Have you ever heard of "Clever Hans," the famous counting horse? A marvel of his time, said to be able to solve arithmetic problems by stamping his hoof. Experts were commisioned to investigate the case in 1904 and concluded that the horse was indeed euipped with mathematical capabilities, and professor Mobius, Director of the Zoological Muusem in Berlin, claimed that the horse possessed “real mental work”.

It turned out, his abilities were not quite as miraculous as they seemed; Hans was just picking up on subtle cues from his trainer, without any real understanding of the math involved. What appears to be a miracle (a horse performing complex mathematical operations) happens to be mundane, coincidental, lucky.

In the same way, scientific realists are pulling an arithmetic horse out of their hat with the 'no miracles argument’ when they claim that predictive success represents ‘reality as it is’, when it could merely be a metaphorical arithmetic horse. The inference from ‘predictive success’ to ‘truth’ is, in other words, an erroneous one. In this article, I explore how the case of Clever Hans can help us understand the limitations of the no miracles argument, and why we should be cautious about making the leap from ‘scientific theories are useful’ to ‘they correspond to reality’.

The Success of the Sciences

The sciences are neat tools for predicting and controlling the environment. The diverse methods sometimes work, and with luck, make our lives richer (though they sometimes do the opposite—most of it is in military research, i.e. where the money is at).

It happens that when scientists have postulated the existence of unobservable phenomena like atoms and molecules that this has tended to generate predictive success. But do those unobservables really exist in virtue of this success? And do scientific theories represent the word accurately as it is, such that Newtonian mechanics is not just more useful than Aristotelian physics, and Einstein’s theory of relativity more useful than Newtonian mechanics, but more useful because they are True, ontologically speaking? Or does a theory simply working well at doing its pre-assigned job (predicting) have no logical bearing on the ontological nature of the phenomena it describes?

Many philosophers of science who are ‘scientific realists’ think that the success of science makes it more likely that unobservables really do exist and that scientific descriptions pick out objects in the world as they are. This idea is presented in the ‘no miracles argument’ in favour of scientific realism which holds that the best explanation of the success of the sciences, without postulating a miracle, is if scientific theories, including their descriptions of unobservables, are true.

A Pragmatist Response to the No Miracles Argument

But the word ‘true’ does a lot of heavy lifting here. The argument presupposes an account of truth as correspondence, such that our best scientific theories correspond to an independent ‘reality’. In other words, the debate between realists and anti-realists is interesting only if you care about whether ‘unobservables’ really exist and whether our descriptions of them represent reality accurately. It is a debate about ontology which a pragmatist like myself would much rather drop.

To a pragmatist who doesn’t know how to make sense of the phrase ‘represents Reality’ it seems like an irrelevant debate. What seems to work is mostly reducible to truth; truth and usefulness are mostly coextensive. So the argument, then, turns out to be trivial; duh, what works is true, and what’s true is what works, if we strip the word ‘true’ from its metaphysical connotations. Scientific theories are true, but so are Shaman rituals, so long as they both work to produce a desirable effect. Are there unobservables? What’s the point of that question, the pragmatist asks, so long as statement which posit unobservables are useful in the long term, generate predictive and explanatory success etc., but the predictive and explanatory success of a statement has no bearing on its ontological status—indeed a pragmatist would like to abjure the very idea of ‘ontological status’. This is not an instrumentalist approach where, for e.g., quarks are ‘useful heuristic fictions’ or ‘mere posits’; but rather quarks, to pragmatists, are just as real as chairs, but they merely add that quark-talk and chair-talk and shaman ritual-talk are all ultimately explicable in terms of human interests, desires, and goals, instead of their relation with an independent ‘Reality’, (and therefore shaman ritual-talk and quark-talk need not conflict because they do not index ‘What Is Anyway Really There’: shaman ritual-talk may serve different human goals than quark-talk does).

