Kuhn and Incommensurability
Introduction
In his book The Structure of Scientific Revolutions Thomas Kuhn advances the incommensurability thesis, probably the most radical idea in the book. I'm going to present an outline of this thesis and then raise some questions about it. However, before doing that we need to understand Kuhn's notion of a “paradigm” which forms the basis of his book.Kuhn's idea of a paradigm
Paradigms relate to scientific communities. What exactly is a scientific community? According to Kuhn, we can identify a scientific community as a group of people who have had a similar education (eg PhD in physics), have read a similar body of technical literature and have drawn similar conclusions from it and, furthermore, this literature marks the boundary of a distinctive subject matter (eg molecular biology). Add to that the attendance at conferences, the various communication networks (eg internet) and the citation of other scientists in the community in the course of publishing books and journal articles. There are different levels in a scientific community - eg physicist, astronomer, radio astronomer; biologist, zoologist. Kuhn asks: What do members of a particular scientific community share that explains their professional communication and relative unanimity of judgements? What unites them? The answer is, a paradigm.What is a paradigm? According to Kuhn, a paradigm has four main components:
- Symbolic generalisations such as F=ma, V=IR, E=mc^2. These symbolic generalisations are accepted without question by members of the group and hence form part of its shared theoretical framework.
- General “metaphysical” beliefs such as “Heat is the kinetic energy of the constituent parts of bodies”, “Molecules of a gas behave like tiny elastic billiard balls in random motion”, “The universe is divided in two separate regions - the sublunary and the superlunary” (Aristotle).
- Certain values concerning theorising: a theory should supply accurate and preferably quantitative predictions; a theory should be consistent with other well established theories; a theory should provide explanations and lead to interesting discoveries eg the way Newtonian mechanics led to the discovery of the planet Neptune; a theory should be simple, meaning that it contain as few concepts as necessary to explain the phenomena eg if certain phenomena can be explained by positing the existence of electrons, then there is no need to posit the existence of x-ons as well. The simplicity requirement is often expressed as “Don't multiply entities beyond necessity”.
- Concrete problem situations which students learn to solve when they learn the subject eg incline plane, conical pendulum, Keplerian orbits. Kuhn calls these problem situations “exemplars”. For students these exemplars serve as models which, in conjunction with the symbolic generalisations, demonstrate how particular problems in a certain branch of science can be solved. Thus an important part of science education involves students solving similar sorts of problems as exercises in textbooks or in laboratory experiments. In this way students are introduced to the relevant paradigm in that branch of science.
“[Paradigms] are ...scientific achievements...that some particular scientific community acknowledges for a time as supplying the foundation for its further practice. Today such achievements are recounted, though seldom in their original form, by science textbooks, elementary and advanced. These textbooks expound the body of accepted theory, illustrate many or all of its accepted applications, and compare these applications with exemplary observations and experiments. [Paradigms] share two essential characteristics. Their achievement was sufficiently unprecedented to attract an enduring group of adherents away from competing modes of scientific activity. Simultaneously, it was sufficiently open-ended to leave all sorts of problems for the redefined group of practitioners to solve”. (p.10)
Thus a paradigm is something like a theoretical framework which a given scientific community shares. Some examples of the major paradigms in the history of science are Aristotelian Physics, Newtonian Mechanics, Darwin's Theory of Evolution, Relativistic Mechanics and Cosmology, Quantum Mechanics. Although paradigms are associated with particular scientific theories such as the ones just listed, a paradigm is not simply a theory. It involves a whole way of viewing the world, as outlined in (1)-(4), and also a whole basis for research, problem solving and discovery. Nevertheless, in the following discussion it will be convenient to use the term “theory” and “paradigm” interchangeably where there is no threat of confusion. We are now in a position to state the incommensurability thesis. Kuhn discusses incommensurability in Chapter 12 of the book and also in the Postscript, pp 198-206.
