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FALSIFICATIONISM UNFALSIFIED (A reply to “Why Popper Is Wrong on Induction” by Gene Callahan[1])


Falsificationism remains very far from commonsense. If there is a pons asinorum in epistemology, then maybe it is being able to understand falsificationism. Many otherwise bright people, including philosophers and logicians, have sometimes got hold of the wrong end of the stick and then used it to beat off anyone who has tried to explain this to them. I fear that Gene Callahan, an otherwise very able fellow, appears to fall into this category.

Callahan thinks that Popper’s “error turns on viewing falsification and confirmation as all or nothing affairs.” He asserts that this is refuted by the fact that “no theory is ever so thoroughly falsified that there is no way to rehabilitate it.” This is badly to misunderstand Popper’s epistemology. First I shall summarise the falsificationist epistemology.

Given that we do not have an omniscient god’s-eye view of the universe, we cannot, in principle, perceive the truth of universal propositions such as “All Swans are white” (where that includes all past, present and future swans). Neither could any finite number of observations of white swans (even if they could be guaranteed to be accurate, which they cannot) add any strength to the universal theory that they are all white: for the observations are, ex hypothesi, an infinitely small number relative to the universal theory. So we cannot even make our theories more probable (except on the basis of assumptions/conjectures about probability that cannot be shown to be independently probable). However, says Popper, nil desperandum. There is an asymmetry between verification and falsification. We could, in principle (though we might always be mistaken), perceive a single non-white swan. And if we in fact (as a matter of reality) do so then that fact would, as a logical implication, falsify the theory that all swans are white. Thus falsification is ultimately about the situational logic of us as finite epistemological beings. This situational-logical argument has to be understood and criticised first (it is not supposed to be an axiom or a dogma), before we proceed to the obvious next issue: how do we know that the apparent refutation is an actual refutation? That too remains a conjecture. We can also test that conjecture, but only by making assumptions that we do not attempt to test at the same time. It is the possibility of falsification that we use, not conclusive falsification. Ultimately, it is ‘conjectures all the way down’ (as opposed to turtles). Thus it is possible we are mistaken about any of our theories—but probably not all of them (that would require that all our theories are consistent with each other as well as themselves, which is very unlikely). There is no need to fall into scepticism, however. Where we know things—are aware of the way the world is—we simply realise this can only ultimately be by conjecture. But we do not need to doubt seriously any particular theory unless someone produces a cogent argument or evidence against it.

We can now return to Callahan’s suggestion that, “given an experimental result that apparently refutes a theory, one can always change an auxiliary hypothesis instead of the central tenet of the theory, and so rescue the theory.” Why should we do that unless we suspect that there is an error in the particular auxiliary hypothesis? We want to find the truth, and we know from Popper that conjecture and testing is the only way to proceed. So we ought to want to find genuine refutations if possible, not avoid them. But if we suspect they are not genuine then it would be folly to embrace them. We not only have to test our theories, we also have to test (or criticise) our tests. This, and the conjectural nature of all such tests, is often overlooked by critics of falsificationism. I should add that, strictly, it is also an error to think that a theory can have a “central tenet”. A theory says what it says and if any part is false then the whole theory is false.

On Copernicus I have my own interpretation, which I concede might differ from that of other falsificationists. Copernicus had the insight that if “the sphere of the stars was ten times farther from the earth than had previously been believed” then the observed lack of parallax is not a problem. This is a good criticism of the parallax test of heliocentrism (though he was, of course, also accepting the refutation of his heliocentric theory that, at least implicitly, supposed they were nearer). As, at the time, scientists had no way of knowing how far away the stars really were it would have been arbitrary to give priority to the first conjecture as to their distance just because it was the first. It was not ad hoc to produce a good criticism of that test. Coming up with our best criticisms of all our conjectures, including our tests, is part of the falsificationist method. All scientific theories have empirically unfalsifiable aspects. It was a consequence of Copernicus’s view at the time that it could not be empirically tested whether the stars were ten times further away than was thought. But the original conjecture is in exactly the same position. It was not empirically testable whether the stars were as near as thitherto supposed. So, again, it would have been arbitrary to give preference to the prior theory. Copernicus had shown that we have two unfalsified and, at the time, unfalsifiable theories (with respect to their disagreements, at least). There is nothing anti-falsificationist with Copernicus’s conjecturing that a heliocentric theory was the correct one. And though Copernicus’s theory did not simply knock out Ptolemy’s by its initial fit with the apparent facts, it is generally acknowledged that it had superior explanatory power and overall cohesion. (By parallel reasoning about the parallax effect, there is also nothing anti-falsificationist with Copernicus’s supposing that the stars might be even further away if better instruments still did not detect the change.)

