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Commensurability or incommensurability is a concept in the philosophy of science to describe comparisons between different unit of measurement. For example, a distance measured in kilometers and a volume of water measured in liters are incommensurable; one cannot convert miles to liters. However, a time measured in weeks and a time measured in minutes are commensurable, because a week is a constant number of minutes (10080); one can convert between minutes and weeks by multiplying or dividing by 10080.
Scientific theories are described as commensurable if one can compare them to determine which is more accurate; if theories are incommensurable, there is no way in which one can compare them to each other in order to determine which is more accurate.
The idea that scientific paradigms are incommensurable was popularized by the philosopher Thomas Kuhn in his book The Structure of Scientific Revolutions (1962). He wrote that "when paradigms change, the world itself changes with them" (see esp. Chapter X of this book). According to Kuhn, the proponents of different scientific paradigms cannot fully appreciate or understand the other's point of view because they are, as a way of speaking, living in different worlds. Kuhn gave three reasons for this inability:
- Proponents of competing paradigms have different ideas about the importance of solving various scientific problems, and about the standards that a solution should satisfy.
- The vocabulary and problem-solving methods that the paradigms use can be different: the proponents of competing paradigms utilize a different conceptual network.
- The proponents of different paradigms see the world in a different way because of their scientific training and prior experience in research.
In a postscript (1969) to The Structure of Scientific Revolutions, Kuhn added that he thought that incommensurability was, at least in part, a consequence of the role of similarity sets in normal science. Competing paradigms group concepts in different ways, with different similarity relations. According to Kuhn, this causes fundamental problems in communication between proponents of different paradigms. It is difficult to change such categories in one's mind, because the groups have been learned by means of exemplars instead of definitions. This problem cannot be resolved by using a neutral language for communication, according to Kuhn, since the difference occurs prior to the application of language.
The philosophy of Paul Feyerabend was also based on the idea of incommensurability to a large extent. Feyerabend argued that frameworks of thought, and thus scientific paradigms, can be incommensurable for three reasons. His list of reasons is similar to that of Kuhn. However, Feyerabend first presented his notion of incommensurability in 1952 to Karl Popper's LSE seminar. Included in the group was Elizabeth Anscombe, Peter Geach, H.L.A. Hart and Georg Henrik von Wright. 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.
Donald Davidson criticised the notion of incommensurability in his article "On the very idea of a conceptual scheme".
Davidson's critique is aimed at conceptual relativism - the idea that reality is relative to a scheme, and hence that what is real in one scheme may not be real in another.
Davidson proceeds by pointing out that "where conceptual schemes differ, so do languages". That is, that to hold to a particular conceptual scheme is to hold to a particular language. It follows then that two conceptual schemes would be incommensurable only in the case that it was not possible to translate the theory expressed in the language of one scheme into the ideas expressed in the language of another. He argues that it is impossible to make sense of a total failure to be able to translate a given theory from one language to another. From this it follows that it is impossible to make sense of the notion of two theories being incommensurable.
Davidson's notion that holding onto a particular conceptual scheme is to hold to a particular language, closely parallels the much earlier writings of Ludwig Wittgenstein. Wittgenstein argued that our communication can be understood as a series of 'language games', in which it is a mistake to take things that sound alike (what we would call the 'same words') from one game, and use them in another game. These individual games are, for Wittgenstein, incommensurable.
- Davidson, Donald. On the very idea of a conceptual scheme in Inquiries into Truth and Interpretation
- Feyerabend, Paul. (1975). Against Method: Outline of an Anarchistic Theory of Knowledge ISBN 0-86091-646-4
- Feyerabend, Paul. (1962). Explanation, reduction, and empiricism in Feigl/Maxwell, Scientific Explanation 28—97
- Feyerabend, Paul. (1988). Farewell to Reason ISBN 0-86091-896-3
- Kuhn, Thomas. (1962). The structure of scientific revolutions ISBN 0-226-45808-3Template:EnWP Commensurability (philosophy of science)