Scientists, and science itself, have been variously accused of being reductionistic, formalistic, atheistic, and imperialistic. Although charges of “scientism”—overreach by science—are occasionally merited, critiques of science often confuse the metaphysical principles of philosophy with the far milder methodological principles observed by scientists. Let us call the attitudes generally held by the scientific community the scientific stance. I will describe some elements of the scientific stance and distinguish them from certain dogmatisms having little to do with practice of science.
Think of the scientific stance as a set of working hypotheses.1 A scientist need not believe in a working hypothesis completely or at all. Indeed, it may well be false. But for purposes of scientific inquiry, it is useful to at least act as though it is true. The same is true of the scientific stance. What this means should become clearer as I consider the specific elements of the scientific stance.2
When critics worry about scientism, they are often reacting against what they perceive to be the excessive reductionism of scientists. As a metaphysical thesis, reductionism holds that everything that exists is reducible to a small number of basic entities and principles, which we might call “the fundamental laws of physics.” People have often found this view to be offensive, especially when applied to human beings.
Reductionism, as a metaphysical thesis, is only loosely connected with the kind of reductionism that scientists practice in their everyday work, as they search for explanations which reduce phenomena of interest to others that are simpler or better understood. To put it differently, adopting Wikipedia‘s terminology, ontological reductionism is not the same as methodological reductionism. The former is a metaphysical principle irrelevant to working scientists, whatever its interest to philosophers and theologians. The latter is a methodological principle essential to scientific practice.
Why is methodological reductionism important to science? Because theoretical reduction is among the most potent forms of scientific explanation. When we take some phenomenon that is poorly understood and reduce it to (derive it from) another that is well understood, we have explained the former in terms of the latter. Moreover, we have achieved a more parsimonious view of the world, because we now need only one scientific theory instead of two.
Many of the great advances in science are theoretical reductions. Newton’s discovery that the falling of an apple and the movements of the celestial bodies are governed by the same natural law, the law of universal gravitation, is a spectacular theoretical reduction, often taken to be the birth of modern science. The unification of electricity and magnetism, initiated by Maxwell and concluded by Einstein, is another, reducing two formerly disparate forces to a single theoretical entity, the electromagnetic field. For a century physicists have been searching for the ultimate reduction in physics: a grand unified theory. Nobody knows when a grand unification will be achieved or whether one is even possible. Nevertheless, according to the scientific stance, we ought to keep looking, because if unification is possible, our only hope of discovering it is to actively look for it. And if unification is impossible, well, there are worse ways to spend one’s life than searching for a theory that does not exist.
Theoretical reductions need not take the form of fully articulated mathematical theories, as they often do in physics. Watson and Crick’s discovery of the double helical structure of DNA was a major advance in science because it marked the first step towards understanding the molecular basis of heritability. Since then, the project of genetics has been to reduce the macroscopic world of phenotypes to the microscopic world of genotypes and molecular biology. So far, these reductions mostly involve identifying biological mechanisms, with mathematical modeling restricted to isolated situations.
As the case of genetics shows, theoretical reductions need not be complete to be useful or insightful. The process by which molecular biology determines heritability is incredibly complex and far from being fully understood. Yet genetics has already radically transformed our understanding of biology and biomedicine.
Of all the scientific disciplines, it is in the cognitive sciences that reductionism tends to provoke the most controversy and the strongest emotional reactions. An enormous quantity of ink has been spilled on the question of whether the mental is reducible, wholly or in part, to the physical. That is a fine question for philosophers but is of little use to scientists. According to the scientific stance, neuroscientists should be methodological reductionists, acting as though the mind is reducible to the body and searching for biological and mathematical mechanisms through which the reduction can be effected. The situation is analogous to that of grand unification in physics. We don’t know whether it’s possible to explain the mental purely in terms of the physical, but we may as well try. Whatever its philosophical merits, mind-body dualism is a fruitless working hypothesis for scientists because it forecloses the very possibility of a scientific understanding of the human mind.
As we have seen, mathematical reasoning is a crucial ingredient in at least some theoretical reductions, namely those deducing one scientific theory as a logical consequence of another. This brings us to the next element of the scientific stance. Scientists, engineers, philosophers, and others should aim to construct mathematical models of the phenomena they study. Of course, in order to be useful, a mathematical model must accurately capture at least some features of phenomena in question. Achieving this seems to be easier in some domains than in others. Nevertheless, we should not give up on building models, even when it’s difficult, because good models are invaluable aids to human understanding.