The alternative in which an authority ‘reality’ or ‘truth’ decides whether to adopt a certain theory rather than another one will always be superfluous table thumping, since, as long as there is disagreement about what the purported authority says, the idea of “authority” is out of place; when there are differing views, it's more fruitful to consider which view is most useful or productive in a given context, rather than trying to definitively establish which one is 'true' in a metaphysical sense.

Also, the no miracles argument assumes that predictive success is a criteria for truth without providing an epistemic reason to prefer this to alternatives. But this is clearly question begging; why should vocabularies that generate predictions be any closer to truth, than, say, vocabularies that generate aesthetic pleasure or world peace? Certainly science is not successful at generating the latter. In this sense, there is nothing interesting or informative being said when scientific realists proclaim that scientific theories are true; its a mere table thumping move, since the criteria for what counts as true (in this case predictive success) will always be indexed to the appraiser (in this case, scientific realists).

Alternatively one can also concede that science has been successful but that this is due to a miracle, while affirming a metaphysical view that accommodates miracles. Or one can circumvent the argument by just endorsing global scepticism—or even more radical, trivialism!

Is Science a Clever Horse or a Trick?

Another way of objecting to the no miracles argument is not by showing that it’s trivial or rejecting the argument’s other presuppositions, but by internally critiquing the view against its own metaphysical presupposition. One way philosophers have done this is to say that it commits a base rate fallacy. In other words, we can use the base rate fallacy to show that scientific realism fails to meet its own criteria for truth.

Though the example I provided of the arithmetic horse Clever Hans works to demonstrate this fallacy, it also presents a novel objection to the argument by showing that explanations of success are not dichotomous between miracles and truth as an isomorphic ‘correspondence to reality’; something consistently working might seem miraculous but can be explained, after the fact, by means of coincidences, tricks, observational biases, overfitting of data or sheer luck. The inference from predictive success to metaphysically substantive truth is simply a chimera.

Clever Hans performed in a circus during the early 20th century. The trainer would ask him questions such as "If the eighth day of the month comes on a Tuesday, what is the date of the following Friday?" and Hans would answer by tapping his hoof eleven times. He apparently knew how to add, subtract, divide, multiply and work with fractions.

Suppose you go watch the performance. Marvellous dexterity, a clever horse, you think to yourself. Greatly impressed, you decide to watch it again, and three times, maybe ten, twenty! The horse fails once during twenty attendances, but only once. So you conclude that Clever Hans successfully performs 95% of the time. It confirms to you that the best explanation for the success of the performance is that it must be the case that this horse is just a special kind of horse in that it knows how to calculate, almost like a miracle!

Science By way of Tricks

The 'no miracles argument' for scientific realism is based on the idea that, since scientific theories successively make accurate predictions, this seems to suggest that there is some sort of deep, underlying connection between the theory, including the entities it describes, and the intrinsic nature of the world - a connection that is not immediately apparent but is nevertheless real. It would be quite surprising that these descriptions that postulate the existence of different entities and end up predicting future states of affairs are not true in the sense of accurately corresponding to an independent reality, and that they rather just miraculously somehow work to do this.

The Case of Clever Hans provides a powerful illustration of how something that appears to be miraculous can actually have a very mundane explanation and of how we can be deceived by apparent correlations. When Hans performs successfully, does it mean that he knows how to count?

The answer is no. It could just be the case that when he does perform successfully, he does so by accident. In other words, it could be a false positive; that Hans is reacting to the specific subtle motions of the trainer, who, by chance and unbeknownst to himself, happened to tense up and finally relax once the tapping reaches the answer, such that, the times where the trainer didn’t know the answer, the horse didn’t also.

By the same token, the sciences make a promissory note that their research programs will continue to be successful in the future, and scientific realists maintain that this success is not some kind of useful trick that works but does not track how things anyway are, but it rather reveals to us the intrinsic nature of the world. But there is no reason to accept this assumption, our best scientific theories might just be useful fictions that work coincidentally, playing a kind of trick.