The incommensurability thesis
To say that, in some domain such as physics, two rival theories, T(1) and T(2), are incommensurable means, broadly speaking, that they can't be compared. As Kuhn says, “...proponents of competing paradigms must fail to make complete contact with each other's viewpoints.” (p. 147). To say that T(1) and T(2) can't be compared means, more specifically, that they cannot be logically incompatible. This is usually taken to have the consequence that there are no logical grounds for choosing between T(1) and T(2). Examples of rival paradigms are Aristotelian and Copernican astronomy. If, as Kuhn says, these paradigms are incommensurable, then there is no logical relation between the two theories. “No logical relation” means that if one of the theories is true it doesn't follow that the other one is false, this despite the fact that they are “rivals”. That is what Kuhn's incommensurability thesis states. This thesis is radically at odds with our view of scientific theories. This view is something like this: Aristotle believed that the earth was at the centre of the universe and that the sun and stars orbited that the earth. However, the view goes, Aristotle was wrong and Copernicus was right. Aristotle's theory was false and Copernicus's theory was true. If Kuhn is right about the incommensurability of theories, then this view will have to be abandoned or at least fundamentally revised. Kuhn goes on to specify in more detail the nature of this incommensurability. There are three main sources of incommensurability.- Incommensurability of values: as mentioned above, a paradigm incorporates certain values relating to theorising such as the values of accurate prediction and simplicity in explanation. Kuhn argues that these values give rise to incommensurability. Thus when comparing two theories T(1) and T(2) with regard to their relative simplicity, for example, there may be disagreement as to which is the simpler and this disagreement can't easily be resolved - the disagreement doesn't necessarily indicate that one of the parties to the dispute is actually mistaken. Moreover, there may a disagreement as to the emphasis being placed on different values. T(1) may be simpler but T(2) may give more accurate predictions. Which of these values should be preferred? Kuhn suggests that there may be no objective grounds for making a choice in these circumstances - hence incommensurability.
- Meaning change: although the theoretical terms of T(1) and T(2) may be the same, they will have different meanings in T(1) and T(2). The theoretical terms of a theory are terms such as “planet”,”electron”,”gene”,”photon”,”force”. Kuhn gives the following example. When the Aristotelians rejected Copernicus's claim that it was the earth rather than the sun that moved, this was more than a mere disagreement. For the Aristotelians, Kuhn suggests, having a fixed position was part of the meaning of the term “earth”. It was meaningless rather than simply false to say that the earth moved. That is to say that , according to Kuhn, the Aristotelian paradigm and the Copernican paradigm were incommensurable. The statements “The position of the earth is fixed” and “The earth moves” do not contradict each other because “earth” has a different meaning in each. This is like saying that the statements “Tom is bald” and “Tom is hairy” do not contradict each other if the first is about Tom Smith and the second about Tom Brown. In this way, then, the change in the meaning of theoretical terms from one paradigm to another provides one ground for incommensurability.
- Ontological change: the second main ground for incommensurability lies in Kuhn's idea that scientists working in different paradigms are in some sense working in “different worlds”. Thus, “...proponents of competing paradigms practise their trades in different worlds. One contains constrained bodies that move slowly, the other pendulums that repeat their motions again and again. In one, solutions are compounds, in the other mixtures. One is embedded in a flat, the other in a curved, matrix of space.” (p. 149) Thus, according to Kuhn T(1) and T(2) are about different worlds in the following sense. Whereas, for example, T(1) asserts the existence of a flat Euclidean space, T(2) asserts the existence of a curved non-Euclidean space-time. (Hence the use of the term “ontological” which relates to existence). The term “space” in T(1) and T(2) refers to quite different realities - flat space in T(1) and curved space-time in T(2). This fact, then, also provides a ground for incommensurability.
The consequences of incommensurability
Suppose Kuhn is right. What would follow from the fact that competing major theories (ie paradigms) are incommensurable? In particular, what would follow regarding our notions of truth and rationality as these apply to scientific theories? If two competing theories T(1) and T(2) are incommensurable, then can we still say, as we want to, that (eg) T(2) is “closer to the truth” than T(1)? If Kuhn is right, how can there be a rational way of choosing between T(1) and T(2)? On what basis could we prefer T(1) to T(2)? And, more generally, if scientific theories are incommensurable, then what account can be given of the notion of scientific progress? If paradigms are incommensurable, then is the history of science nothing more than a sequence of paradigms no one of them any better or “closer to the truth” than any of the others? Can we still say that the aim of science is to search for the truth?Discussion of incommensurability
- As we have seen, incommensurability is based on the idea of meaning change. To take Kuhn's example, the term “earth” for Aristotle had a different meaning than it had for Copernicus. But how do we know this? Who's to say that, for Aristotle, it is part of the meaning of the term “earth” that it has a fixed position? We can agree that for Aristotle the earth is fixed and for Copernicus the earth moves. But why describe this situation as a “change of meaning”? Consider another of Kuhn's examples. In Newtonian mechanics the mass of a body does not depend on its velocity, whereas for Einsteinian (ie relativistic) mechanics the mass of a body does depend on its velocity, this difference especially significant when a body is travelling at close to the speed of light. But, again, why describe this situation by saying that the term “mass” has undergone a meaning change between Newtonian and Einsteinian mechanics? Note that this is not merely a verbal issue. Without accepting that there has been a meaning change, Kuhn's notion of incommensurability doesn't get off the ground. If the meaning of “mass” is more or less the same in Newtonian and Einsteinian mechanics, then there is no reason why statements about mass in both theories cannot be logically compatible or incompatible.
