Beyond Kuhn and Feyerabend

After the fourth stage of philosophy of science

From Aristotle to Feyerabend, the history of the philosophy of science can be mapped out across four stages. Systematicity Theory might lead the way to the fifth, writes Paul Hoyningen-Huene.

When discussing a philosophical question, it is sometimes useful to investigate the history of that question and its answers. The question I am dealing with here is: what makes science special? I assume that scientific knowledge is indeed special primarily by being more reliable than other kinds of knowledge, but also better in some other senses.

This question of the special status of science has first been dealt with very soon after science was invented in ancient Greece, having integrated influences from other cultures. In the course of history, the Greek answer had to be seriously modified due to two main factors. First, the sciences developed enormously ever since and a theory of what makes science special had to adapt to this profound change of its subject matter. Second, not only doing science but also thinking about science became more sophisticated, especially regarding what different kinds of logic could and could not achieve in science. In the following, I shall sketch this historical development in order to characterize our current stance with respect to the question of what makes science special.

During the second half of the nineteenth century, however, the belief in the possibility of certain scientific knowledge eroded.

I shall do so by distinguishing four phases or periods. This subdivision of almost two and a half millennia of history of philosophy of science is crude and schematic. It does by no means feature sharp boundaries: the phases are meant to characterize the mainstream answers. We should therefore handle the proposed periodization with a grain of salt.

In the first phase, starting around the times of Plato (about 428–348 BC) and Aristotle (384–322 BC), two fundamental traits of scientific knowledge were postulated. First, the epistemic ideal of absolute certainty of scientific knowledge and, second, the methodological idea of an axiomatic procedure as the appropriate means to realize this ideal. Scientific knowledge conceived in this manner, or with the Greek word, episteme, stands in sharp contrast to mere belief, or doxa. Only episteme, by being certain, qualifies as scientific. Its certainty is derived from being based on true first principles and deductive proofs. The truth of the first principles is, in some (problematic) sense, taken to be evident. Deductive proofs are used to demonstrate the truth of theorems, that is, of propositions derived from the principles. Formal logic as the theory of truth-transferring deduction is developed at the same time (by Aristotle).

It is no accident that at about the same time these ideas emerged Euclidean geometry was codified. This is because Euclidean geometry precisely exemplifies the ideal of scientific knowledge articulated above. It is based on presumedly self-evident axioms, and it proves its theorems by logical deduction from these axioms. Being based on self-evident principles and theorems that are cogently derived from them, geometry presents a kind of knowledge far superior to all other kinds of knowledge and belief. As there was no reason that this kind of knowledge should be restricted to geometry, it was thought to serve as a model for rigorous science in general. From Plato and Aristotle onward and during the Middle Ages, this ideal of scientific knowledge was universally upheld in the Western tradition.

The diversity of the sciences precludes the hope that they are methodically united, unmasking as a myth the idea of a universal scientific method as constitutive of science.

The second phase in our schematic history of philosophy of science begins in the early seventeenth century and stretches well into the second half of the nineteenth century. It continues the first phase in also subscribing to the epistemic ideal of the certainty of scientific knowledge. However, it is discontinuous regarding the means by which this ideal is to be achieved. Whereas in the first phase, only deductive proof is a legitimate means, the second phase liberalizes this requirement to what will eventually be known as the “scientific method.” This expression either denotes one single method, or it is taken as a collective singular referring to a certain set of methods. Deductive proof is still a part of the scientific method, but the most important extension concerns inductive procedures. They somehow proceed from data to law and are, when applied properly, mostly perceived as also leading to certain knowledge. The most famous protagonists of this scientific method are Galileo Galilei (1564–1642), Francis Bacon (1561–1626), René Descartes (1596–1650), and a little later, Isaac Newton (1642–1727). The scientific method was mainly conceived of as strict rules of procedure, and it is the strict adherence to these rules that makes scientific knowledge special. During the second half of the nineteenth century, however, the belief in the possibility of certain scientific knowledge eroded, even if this knowledge was produced under the rigid auspices of the scientific method. This leads to our third phase.

Timing the start of the third phase is necessarily imprecise because it is the result of a process of slow erosion of the belief in scientific certainty. For reasons whose details still await in-depth historical research, the conviction of the certainty of scientific knowledge begun to decay in the late nineteenth century. This is true both with respect to the mathematical, the natural, and the human sciences, although mathematics was able to restore its claim for conclusiveness by a decisive turn. For mathematics, the discovery of non-Euclidean geometries in the nineteenth century was dramatic. These geometries demonstrated that the unquestioned belief in the uniqueness of Euclidean geometry, and thus the conviction of its unconditional truth, was unfounded. However, the conclusiveness of mathematics was restored if the axioms of any mathematical theory were taken as assumptions whose truth or falsehood was not up for grabs. Mathematical claims then no longer concern the categorical truth of theorems, but only their conditional truth; they are conditional upon the hypothetical acceptance of the pertinent axioms. This constituted a fundamental turn of mathematics in the nineteenth century.

