Irrefutable Yet False
On Popper and criticizing metaphysical theories
I
Popper is widely known, and lauded, for his theory of knowledge1. It goes something like this. Knowledge is not something we can prove through observation, it is something we arrive at through creative conjecture, proposing theories that are testable, and then testing them. By discarding those theories that fail our tests, we create good explanations of the world, even if we can never be sure whether they are objectively true.
Our ignorance is sobering and boundless. […] With each step forward, with each problem which we solve, we not only discover new and unsolved problems, but we also discover that where we believed that we were standing on firm and safe ground, all things are, in truth, insecure and in a state of flux.
One apparent consequence of Popper’s epistemology is that it is only rational to say that a theory is false if we are able to refute it. In Chapter 8 of Conjectures and Refutations, Popper makes the surprising argument that theories can be both irrefutable and false. In particular, metaphysical, or what he calls ‘philosophical’, theories. This seems strange; how can a rationalist like Popper argue that a theory which is impossible to refute is false? If one cannot refute it, how can one prove it false?
To make his case, Popper distinguishes between two types of irrefutability: logical irrefutability and empirical irrefutability.
A theory is logically irrefutable simply if it is consistent, that is, it doesn’t contradict itself. In logical terms, you shouldn’t be able to derive both proposition P and its negation ¬P from the theory’s axioms using valid inference rules. “All eagles are green” is a logically irrefutable statement.
A theory is empirically irrefutable if it is consistent with every possible observation in the world. An example might be weak financial commentary: “stocks went up today because [x], stocks fell yesterday because [y]”. If we can bend the theory to fit the evidence, it is empirically irrefutable.
It’s clear that a theory or statement can be logically irrefutable and false. Popper’s example of two such statements are “Today is Monday” and “Today is not Monday”. Both statements are logically irrefutable, and at least one must be false. Therefore, a statement can be both logically irrefutable and false.
Empirically irrefutable and false statements are a little trickier. Popper uses strict or “pure existential” statements as examples. A strict statement is of the form (using Popper’s example):
There exists a pearl which is ten times larger than the next largest pearl.
This statement is empirically irrefutable because it is unrestricted; it does not refer to any one time and space, but to the entire universe. It is impossible to carry out an exhaustive search for such a pearl, so the statement cannot be refuted by observation.
Importantly, says Popper, we cannot prove that this statement is false. But it is much more reasonable to assume that such a pearl does not exist.
This is where I think Popper’s line of argument becomes a little weaker. The empirically irrefutable example, ‘more reasonable to assume as false’, is not as strong as the logically irrefutable and false example. His explanation is less like a proof and a bit more hand-wavy to arrive at his desired conclusion.
II
Having shown that theories can be both irrefutable and false, Popper sets up the main aim of the chapter: to demonstrate that all metaphysical theories are irrefutable, but many are false.
Popper uses five metaphysical theories to make this point, all of which he believes to be both irrefutable and false:
Determinism: Kant’s doctrine that full knowledge of our psychological and physiological conditions and the environment would make it possible to predict perfectly our future behaviour;
Idealism: Sensations are all that is real, or “The world is my dream” (Hume, Berkeley, Schopenhauer);
Irrationalism: Kant tells us that human reason cannot grasp the world of things-in-themselves, so we must resort to irrational means. This is supposed to work because we are ourselves things-in-themselves, so by gaining intimate knowledge of ourselves through literature, poetry, introspection we can understand what things-in-themselves are like.
Voluntarism: We can know things-in-themselves through our own volitions. Since we as things-in-themselves are will, then will must be the thing-in-itself, and the world is will (Schopenhauer);
Nihilism: Through our boredom we realise the thing-in-itself is nothingness.