Callahan thinks it is a big problem for “the Popperian” (the Popperian falsificationist, at least) that it was only after more accurate instruments were able to measure the parallax that “heliocentrism became scientific!” But not all theories are scientific in the sense of being empirically falsifiable. Moral, metaphysical and mathematical theories are not, for instance. When atomism was first proposed by pre-Socratic philosophers it was unscientific. Until we can find a way to test a theory empirically it is not scientific in this sense. So what? Does Callahan want to insist that the heliocentric theory must have been essentially scientific? Why? It does not much matter how we label things as long as we know what is really going on. Both the heliocentric and geocentric theories were not testable with respect to their differences. Thus far they were not scientific in the empirical sense. One might wish to say that they were part of ‘science’ more broadly conceived to include all the theories about the material world that are as yet, or currently, unfalsifiable (just as even falsifiable scientific theories have unfalsifiable aspects and assumptions). Thus much modern theoretical physics is currently unfalsifiable but is unproblematically called ‘science’ nevertheless. Such labels are of no theoretical significance.

We are then told that “[i]t is true that no theory is ever completely confirmed” and that “each piece of evidence supporting the theory raises the degree to which it is confirmed.” But it is not explained how, given an infinite theory and finite evidence it can possibly make any sense whatsoever to suppose that a theory could even begin to be confirmed. How, is it logically conceivable? Callahan ignores the fundamental epistemological arguments; and he even ignores the universal scientific theories they are primarily about. Instead, he alights on particular historical events to illustrate his point. But history is not science: history is about unique past events that cannot be replicated as science requires. However, falsificationism can still be applied to unique past events albeit with more difficulty. Callahan imagines that two historians tell us two different theories: “Caesar crossed the Rubicon in a deliberate act of defiance of the Roman Senate and constitution” and “King Arthur took on a dozen wives in order to cement diplomatic relationships with neighbouring kingdoms.” Callahan thinks all a falsificationist can say is that “neither theory has been falsified.” However, as the best evidence suggests that King Arthur never existed (and not that “no one is even sure if King Arthur was a real person”) then that would seem to falsify the second theory (even though that theory has nothing to do with science). Where is the “abundant, indeed, overwhelming evidence that leads us to believe the first historian’s theory”? I suspect that one or two written accounts, recorded well after the event by people not present, have merely been repeated. But even if we grant that there were dozens of eyewitness statements, so what? There are far more numerous and recent eyewitness accounts of ‘miracles’, ‘extraterrestrial abductions’ and so forth. In any case, how can the appearance of something even before our own eyes be any guarantee that it is what it appears to be? Even if we test it and can be sure our tests are infallible, we have only a finite number of tests of what is implicitly a theory with universal aspects—many being counterfactual—despite being an apparent ‘singular observation’.

So, again, how can a theory be “more or less confirmed”? How can “different degrees of belief ...[be]... scientifically founded” and “different pieces of evidence [...] offer varying degrees of confirmation for a theory”? Belief has nothing to do with science, in any case. Scientific theories can be stated objectively and any evidence against them is objective and can be replicated. It is not a scientific matter whether anyone believes a theory or with how much psychological certainty. Merely invoking the name of “Bayesianism” adds nothing here. Callahan’s title mentions “induction” and he eventually reaches the subject. But then Callahan’s entire explanation appears to be as follows: “The regularity of physical events, and therefore the ability to induce causes from effects, is not a conclusion of the physical sciences, but, rather, a premise of them.” Any falsificationist can agree that there are regularities in physical events and that particular regularities appear within theories as premises (i.e., as parts of the theory not presuppositions of it). But what does it mean to “induce causes from effects”? What is induction? Callahan nowhere explains it. Neither do I, but then I deny that it exists except as the erroneous thesis that singular occurrences can somehow support a universal theory. By contrast, falsificationism is a definite theory with definite arguments. They are not fiendishly difficult to follow, just somewhat counterintuitive given current commonsense.

It is quite confused of Callahan to think it is Popper’s “situational logic” (as I have called it) that has “supposedly demolished inductivism”. Induction had long been shown to be a fallacy for the simple reason that it goes beyond the evidence. David Hume (1711-1776) is the, relatively, modern person who rediscovered and emphasised the fallacy. But there are similar arguments going back many hundreds of years, most famously perhaps to Sextus Empiricus (writing some time in the second and third centuries CE). What Popper did, is show that we can, and must, use the hypothetico-deductive method instead. So we do not need to keep trying to make sense of induction. There is no role “induction plays in the physical sciences”.

Let us conclude with Callahan’s final point of “logic”. It is, in fact, a logical howler to suppose that “logic can never be employed to ‘refute’ premises”. If A entails ~A then the premise A is refuted. That is actually a theorem in logic (provable not hypothetically but as necessarily true). And where any premise entails inconsistent conclusions, that also refutes the premise. That is also a theorem. Moreover, we can never use logic to refute conclusions (though we might use it to show that they are not entailed). More relevantly here, however, if we state the inductivist assumption as ‘finite evidence can support universal theories’ then we can apparently use the same evidence to ‘support’ different theories that are inconsistent with each other. And this inconsistency therefore refutes the inductivist assumption that entails it.

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See Also:

Falsification Redux by Gene Callahan.