- If, because of incommensurability, theories could literally not be compared, then we would be able to believe all of them. Yet that suggestion seems crazy. We have abandoned epicycles, possession by demons, phlogiston, caloric fluid, the aether, spontaneous generation, flat earth, geocentricism and so on. If theories can't be compared then there is no rational basis at all for the rejection of these notions.
- Which terms exactly would be subject to meaning change if Kuhn is right about the incommensurability of theories? The examples given are terms such as “earth”,”mass”,”space”,”compound”. But what about “blood”, “water”, “soil”, “telescope”, “volcano”, “ocean”, “skin”, “fire”, “heart”, “pigeon”? These latter terms are more low-level, which means that they less affected by changes in theory, yet are nevertheless terms which are part of our theories - biological, physical, geological or whatever. At this level incommensurability seems far less plausible. Furthermore, since there is no sharp distinction between theories and paradigms, the actual scope of this supposed incommensurability is unclear. Are all competing theories incommensurable? Consider theories about the extinction of the dinosaurs, the causes of cot death, the causes of earthquakes and so on. Will they be incommensurable? It seems implausible to say that terms like “dinosaur”,”baby”, “breathing”, “fault line” somehow undergo changes in meaning. What would be the source of incommensurability in these cases? Of course these theories are fairly low level - they don't have the scope and generality of say Newtonian mechanics or the Theory of Evolution. But this difference is a matter of degree. If we were to arrange scientific theories in an order of increasing scope and generality, it is hard to see at what point meaning change, ontological change and hence incommensurability sets in.
Some more questions
- Is there genuine progress in science? In what sense precisely does science progress? Do you think that science progresses by getting closer to the truth? Can there be genuine progress in science if theories are incommensurable? If there is no such thing as scientific progress, what makes science worth doing? What makes it rational? Is it possible to give an account of scientific progress without the notion of truth?
- If theories are incommensurable, then are there any rational criteria of theory choice? On what grounds should we choose between theories T(1) and T(2)? If Kuhn is right, then we can't choose on the basis of truth. On what basis then?
- Incommensurability and relativism: relativism is the view that there is no such thing as absolute truth. That is to say that truth is relative. Relative to what? According to relativists, truth is relative to (for example) people, communities, historical periods or, in Kuhn's case, to paradigms. For Kuhn there is no absolute truth which, say, Einstein has got closer to than Newton or Aristotle, or which Bohr got closer to than either Thomson or Rutherford. Kuhn does believe in scientific progress but only in the sense that (eg) Einstein's theory gives more accurate predictions and solves more problems than Newton's theory. But not in the sense that Einstein's theory gives a better picture of what is “really there” than Newton's theory. Of course this is just what we do believe, a better example of this being the comparison between Aristotle and Copernicus. Aristotle and Copernicus described two ways in which (a certain part of) the universe could be. It could be that the earth was the centre of the universe and all the planets and stars orbited the earth (as Aristotle believed), or it could be that the sun was at the centre of the solar system and the earth revolved around the sun (as Copernicus believed). The point here is that one of these views (Copernicus's) represents the way things really are. Or so most of us believe. Kuhn's reason for rejecting this widespread belief of ours is that, as he says, “there is no theory-independent way to reconstruct phrases like “really there”; the notion of a match between the ontology of a theory and its “real” counterpart in nature now seems to me illusive in principle.” (p.206) By “ontology of a theory” Kuhn means the sorts of things which exist according to the theory. For example, the ontology of atomic physics includes such things as electrons, protons, muons, neutrinos and so on. Electrons, protons, etc. are entities which exist according to atomic physics. What Kuhn has not shown is why the belief that electrons really exist is “theory independent”. Why can't it be the case that electrons really exist and also the case that the statement “Electrons exist” is theory dependent? The statement “Electrons exist” is clearly not theory independent - it depends on the theory of atomic physics. But what exactly is the objection to saying that a theory dependent statement can describe the world as it really is? Kuhn has not shown us why theory dependence conflicts with absolute truth, and has therefore given us no reason to believe relativism in anything other than a fairly trivial sense.