Why is a good mathematical model so useful? Because it enables formal mathematical reasoning in a domain where such was previously not possible. Unaided human thinking faces fundamental limits to its complexity and precision; mathematics is a tool of thought for raising those limits. As a result, there is often a striking difference between the pre-mathematical and post-mathematical phases of a science.
Consider a few important examples of mathematization in the history of science. The mathematization of physics began with the invention of calculus by Leibniz and Newton. That this invention coincided with the first general, quantitative theory of mechanics, and the beginning of modern science, is no coincidence. The mathematization, by Church, Turing, Gödel, and others, of the intuitive idea of an algorithm made it possible reason systematically about what is computable. Computational complexity theory, officially beginning with Hartmanis and Stearns’ 1965 paper,4 extends this program of mathematicization to reason about how quickly computational problems can be solved.5 In a remarkable 1948 paper,6 Shannon introduced a mathematical theory of communication (information transmission), where previously there had been none, thus giving birth to the field of information theory. All these examples, and others besides, illustrate the thesis that a successful mathematization of a new domain is a significant scientific achievement, which may have profound consequences.
In analogy to methodological reductionism, we might say that methodological mathematicism is the view that scientists should try to construct mathematical models of the world. It should not be confused with the traditional, metaphysical versions of mathematicism. In its strongest sense, attributed to the Pythagoreans, mathematicism asserts that everything that exists is mathematics. This view has not attracted many adherents, because it doesn’t seem to make much sense. Milder forms of metaphysical mathematicism assert that everything that exists can be defined by or modeled by mathematics. Such positions are somewhat more plausible, but are still far stronger than the methodological mathematicism of the scientific stance.
According to metaphysical naturalism, also known as ontological naturalism, everything that exists is natural, as opposed to supernatural or spiritual. The universe is governed by impersonal natural laws, not the will of a divine being. Gods, ghosts, spirits, and souls do not exist.
As in the cases of reductionism and mathematicism, this metaphysical version of naturalism is far stronger than the methodological naturalism practiced by scientists. The scientific stance tells us to seek naturalistic explanations of the world. In doing so we need not assume anything about the supernatural. From a methodological standpoint, the question of whether the supernatural exists is quite irrelevant. Almost by definition, supernatural forces transcend the natural world: they are unobservable and they have no derivable, observable consequences. Consequently, if they exist at all, supernatural forces have no predictive or explanatory power and they lie beyond the reach of science.
A religiously minded person might object that many important scientists were deeply religious. Isaac Newton is perhaps the most famous example. Besides writing a certain notable book about mechanics, Newton wrote voluminously on Christian theology and the occult. As I understand it, scholars disagree about whether Newton’s religious beliefs influenced the development of his physics in any significant way. What is clear is that the scientific content of Newton’s mechanics is completely independent of his theology. If this not obvious, consider that Newtonian mechanics is taught to teenage children throughout the world, yet few outside Newton’s most dedicated biographers have the faintest idea what he thought about the Bible.
Modern scientists seem to have internalized the methodological separation of science and religion, implicit already in Newton’s scientific work. Summarizing a survey of 1,646 scientists, supplemented with 275 in-depth interviews, sociologist Elaine Ecklund writes:
Scientists who considered themselves part of a traditional religion generally did not want to keep their faith entirely compartmentalized from their scientific lives… But they never saw religion as influencing how they applied their scientific methods (that is, how they did their science). Rather they emphasized their uniqueness in considering the broader relevance for humanity of the particular science in which they were engaged.7
In other words, religious scientists claim to draw on their religious beliefs when assessing the ethical and societal implications of their scientific work, but not when doing the work itself. This position is consistent with the scientific stance.
Naturalism says that the world is governed by natural laws, but that doesn’t necessarily mean that natural laws are discoverable or predictive. As a further element of the scientific stance, scientists ought to proceed as though nature is predictable and aim to create predictive mathematical models. I will call this injunction “predictionism,” for lack of a better term.8
Mathematical models serve two complementary purposes in science. The first, emphasized by mathematicism, is to provide structure and organization to our knowledge and to enable us to reason systematically about the world. We expect such models to fit the existing data reasonably well but not necessarily to predict future data. The second purpose of models is to make quantitative predictions about unobserved, possibly future, events. The ability to accurately predict the course of nature has obvious practical utility and is the basic source of all technological progress. From the standpoint of pure science, however, the real utility of prediction is to assess the quality of scientific theories. Of course, predictivity is not the only criterion against which scientific theories are measured, but it is arguably the most important.
