannot be certain that a theory is true, then how are we to assess the worth of a theory?

Is Falsifiability the Main Criteria to Assess a Theory?

According to the philosopher of science, Richard Dawe, it certainly is an important one.

“Physicists have long relied on a notion advanced by philosopher Karl Popper, that a theory is scientifically valid if it is falsifiable.”

Richard Dawe, “Philosophers Want to Know Why Physicists Believe Theories They Can’t Prove”

Indeed, it is widely accepted that for a theory to be accepted as true, it must be possible to test the theory and show that the theory is falsifiable.

Generally, I do not consider the issue of falsification to be the essential issue when it comes to testing a theory. And this is not widely considered the central issue, not to the extent Popper advocated.

Let us further explore why I do not think this is the central issue Popper makes it out to be.

Yes, a theory needs to be tested. It should be possible to show that the observable facts of reality are consistent with the theory. One needs to demonstrate that the observable facts lead one inexorably to that theory.

One should try to prove that the theory in question and only that theory is the logical implication of the observable facts of reality.

If the theory is not consistent with the facts, it should be possible to show that the theory is false.

It is important to be able to show that a given theory is false. But if a theory is false, then it would be nice if the experiment was designed so that this could be determined.

Take the Michelson-Morley experiment. This was intended to detect the presence of a luminiferous aether. It was so designed that if there was not one, then the experiment would indicate this.

In other words, this experiment was designed so that the existence of the aether could be falsified.

Generally, the focus of science is not on trying to show a theory to be false. Generally, the point is rigorously making observation and seeing what they imply about the validity of the theory.

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