Commensurability is a concept in the philosophy of science whereby scientific theories are said to be "commensurable" if scientists can discuss the theories using a shared nomenclature that allows direct comparison of them to determine which one is more valid or useful. On the other hand, theories are incommensurable if they are embedded in starkly contrasting conceptual frameworks whose languages do not overlap sufficiently to permit scientists to directly compare the theories or to cite empirical evidence favoring one theory over the other. Discussed by Ludwik Fleck in the 1930s,Ludwik Fleck (Stanford Encyclopedia of Philosophy); Fleck's term for incommensurability was "niewspółmierność". and popularized by Thomas Kuhn in the 1960s, the problem of incommensurability results in scientists talking past each other, as it were, while comparison of theories is muddled by confusions about terms, contexts and consequences.
Introduction of the term
In 1962, Thomas Kuhn and Paul Feyerabend both independently introduced the idea of incommensurability to the philosophy of science. In both cases, the concept came from mathematics; in its original sense, it is defined as the absence of a common unit of measurement that would allow a direct and exact measurement of two variables, such as the prediction of the diagonal of a square from the relationship of its sides.
The term commensurability was coined because of a series of problems that both authors found when trying to interpret successive scientific theories. Its implementation is better understood thanks to the critiques that both Kuhn and Feyerabend have made in response to certain theses proposed by followers of the received view of theories. These include the famous thesis on the accumulation of scientific knowledge, which states that the body of scientific knowledge has been increasing with the passage of time. Both Kuhn and Feyerabend reject this thesis, in favor of a model that sees both revolutions and periods of normalcy in the history of science.
Another equally important thesis proposes the existence of a neutral language of comparison which can be used to formulate the empirical consequences of two competing theories. This would allow one to choose the theory with the greatest empirically verified contents or explanatory powers—or the greatest content that is not falsified if the formulation is Popperian.
The idea at the root of this second thesis does not just relate to the existence of said language but also implies at least two further postulates. Firstly, this choice between theories presupposes that they can be intertranslated, for example between theory A and its successor B – and in the case of Popper that B can be deduced from A. Secondly, it is assumed that the choice is always carried out under the same standards of rationality.
In both cases, the concept of incommensurability makes the viability of the thesis impossible. In the first, by showing that certain empirical consequences are lost between successive theories. In the second case, by confirming that it is possible to make a rational choice between theories even when they can not be translated into a neutral language. However, although the reasons for the introduction of these counter arguments, and the criticism from which they arise, are the same, the sense in which the coauthors use them are in no way identical. For this reason the idea of incommensurability will be discussed for each coauthor separately.
Perspectives
Feyerabend's perspectives Feyerabend locates incommensurability within a principle from the field of semantics which has the underlying idea that the change in significance in the basic terms of a theory changes the totality of the terms of the new theory, so that there are no empirically common meanings between T and .
Feyerabend is credited with coining the modern philosophical sense of "incommensurability",Oberheim and Hoyningen-Huene. "The Incommensurability of Scientific Theories" in The Stanford Encyclopedia of Philosophy. "...he had developed his notion of the incommensurability of scientific theories more than ten years prior to the appearance of Kuhn's Structure of Scientific Revolutions (1962)" which lays the foundation for much of his philosophy of science. He first presented his notion of incommensurability in 1952 to Karl Popper's London School of Economics seminar and to a gathering of illustrious Wittgensteinians (Elizabeth Anscombe, Peter Geach, H. L. A. Hart and Georg Henrik von Wright) in Anscombe's Oxford flat. Feyerabend argued that frameworks of thought, and thus scientific paradigms, can be incommensurable for three reasons. Briefly put, Feyerabend's notion of incommensurability is as follows: The interpretation of observations is implicitly influenced by theoretical assumptions. It is therefore impossible to describe or evaluate observations independently of theory. Paradigms often have different assumptions about which intellectual and operational scientific methods result in valid scientific knowledge. Paradigms can be based on different assumptions regarding the structure of their domain, which makes it impossible to compare them in a meaningful way. The adoption of a new theory includes and is dependent upon the adoption of new terms. Thus, scientists are using different terms when talking about different theories. Those who hold different, competing theories to be true will be talking over one another, in the sense that they cannot a priori arrive at agreement given two different discourses with two different theoretical language and dictates.