The fundamental limits to predictability are largely unknown, but the scientific stance urges us to continuously push the limits of our best theories and models. There is nothing to be gained by assuming that complex systems, such as economies or political bodies, are inherently unpredictable. That being said, the kind of the mathematical models scientists employ may have to evolve. The classical models cited above, in the context of mathematicism, tend to be simple, parsimonious, and almost entirely hand-made. It is possible that certain complex phenomena simply do not admit such models. With the availability of ever larger datasets and ever greater computing power, it is becoming possible to generate far more complex models, of a distinctly statistical character. It is too early to say how this development will affect our understanding of the scientific method.
The preceding four elements—reductionism, mathematicism, naturalism, and predictionism—can be distilled into a single assertion: that the world is intelligible. It is structured, predictable, and governed by natural laws, which can be discovered by observation and experimentation and modeled using mathematics and statistics. That we should act as though this is true is the positive thesis of the scientific stance.
The scientific stance, as described so far, would be unduly optimistic were it not tempered by an opposing force. The negative thesis of the scientific stance is that all scientific knowledge is fallible and subject to revision.
Scientific knowledge is fallible because it is based on inductive inferences from finite data to statistical regularities, which are expected to hold now and in the future. Yet there is no incontrovertible a priori law which says that nature should behave tomorrow exactly as it does today; this is the famous problem of induction. More important, practically speaking, is that scientific theories are expected to hold only under certain background conditions. For example, non-relativistic mechanics is accurate only when the velocities of all relevant objects are small compared to the speed of light. In mature sciences like physics, such boundaries are very carefully delineated; in less mature sciences, this is not necessarily the case. In the social sciences, such as psychology and economics, it is extremely difficult to determine with any precision the background conditions under which a theory should be predictive. Closer to home, I find much empirical research in machine learning to be sloppy in its treatment of background conditions.9
Throughout the history of science, scientific theories have been continuously revised to expand their scope and increase their predictive accuracy. No one knows whether this process will continuously indefinitely or whether there is an ultimate limit to scientific progress, to which we may hope to converge. However, the scientific stance urges us to adopt the former view. The belief that a scientific theory has been perfected, beyond any possible improvement, cannot be the start of any new investigations, but only an end to them. Moreover, history has consistently embarrassed those who declare the end of science, as when Kant claimed a priori proof of Newtonian mechanics, on par with the propositions of Euclidean geometry.
In defense of the scientific stance, I have mostly offered conditional arguments in this essay, to the effect that we may as well act in this way when we investigate the world, because the alternative is certain to be unproductive. But why should we think that the scientific stance will itself be productive—that the universe will be cooperate with our best intentions?
I will not try to offer a complete answer to this question, but I will point to history as grounds for optimism. Although antecedents of the scientific stance, such as determinism, naturalism, and mathematicism, can be traced back to the pre-Socratic philosophers, I don’t think that the scientific stance became a central feature of scientific culture until around the time of the Enlightenment. Since then, we have witnessed a steady, perhaps even accelerating, accumulation of scientific knowledege and technological prowess. This suggests that the scientific stance has served us well. That is not to say that we have perfected it. Perhaps we will need to make adjustments in response to new scientific problems. That would itself be in keeping with the spirit of the scientific stance.
Perhaps I should say “meta-hypotheses,” because these hypotheses are not first-order, scientific hypotheses about the world. They are higher-order, philosophical hypotheses about how to approach learning about the world.
Gian-Carlo Rota, 1997. Indiscrete Thoughts. Springer Science and Business Media. DOI.
Juris Hartmanis and Richard E. Stearns, 1965. On the computational complexity of algorithms. Transactions of the American Mathematical Society. DOI.
Computability and complexity theory have implicit physical content because what is computable and how quickly depends on the laws of nature. Quantum information theorists give a punchy expression to this idea in the slogan that “information is physical”.
Claude Shannon, 1948. A mathematical theory of communication. Bell System Technical Journal. PDF.
Unlike the other “-isms” of this essay, the term “predictionism” (alternatively, “predictivism”) does not seem to have a widely agreed upon meaning, although it does appear in the literature on philosophy of science. The idea of predictability is closely connected to that determinism, and I had originally intended to invoke a kind of “methodological determinism” in this section. However, I would have inevitably had to say something about the apparent nondeterminism of quantum mechanics, a notoriously subtle issue, so I decided to forgo the topic of determinism altogether.