The miracle—intrinsic nature of the world dichotomy, is a false dichotomy since it is always possible that a scientific theory might appear to be successful but is actually based on something much more mundane, like biases in our observational methods, or making use of some sort of trick or shortcut that is not immediately apparent, or relying on certain simplifications or idealisations that only hold under certain conditions. This would mean that the theory is not actually a reflection of the underlying structure of the world, but rather a product of our own ingenuity. This is particularly relevant in cases where the phenomena being studied are complex and difficult to observe directly, as in the case of quantum mechanics or string theory.

Consider the kinetic theory of gases. This theory assumes that gases are made up of a large number of tiny, independent particles in random motion. Based on this assumption, the theory can make accurate predictions about the behaviour of gases, such as their pressure, temperature, and volume. But the theory's assumptions are not strictly true. In reality, gases are not made up of independent particles in random motion - they are made up of molecules that interact with each other in complex ways. The kinetic theory of gases is therefore a simplification, or a useful fiction, that allows us to make accurate predictions about the behaviours of gases without having to account for all of the complexities of molecular interactions.

In the case of Newtonian mechanics, the theory works well for predicting the motions of large bodies in our everyday experience, but it breaks down when we consider the motions of very small particles or objects moving at high speeds. This is because Newtonian mechanics assumes that the laws of physics are the same for all observers and that time and space are absolute and unchanging. We still use Newtonian mechanics to launch things into space because its simpler but we now know that these assumptions are not strictly true, and that the laws of physics change under certain conditions (such as in the theory of relativity).

In the case of quantum mechanics, the theory uses idealisations such as the wave-particle duality and the uncertainty principle to generate successful predictions, but these idealisations do not reflect a literal or accurate ‘representation of the world’ (whatever that means). They are simply useful tools for making predictions and calculations.

Similarly, other scientific theories, such as the laws of thermodynamics, the ideal gas law or the black-body radiation formula, are based on idealised assumptions that do not “correspond to reality”. They generate predictions but they’re not literally true when given a substantive account of ‘truth’, in the way the scientific realist does. (See: Nancy Cartwright, How the Laws of Physics Lie).

Base Rate Fallacy

The base rate fallacy occurs when the prior probability of a hypothesis is ignored in favour of the likelihood ratio of the evidence, leading to a distorted estimation of the posterior probability of the hypothesis. In the case of Clever Hans, the prior probability of a horse being capable of arithmetic is very low, as there is no known precedent for such a feat. However, the likelihood ratio of the evidence (i.e., the horse seeming to provide correct answers to arithmetic questions) was mistakenly taken as strong evidence for the hypothesis that the horse was actually performing arithmetic.

Similarly, the no miracles argument for scientific realism claims that the success of scientific theories in predicting and explaining phenomena is strong evidence for the truth of those theories. However, this does not follow since there is no base probability assigned to theories being true. This is similar to the situation with Clever Hans, where the horse's apparent success in arithmetic was overestimated because the cues it was picking up on were not properly accounted for.

The ‘success’ of the sciences as indication of truth, of unobservables actually existing, assumes a low rate of false positives in which false theories are nevertheless successful. But when we consider how many scientific theories have been proposed over the years and compare that to the number of successful scientific theories, we see that the success rate is actually quite low. In other words, most scientific theories are failures, coupled with the fact that there is always a prior probability that the success of those theories may be due to factors other than their truth, such as luck, trickery, or overfitting to data or some other factor besides ‘representing reality’.

This ‘base rate fallacy’ rejoinder is usually argued for in terms of the false positive paradox, a paradox where a highly accurate test is worthless if the testing condition is rare enough, or in terms of the vaccinated proportion of the total population—which are probably much better ways of demonstrating the fallacy than my example:

The circularity of the Argument

From an epistemological point, the situation is even worse.

In the case of Clever Hans, the audience assumed that the horse was truly performing arithmetic. But in principle, it is possible to obtain a base rate by observing multiple performances and comparing the proportion of correct answers to the proportion of incorrect ones.

