Falsificationism: No Redux without Dux

Many readers of Gene Callahan’s reply will have found it self-refuting. However, I have been persuaded that it is worth having another round of replies if only because Callahan’s responses are fairly typical of the would-be ‘inductivist’ and it might help some of those who have yet to see how these responses fail.[1]

Callahan states that “denying any validity to induction clears the way to a full-blown skepticism about the claim that science yields any genuine knowledge about the world we occupy.” But just because all knowledge, even a priori knowledge, remains ultimately conjectural (unsupported), does not mean that we cannot possess true theories about the world.[2] On the contrary, it is the person that demands an impossible epistemology who “clears the way to a full-blown skepticism...”.

Perhaps one “could join with most scientists and many philosophers in regarding reliance on induction as an essential aspect of how science moves closer and closer to the truth.” But no one would do that once they grasp that induction makes no sense. All induction is fundamentally “naļve”. Au fond, there is no logical difference between the simplest and the most complicated versions. How can there be such a thing as “supportive instances of a theory”? How can even “risky predictions” support? What is “inductive reasoning”? I ask because I want to know. Callahan gives us no actual explanation of what induction is and how it works.

Again, what is the repeatedly alleged “difference between naļve and sophisticated inductivism”? In what way, exactly, is Karl Popper “demonstrating his ignorance” by stating that the “fundamental doctrine which underlies all theories of induction is the doctrine of the primacy of repetitions”? Repetition must have primacy. Where would induction be without repetition? It would have only conjecture and testing. Thus it would be falsificationism. That self-styled ‘inductivists’ use falsification does not make falsification part of “sophisticated inductivism” nor does it make repetition not basic to inductivism. It is quite a piece of cheek (or confusion) to claim falsification as part of “sophisticated induction” that trumps the “primacy of repetition” (although this cheek goes back at least to Francis Bacon [1561-1626], with his “induction by elimination”).

Yes, “any verdict reached on the basis of the evidence available is fallible ... But that is no reason to conclude that juries never arrive at the correct verdict.” This is hardly a point against falsificationism. Of course, “jurors ... consider ... also whatever positive (confirming) evidence for the defendant's guilt or innocence was presented.” But, although there are some analogies, this is not the theory of science that Callahan is supposed to be discussing. How can we support a universal scientific theory with finite examples?

We are informed that “it is quite reasonable for a scientist to increase her confidence in her theory when she finds her experiments yield the results called for by it.” Her confidence is irrelevant. How can finite positive instances support an infinite universal theory? As a matter of logic, they cannot. But this lady scientist is not like a crude inductivist, “reasoning from the bare fact that every swan she has seen was white to the generalization that all swans are so”. Rather, we are told, “she believes, for instance, that she has discovered a genetic feature of swans that will always bring about white feathers, and, quite sensibly, she regards encountering thousands of swans, all of which are white, as evidence that she may be on to something.” This example is perfect. It perfectly demonstrates the nonsense that there is a real difference between “crude” and “sophisticated induction”. Consider:

1. All observed swans are white; therefore all swans are (probably) white.

2. All observed swans have a genetic feature that makes them white; therefore all swans (probably) have a genetic feature that makes them white.

There is no logical difference between these two arguments.

Callahan goes on to invite us to “notice” that, “in the latter case, discovering a black swan need not even be taken to falsify her theory ... she only needs to add the proviso ... ‘unless the swan has wildly abnormal genes.’” It is simply absurd to suggest that one can avoid falsification of a particular theory by changing it to a different theory. One could, of course, also do the same devious trick with the first theory; one “only needs to add the proviso ‘unless the swan is wildly abnormal.’”

“Boyle's conception of science” has nothing to do with explaining and defending induction. But it is even more perverse to try to apply it to a “rape trial” when we are supposed to be discussing universal scientific theories. Popper’s generalised epistemology of critical rationalism has applications outside of science, but that is simply not the topic under discussion. It can only complicate matters to muddle the two.