Methodological prescriptions are, at best, rules of thumb and as such cannot found a special nature of scientific knowledge.

In the natural sciences, the process of erosion of scientific certainty is often associated with the advent of the special theory of relativity and of quantum mechanics. However, the said process begins earlier and is, in the first third of the twentieth century, only massively reinforced by the advent and deeper understanding of these revolutionary new theories. After the revolution in physics, the belief that scientific knowledge is not certain and can never be, but is hypothetical and fallible, became dominant both in scientific and philosophical circles. For instance, almost all philosophical schools in the twentieth century stress the hypothetical nature of scientific knowledge, even if it is produced by rigorous scientific methods.

At present, we are in the fourth phase, which started sometime during the last third of the twentieth century. In this phase, belief in the existence of scientific methods conceived of as strict rules of procedure has eroded. Historical and philosophical studies, especially by Thomas S. Kuhn and Paul K. Feyerabend, have made it highly plausible that scientific methods with the characteristics posited in the second and third phases simply do not exist and cannot exist. Scientific research situations, i.e., specific research problems in their specific historical contexts, are so immensely different from one another that it is utterly impossible to come up with some set of universally valid methodological rules to tackle them. The diversity of the sciences precludes the hope that they are methodically united, unmasking as a myth the idea of a universal scientific method as constitutive of science. Methodological prescriptions are, at best, rules of thumb and as such cannot found a special nature of scientific knowledge. However, as the principal fallibility of science was established already in the third phase, in the fourth phase we are left empty-handed: all we can say about scientific knowledge is that it is fallible. This is, of course, extremely dissatisfying because science appears to be special in comparison to all knowledge-gathering enterprises, and this special status should be spelled out by philosophy of science.

Systematicity theory claims that science is more systematic than other forms of knowledge, especially everyday and professional knowledge of various sorts.

A fresh attempt at this task has been made with systematicity theory (Paul Hoyningen-Huene: Systematicity: The Nature of Science, Oxford University Press, 2013). The basic idea is to somehow generalize all the earlier attempts, which concerns especially the older idea that science is characterized by strict methodological rules. Systematicity theory claims that science is more systematic than other forms of knowledge, especially everyday and professional knowledge of various sorts. Clearly, this generalizes the older idea of the sciences being directed by methodological rules. The higher degree of systematicity of science can be specified in nine dimensions (or aspects) of science, which generates the internal structure of systematicity theory. The most obvious and immediately plausible dimensions are descriptions, explanations, predictions, the defense of knowledge claims, the generation of new knowledge, and the representation of knowledge. This means that scientific descriptions, in whatever field, are more systematic than corresponding everyday descriptions; scientific explanations, in whatever field, are more systematic than corresponding everyday explanations, etc. Especially, the defense of knowledge claims is more systematic in the sciences than in other knowledge generating enterprises, making scientific knowledge the most reliable, although still fallible, kind of knowledge available to us. Other dimensions of higher systematicity concern the epistemic connectedness of scientific knowledge, the social institutions that foster critical dialogue, and an ideal of completeness that the scientific enterprise aims at.

All in all, systematicity theory departs considerably from earlier attempts to demarcate science, especially from Karl Popper’s criterion of falsifiability. Whereas Popper tried to demarcate science from devaluated forms of knowledge like pseudoscience and metaphysics, systematicity theory tries to contrast scientific knowledge with legitimate forms of knowledge like everyday knowledge (where it functions), professional knowledge, and even traditional knowledge of non-Western cultures (where it functions). In this way, the specificity of scientific knowledge comes into focus, and not only properties of any knowledge that is legitimate and therefore defensible. Furthermore, systematicity theory not only covers the natural sciences, but also the engineering sciences, the social sciences, the humanities, and the formal sciences. In these fields, the pertinent notions of systematicity differ slightly in meaning from one another.

It should be noted that the idea that a comparative notion of systematicity characterizes the sciences is not entirely revolutionary. In many papers and books from a large variety of academic disciplines, authors have used systematicity in passing to characterize science. However, these hints have invariably been partial and, in themselves, unsystematic. Systematicity theory tries to systematize and complete all these different aspects in the attempt to let us understand what makes science special.



Acknowledgement. This article profited a lot from two papers by Oliver Scholz on systematicity theory which appeared, unfortunately in German, in Netzwerk Hermeneutik Interpretationstheorie (NHI) Newletter, Nos. 6 and 7, 2020. URL:


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Savannah Addison 10 February 2021

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