Commensurability in general

Generally, two quantities are commensurable if both can be measured in the same units. For example, a distance meausured in miles and a quantity of water measured in gallons are incommensurable. A time measured in weeks and a time measured in minutes are commensurable because a year is a constant number of minutes (10080), so that one can convert between the two units by multiplying or dividing by 10080. Measurement is the determination of the size or magnitude of something. ...

Commensurability of scientific theories

In the philosophy of science, two theories are said to be incommensurable if there is no common element that can be used to compare them. If two scientific theories are incommensurable, there is no way in which one can compare them to each other in order to determine which is the better. The philosophy of science is the branch of philosophy which studies the philosophical foundations, assumptions, and implications of science, including the natural sciences such as physics and biology, and the social sciences, such as psychology and economics. ... Theory has a number of distinct meanings, depending on the context. ...

In ethics and value theory, two imperatives, two values, two consequences, two norms, etc. are incommensurable if, when they give conflicting reasons, there is no way of telling which should prevail or even whether they have equal significance. As incommensurable theories to philosophy of science, they cannot be compared. Ethics is the branch of axiology – one of the four major branches of philosophy, alongside metaphysics, epistemology, and logic – which attempts to understand the nature of morality; to define that which is right from that which is wrong. ... Value theory concerns itself with the utility, trading value, moral value, legal value or aesthetic value of people and things - or the combination of all these. ... Imperative programming, as opposed to functional programming, is a sort of programming employing side-effect as central execution feature. ... Value is a term that expresses the concept of worth in general, and it is thought to be connected to reasons for certain practices, policies, or actions. ... Consequentialism is the belief that what ultimately matters in evaluating actions or policies of action are the consequences that result from choosing one action or policy rather than the alternative. ... Norms are a sort of sentences or sentence meanings, the most common of which are commands and permissions. ...

Kuhn

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 make full contact with each other's point of view because they are, as a way of speaking, living in different worlds. Kuhn gave three reasons for this inability: Since the late 1800s, the word paradigm (IPA: ) has referred to a thought pattern in any scientific discipline or other epistemological context. ... Thomas Samuel Kuhn (July 18, 1922 – June 17, 1996) was an American intellectual who wrote extensively on the history of science and developed several important notions in the philosophy of science. ... The Structure of Scientific Revolutions (Thomas Kuhn, 1962) is an analysis of the history of science. ...

1. Proponents of competing paradigms have different ideas about the importance of solving various scientific problems, and about the standards that a solution should satisfy.
2. The vocabulary and problem-solving methods that the paradigms use can be different: the proponents of competing paradigms utilize a different conceptual network.
3. 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, since the difference occurs prior to the application of language.

Feyerabend

The philosophy of Paul Feyerabend was also based on the idea of incommensurability to a large extent. Feyerabend argued that frameworks of thought, including scientific paradigms, can be incommensurable for three reasons. His list of reasons is similar to that of Kuhn, although Feyerabend claims it predates Kuhn's work: Paul Karl Feyerabend (January 13, 1924 - February 11, 1994) was an Austrian-born philosopher of science, who later lived in England, the United States, New Zealand, Italy, and finally Switzerland. ...

1. The interpretation of observations is implicitly influenced by theoretical assumptions. It is therefore impossible to describe or evaluate observations independently of theory.
2. Paradigms often have different assumptions about which intellectual and operational scientific methods result in valid scientific knowledge.
3. Paradigms can be based on different assumptions regarding the structure of their domain, which makes it difficult to compare them in a meaningful way.

According to Feyerabend, the idea of incommensurability cannot be captured in formal logic, because it is a phenomenon outside of its domain.

Donald Davidson

Donald Davidson criticised the notion of incommensurability in an article entitled On the very idea of a conceptual scheme. Donald Davidson (March 6, 1917 – August 30, 2003) was an American philosopher and the Willis S. and Marion Slusser Professor Emeritus of Philosophy at the University of California, Berkeley. ...

Davidson's target is broader than the scientific theories addressed by Kuhn and Feyerabend. His 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. Relativism is the view that the meaning and value of human beliefs and behaviors have no absolute reference. ...

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.

References

• Davidson, Donald. On the very idea of a conceptual scheme in Enquiries into Truth and Interpretation
• Feyerabend, Paul. (1975). Against Method: Outline of an Anarchistic Theory of Knowledge ISBN 0860916464
• Kuhn, Thomas. (1962). The structure of scientific revolutions ISBN 0226458083