Likewise, scientific realists assume that the success of scientific theories indicates their truth. But to assess the probability of scientific theories being ‘true’ in the sense of ‘representing reality’, we would need a comprehensive understanding of all possible theories and their relationship to reality. In the case of scientific theories, there is no intelligible way of knowing the base rate of true theories outside of a God's Eye View or having access to a bunch of other 'sciences' that have access to "what reality really is" over and above our 'sciences'. Without such knowledge, assigning the label of "true" to scientific theories is essentially based on a gut feeling, without any prior basis for estimation.

Therefore, the statement "It would be a miracle if the sciences were as useful as they are without also being true" does not follow from any intelligible base probability assignment as we lack the necessary information to make such an assessment. It is similar to watching Clever Hans perform and being tricked into thinking he is truly counting, without having any reliable way to test the truth of the performance.

The idea is that in order to determine whether a scientific theory is true, scientific realist think that we need to compare it to ‘reality’, or what ‘actually exists in the world’. But the best we can do is to test our scientific theories based on our (background) theories; based on our other linguistic and conceptual frameworks. There is no way to temporarily step outside of these frameworks to gain a framework-less point of view. We will need to test our scientific theories against something over and above those frameworks to make intelligible the notion of them corresponding to a framework-less reality. But there is no such test.

The scientific realist maintains that we rely on scientific theories to represent reality accurately, and we assess their truthfulness by checking their predictions against empirical evidence. But this process of checking predictions against evidence is itself only tested based on other theories, that is, it is itself based on assumptions about what counts as evidence, what counts as a good explanation etc. These assumptions are themselves based on other theories, and therefore, they are not independent of the theories we are trying to test. This creates a circularity problem, where we cannot escape from our own assumptions in evaluating the truthfulness of scientific theories.

So the no miracles argument ends up begging the question; the conclusion of the argument is already contained in the premises. In this case, the argument for the truth of scientific theories assumes that the methods used to evaluate them are based on something over and above our language (methods, criteria, theories etc.) used to describe them, but they’re not; those methods themselves are based on the assumption that the theories are true.

This is the challenge famously posed by the ‘problem of the criterion’ which applies to all knowledge-claims: before we can determine whether a theory is true or reliable, we must have a criterion for evaluating it, but to establish the validity of that criterion, we must already possess a method for assessing its reliability. This creates a circularity, as any attempt to justify a criterion relies on another criterion, which in turn requires justification. Scientific methods, such as observation, experimentation, and hypothesis testing, are often considered reliable means of acquiring knowledge. However, the problem of criterion raises the question of how we can justify the reliability of these methods without relying on another criterion or method, which in turn requires justification.

The circularity of the no miracles argument cannot be resolved without appealing to some external criterion of truth, which is what the no miracles argument tries to do by claiming that the predictive success of scientific theories is evidence of their truthfulness; on and on it dances in circulars.

Let's take a closer look at the steps involved in evaluating the truth of a scientific theory by scientific realists:

1. Scientific methods are reliable mediators to reality.

2. We use these scientific methods to come up with theories that make predictions about empirical phenomena.

3. We check whether these predictions are borne out by the empirical evidence.

4. If the predictions are borne out, we take this as evidence that the theory is true.

The problem is that step 1 assumes what we are trying to prove, namely that scientific theories are true in the sense that they are representations of reality. This means that our evaluation of the truth of scientific theories is circular, since it relies on assumptions that are themselves based on the very theories we are trying to evaluate.

Anyway, was it then a clever horse or a magic trick or a coincidence? All are assumptions we can make but, if you’re a pragmatist like me, it doesn’t really matter, a trick or not, a coincidence or not, when it worked, it was marvellous and it produced a desirable effect—it made you happy! That’s all that matters. If you want to affix the predicate ‘is true’ to the phenomenon, be my guest.