I repeat that it is no news that induction is a fallacy. It is no news that we cannot make any sense of it. The fact that some people still hanker after some form of induction is neither here nor there. To think it significant that many of them are prominent philosophers smacks of the fallacy of arguing from authority (though to call all of those on Callahan’s list ‘inductivists’ would be confused). So does citing philosophers who once apparently rejected induction but then later accepted it again. To repeat myself again, Popper’s “situational logic” (as I call the logical implications of our being finite observers in an infinite world; not that Popper used the expression this way) did not itself “demolish inductivism”. Rather, it showed what we have instead of induction. And it is indeed confused to think that 1. showing that induction does not make sense, and 2. showing what we have instead of induction, are the same thing. When Popper claimed to have “solved ... the problem of induction” he meant, as he went on to explain, just 2. I am happy to call 2 “a breakthrough on the topic of induction” as long as this is not misunderstood as conflating 1 and 2.

What is the point of “arguing that inductive inference, when employed sensibly, with caution and humility, has a valid role in the evaluation of scientific theories” when we are simply not told what inductive inference is and how it could be other than illogical? Callahan goes on to misunderstand corroboration when he states that “the best corroborated theory ... was the only rational means available for making predictions regarding future events falling within the scope of that current champion.” It is only ‘irrational’ (in a falsificationist sense) to use a falsified theory (if even then: Newton’s falsified theory is often still applied as sufficiently approximating the truth). The corroborated theory has no higher epistemological status than any unfalsified theory. While unfalsified theories are in principle infinite, we actually usually have only a handful of real competitor theories. Even if we do use the corroborated theory to make a prediction, that is not to assume it is known to be reliable. It is merely to use it. And we are not in any sense trying to “increase our belief” in a theory by testing it. Belief is a matter of personal psychology, not science.

How is it an analogy with a scientific theory, corroborated or otherwise, to state that “[c]hess is a rational pastime, but that doesn't imply that it is rational to use chess results to forecast the weather”? There is no theoretical connection between chess and the weather. And the same applies, mutatis mutandis, with Callahan’s ‘analogy’ about “Aristotle's system of logic”.

In response to Popper’s view that we should use scientific theories for our predictions, Callahan says he agrees with Wesley Salmon (without a reference) that “we could decide to read tea leaves or examine the inner organs of chickens instead.” But the theory that these have any connection with discovering the truth has been refuted, albeit mostly in an informal way perhaps. Those who really claimed to read them have been seen to be charlatans. Hence it is ‘irrational’ to use them.[3] And the same argument applies with the suggestion that unless we have “inductive inference” then “it is no less rational to consult an astrologer or palm reader than an engineer when designing a new bridge” (although this is clearly about technology and not science). Similarly, the theory that it is safe to leave a tall building by jumping down from high windows has been falsified. Most people take the stairs or the lift, the relative safety of which have not yet been falsified.

A more relevant general question could be to ask why we might prefer tested to untested theories in the realm of practical applications. And the simple answer is that with tested theories we have at least falsified the theory that they are always dangerous. But we have not done so with an untested theory. However, that is no guarantee that the tested theory really is safer. And testing itself never ends. In the realm of science, however, (which is what we are supposed to be discussing) we need not fear a theoretical error, because only the theory is at risk of being rejected—and even that is revisable. Au contraire, we want to seek out bold new theories in order to stand a chance of capturing interesting new truths. So we ought to behave quite differently than with immediate practical matters. Thus there is no reason to think that ‘corroboration’ is “the new name” for induction.

What of the charge that “falsification itself depends on inductive inferences”? In explanation of this we are told that our measurement could be in error, and we cannot “consider previous tests of the reliability of the measuring device” since this “clearly relies on inductive inference in extrapolating from the past performance of a device to the present case.”[4] The key error here is in implicitly requiring that falsifications be justified. Falsifications are themselves conjectures open to testing (but we cannot test all our conjectures at once). If someone doubts that some test is accurate, then he is welcome to try to test the test. It is not relevant to falsificationism that this might be difficult with measurement, as Callahan also claims, but that is a problem for those who want their theories supported. Unless the test can be faulted we are logically entitled to conjecture that it was indeed a falsification.