According to Feyerabend, the idea of incommensurability cannot be captured in formal logic, because it is a phenomenon outside of logic's domain.
Theories In 1989, Feyerabend presented an idea informed by Popper's critical rationalism whereby "investigation starts with a problem. The problem is the result of a conflict between an expectation and an observation, which, in its turn, is formed by the expectation." (Feyerabend, 1989; pp. 96). Scientific methodology then resolves problems by inventing theories that should be relevant and falsifiable, at least to a greater degree than any other alternative solution. Once an alternative theory is presented the critical phase commences regarding which must answer the following questions: (a) why has theory T been successful up until now and (b) why has it failed. If the new theory answers both questions then T is discarded.
That is, a new theory , in order to be an adequate successor to the refuted theory T, must have a collection of additional predictions regarding T (Class A), as well as a collection of successful predictions that coincide to a certain degree with the old theory (Class S). These Class S predictions constitute those parts of the new theory containing new truths, and they therefore exclude a series of consequences of T—the failures in the old theory—which are part of the untrue (false) contents of the new theory (Class F).
Given this model it is possible to construct relational statements between certain terms from T and from , which will be the basis for the comparison between the theories. This will allow a choice between the two in the light of their empirical contents. But, if we come across a theory in which Class S is empty then the theories are incommensurable with each other.
However, Feyerabend clarifies this by stating that, incommensurability between T and will depend on the interpretation given to the theories. If this is instrumental, every theory that refers to the same language of observation will be commensurable. In the same way, if a realist perspective is sought then it will favour a unified position which employs the most highly abstracted terms of whatever theory is being considered in order to describe both theories, giving a significance to the observational statements as a function of these terms, or, at least to replace the habitual use they are given.
It can be noted that the instrumentalist interpretation recognizes the existence of certain statements whose truth is not only dependent on the observational statements but also on the evaluation criteria they are subjected to, which are anchored in the theories. For example, to affirm the relational character of longitude, this asseveration can not be decided solely using observational terms. Its truth value, in part, depends on the theory that establishes the sense in which the terms are used. In this case they relate to quantum mechanics (QM) as opposed to classical mechanics (CM). In this sense, the instrumentalist position only deals with the empirical consequences and leaves to one side the relationship that the concepts have with each other.
In this same way Feyerabend comments that:
Realist objections
In relation to realist objections, Feyerabend returns to an argument elaborated by Carnap and comments that the use of such abstract concepts leads to an impossible position, as "...theoretical terms receive their interpretation by being connected with an observational language and those terms are empty without that connection." (Feyerabend, pp. 373). As before it follows that they can not be used to confer significance to the observational language as this observational language is its only source of significance, with which it is not possible to make a translation but only a restatement of the term.
Therefore, Feyerabend considers that both the instrumentalist and the realist interpretations are flawed, as they try to defend the idea that incommensurability is a legitimately unsolvable idea with which to revoke the theses of the accumulation of knowledge and panrationalism in science.
This leads to the following consideration: if each new theory has its own observational basis, within the meaning of the theoretical framework, how can we hope that the observations that are produced could eventually refute it. Furthermore, how can we actually recognize that the new position explains what it is supposed to explain or if it is deviating off into other areas and therefore how can the theories be definitively compared.
Feyerabend's answer to the first consideration lies in noting that the initial terms of a theory depend on the postulates of the theory and their associated grammatical rules, in addition, the predictions derived from the theory also depend on the underlying conditions of the system. Feyerabend doesn't explore the point further, but it can be assumed that if the prediction does not agree with the observation and if we have a high degree of confidence in the description that we have made from the initial conditions than we can be sure that the error must be present in our theory and in its underlying terms.
In dealing with the second consideration Feyerabend asks "why should it be necessary to have a terminology that allows us to say that two theories refer to the same experiment. This supposes a unificationist or possibly a realist aspiration, whose objective appears to be the truth, however, it is assumed that the theory can be compared under a criterion of empirical adequacy. Such an approach would build on the relationship established between the observational statement that describes the outcome of an experiment formulated for each theory independently, which is compared with the predictions that each theory posits. In this way the selection is made when a theory is an empirically better fit. If the objection to the possible deviation of the new theory is not answered it is irrelevant as often history has shown that in fact differing points of view change or modify their fields of application, for example the physics of Aristotle and Newton."
Theory selection