Popper chose these theories specifically because he thinks they are false. In his words:
To put it more precisely; I am first of all an indeterminist, secondly a realist, thirdly a rationalist. As regards my fourth and fifth examples, I gladly admit - with Kant and other critical rationalists - that we cannot possess anything like full knowledge of the real world with its infinite richness and beauty. Neither physics nor any other science can help us to this end. Yet I am sure the voluntarist formula, ‘The world is will’, cannot help us either. As to our nihilists and existentialists who bore themselves (and perhaps others), I can only pity them. They must be blind or deaf, poor things, for they speak of the world like a blind man of Perugino’s colours or a deaf man of Mozart’s music.
[…]
Although I consider each one of these five theories to be false, I am nevertheless convinced that each of them is irrefutable.
Popper defines metaphysical theories as non-empirical, and therefore irrefutable by definition. (The possibility of empirical refutation is what, he says, distinguishes scientific statements from non-empirical ones). But if all metaphysical theories are irrefutable, how are we ever to distinguish between which are true and which are false?
There are three types of theories we can ask whether are true or false. Mathematical or logical theories, empirical or scientific theories and philosophical or metaphysical theories. How do we show whether each is true or false?
The first case, mathematical theories, is the simplest. If we do not know whether a mathematical theory is true or false, we can try to refute it, or to prove its negation, using mathematical or logical arguments.
The second case is an extension of the first. The difference is we can now use empirical observations in our goal to refute the theory. As Popper puts it, “Critical thought as such remains our main instrument.”
The challenge with the third case is how to critically examine an irrefutable philosophical statement. What even is a critical discussion on the truthiness of a statement if not an attempt to refute it?
Popper’s answer to this question is that each theory must be discussed in the context of the problem it is trying to solve. A theory without connections to the world cannot be critically discussed, regardless of whether it is philosophical or empirical.
We must study its connection to the problem it is trying to solve, or “look upon a theory as a proposed solution to a set of problems.” This approach opens the theory up to critical examination, even if the theory itself is irrefutable.
For we can not ask questions such as: Does it solve the problem? Does it solve it better than other theories? Has it perhaps merely shifted the problem? Is the solution simple? Is it fruitful? Does it perhaps contradict other philosophical theories needed for solving other problems?
III
From this starting point, Popper can now explain why he believes each of the five philosophical theories above to be false as well as irrefutable. He must understand the problem situation that created such metaphysical theories. A theory’s merit depends on whether the problem it is addressing is genuine.
This allows us to sidestep tackling the irrefutable theories head-on, which would of course be futile. Instead, we focus upstream of the theory, on the problem that led to its conjecture as a solution. If the problem is unreasonable, unnecessary, or invalid, then there is little need for the theory, whether or not we can directly refute it.
Let’s start with idealism. Berkeley and Hume arrived at idealism as a result of their sensualistic theory of knowledge. They believed that knowledge is built of sense impressions and links between memory images. Popper points out that we have better theories of knowledge than this sensualistic one, and so the problem that brought about idealism is not really a problem in need of addressing at all. With that, he concludes idealism—an irrefutable metaphysical theory—is false.
Similarly with Kant’s determinism. Kant himself held a longstanding internal conflict: he rationally believed in determinism as a consequence of Newton’s theories, but also believed man is a moral being and thus undetermined. Again, considering the problem situation: does determinism actually follow from Newton’s laws?2 If it doesn’t, there is little need to adopt determinism.
Similar arguments can be made for the theories of irrationalism, voluntarism and nihilism. In each case, once we question the problem situation, the problem itself seems to disappear, and the proposed and irrefutable theory with it.
I am quite sure that Popper’s theory of knowledge is true (although of course I can never know if it is objectively true). But it is often used to justify only refutable theories, disregarding theories that are irrefutable as irrelevant. Here, Popper shows that there is no link between the irrefutability of a theory and its truthiness within his epistemological framework.
Popper is less often praised for his writing. I didn’t fully appreciate the clarify of his writing and thought until reading him directly, ironically after trying to read his less clear contemporary and sometime rival, Wittgenstein.
Popper argues in Chapter 6 of his *Objective Knowledge that no, it does not.