Callahan himself correctly states that “there is no possibility of testing all of our ideas at the same time”. But he incorrectly infers from this that tests “always rely on the past success of other theories as a valid indication of the confidence we can place in them”. We do not “rely” on other theories when doing our tests. We merely use those theories. We are not trying to justify our falsification. It is also an error to think that this means that we have a “choice as to which theory, among the multitude relevant to an experiment, a negative result should be taken as falsifying”. This is because, ex hypothesi, we are only testing one theory. And that theory is then—as a matter of logic—falsified (or not) by assuming the truth of the background theories. We can go on to test any background theory we like, of course. But that is where the choice lies, and not in changing the assumptions of the original test. It is hardly “arbitrary” to test the theory we were intending to test instead of switching to ‘testing’ another assumption instead (which is not only arbitrary but incoherent: the whole idea of a test vanishes).

In an infinite universe, that our universal scientific theories are probably false is not a sufficient reason to reject them. As conjecture is all we have to go on, we need evidence against a theory in order to rule it out. So to “suspect that there is an error in the particular auxiliary hypothesis” is, in the Popperian sense, not merely to suspect that it is false but to hope that one can find evidence against it. And, in any case, far from all auxiliary hypotheses will themselves be universal theories.

Yes, the falsificationist does not “count on the past as offering some basis for judging what he is now observing” and readily admits he “has no reason to suspect he might not be mistaken”. This is because observations are not justified or supported. They too are conjectures (and universal in some sense). So they are in court until we can find falsifying evidence. It might still be asked why some single observation, which is also fallible, ought to be regarded as falsifying the universal theory rather than the universal theory falsifying it. The answer is that we can never perceive all instantiations of a universal theory (e.g., see all possible swans being white), but we can and, ex hypothesi, do appear to see a single falsifying counter instance (a black swan) and one which, in science, withstands testing. Although logically allowed, it is scientifically perverse simply to assume the truth of an unobservable universal theory in order to falsify unproblematic observations. That is to engage in metaphysical dogmatism instead of empirical science.

Contra Kant and Callahan, science as such does not presuppose “the existence of regular causal forces in the universe”. Science is about trying to find out what there is in the universe. Randomness in most of it cannot be ruled out a priori. But even if there were “regular causal forces in the universe” without exception, that would have no relevance to anything Callahan has to say. We could still only detect them by conjecture and refutation. Popper would agree that “the fact that we often make mistakes does not imply that we never get it right.”

On Copernicus, Callahan thinks it a “peripheral error” when I state that “[a]s, 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.” Callahan thinks it was not arbitrary. He states that, according to the then standard theory, “the very essence of space made the existence of a vacuum impossible. Therefore, the sphere of the fixed stars had to be immediately beyond the far edge of the sphere of Saturn.” I do not see why being farther away entails a vacuum. Whatever is supposed to fill the space between Earth and the next planet could, presumably, fill the space between Saturn and the stars. In any case, that heliocentricism clashed with Aristotle’s “whole system” is not a problem for falsificationism. There is nothing wrong with contradicting incompatible theories that are “well corroborated”. Being well corroborated adds no strength to a theory. However, there were known to be severe problems with the Aristotelian system. Copernicus was, in fact, offering a bold alternative in an entirely Popperian way. That the new theory was not yet independently testable was unfortunate. Often, independent, testability comes with time; but it cannot come if we require it immediately for any theory ever to be considered. Popper stressed the importance of falsifiability in science but he did not anathematise theoretical physics where, independent, testing is not yet possible.

Callahan objects to this last point. He says the “whole point of [Popper’s] criterion was ... to sort out truly scientific theories from pseudo-scientific ones, such as Marxism and Freudianism.” So either the latter two theories are scientific after all or “we are forced back into the strange position of excluding Copernicanism from the realm of science until the 1800s.” First, it was only the distance to the stars that was untestable (which was also a problem shared with the earlier competing theory), not every aspect of Copernicanism was untestable. However, Callahan misses the real point here. Marxism and Freudianism, though aiming for truth, somehow aspired[5] to complete unfalsifiability (although, as many have observed, they failed and so are really scientific theories after all—and falsified ones). But Copernicus and modern theoretical physicists want to find tests for their theories. That they thus aspire, and often eventually succeed, makes it reasonable to say they are engaged in theoretical science rather than experimental science. So the Popperian criterion of falsifiability does still mark a crucial distinction. But what had started out as a way of demarcating theories as such evolved into demarcating the approach to theories.

As none of Callahan’s arguments is sound, his conclusion that summarises them is similarly unsound so I won’t comment on that summary further save for one point added to it. Callahan attempts to put the cherry on the cake when, in an argument from (the person he supposes to be my) authority, he claims that “in the end, even Popper agreed that his system contained ‘a whiff of induction.’” But Callahan fails to give a reference. As far as I can determine, the nearest Popper used something like this expression in print was just once: in the Library of Living Philosophers series edited by Paul Schillp, p.1192, note 165b. In fact, Popper put ‘whiff’ in inverted commas and referred to “inductivism” rather than “induction”. At worst, this singular and obscure instance is a small slip on Popper’s part. David Miller quotes this in his 1994 book, and explains why Popper was wrong to admit to even a “whiff”.[6] A minute or two on an internet search engine would refute the fanciful theory that I am the “only remaining Popperian who has not folded on this issue!”[7]

Finally, Callahan begs the question when he states that my warning about a high crime rate “only reflects past crimes.” It would reflect only past crimes if past crimes were all that were intended. Surely he understood that I implied an ongoing propensity to crime in that area, which is clearly a conjecture going beyond the evidence. How is that conjecture “an inductive inference”? Callahan does not know. He has no theory of induction. I am not inferring “from past incidence of crime in the area to the future incidence”[8] I am conjecturing ongoing causal factors that are responsible for crime. As that conjecture logically cannot be based on “the past prevalence of crime” then it is not based on it. Callahan is confusing evidence that is merely suggestive of a theory (it is a theory that anyone might first leap to in order to explain the phenomena), with evidence that somehow positively supports a theory. I urge him to pay more attention to the logic of the arguments. If he does this he may yet cross the bridge.

J C Lester (August 2005)

[1] My main reluctance is, as ever, that the cost to me is not writing on libertarian theory instead, which always has a strong moral aspect as well as the delight of new problems and issues. I cannot write to a standard that satisfies me at the speed that some others manage—though not always to a standard that satisfies me.

[2] And, as Popper observed, that a theory is false does not mean it cannot have verisimilitude. I know this idea has proven logically problematic, to put it mildly, but it makes intuitive sense to me in the same way that a description of a person can be more or less accurate.

[3] Though if tea-leaves or chicken-entrails readers were to start to be significantly successful in their predictions, then scientists might quite reasonably want to examine the evidence carefully.

[4] Strictly, induction is not about “extrapolating from the past... to the present” (or future) but about the logic of attempting to use known cases to infer unknown cases.

[5] I doubt they had unfalsifiability as an explicit aim; they were just muddled. A true theory ought not to be falsified and ought to explain all relevant phenomena. So it looked like all was well.

[6] Critical Rationalism: A Restatement and Defence, Open Court, 1994 (p.24 and p.47). I cannot recommend too highly David Miller’s work on this subject. See also his Out Of Error: Further Essays on Critical Rationalism, Ashgate, 2005.

[7] I am not really a “Popperian” (Popper had many philosophical theories and I don’t hold, or even know, all of them), although I am most certainly a critical rationalist.

[8] I am not even inferring ‘from known incidence of crime in the area to the unknown incidence’.