Towards an Objective Theory of Rationality

8. Logical and Rational Incommensurability

Book cover: The Structure of Scientific Revolutions by Thomas S. Kuhn

A number of other outstanding problems require detailed solution. The two most important ones are the problem of logical incommensurability and the problem of implicit rationality. The problem of the logical incommensurability of at least some rival high-level theories had been pushed hard by Kuhn and Feyerabend. This problem is critical for two reasons. Firstly, if the epistemic status of an evidence-statement is not determinable independently of such theories, my Criterion 4 above (§4.3) cannot be satisfied. Secondly, if there are no evidence-statements that simultaneously bear logical relationships of consistency with one theory (in conjunction with auxiliary hypotheses) and inconsistency with its rival, then it appears that such theories cannot be directly compared in the way that I have envisaged in my application of Criterion 5 above (§4.3). It seems that on this account, crucial experiments used to decide between rival theories in the history of science are in name only.

Candidates often touted as a pair of logically incommensurable theories are Newtonian and Einsteinian mechanics. Both served to explain the motions of terrestrial and celestial bodies. The discrepancy between the theoretical and measured advance of the perihelion of the planet Mercury is widely taken as leading to the demise of Newton's theory and the confirmation of Einstein's. It is undeniable that the advance of the perihelion of Mercury cannot be described in an observation language that is interpretable independently of a theory of space and time. Even though the terms 'mass', 'space', 'time', and so on, are not invariant between Newton's and Einstein's theories, it is plausible to suggest that, at the very least, they are implicitly contradictory in their existential claims. Relativity theory, for example, implicitly denies that there are any entities that satisfy the postulates of Newtonian mechanics. It excludes the possibility of bodies that are mass-invariant with respect to velocity. Tied to an adequate theory of reference, such a realist interpretation may provide a comprehensive and compelling solution to the problem of logically incommensurable theories.

Notwithstanding a semantic solution to the problem of incommensurability, rival theories can be compared for adequacy. This is because the predicted and actual results of crucial experiments are described in a language that is neutral between the rival theories. The observation statements, for example, describing the advance of the perihelion of Mercury are the same from both the Newtonian and the Einsteinian point of view. The position measurements that are read off the astronomical instruments used in measuring the advance of Mercury's orbit are decipherable independently of the two theories. In consequence, we can say that the evidence-statements in support of Einsteinian Relativity and against Newtonian mechanics are 'independent' of the two theories. Thus, an analysis of the way scientists actually conduct experiments saves the application of my Criterion 4 and 5. And this is while conceding that the theories in contention do not stand exhaustively in the same logical and semantical relationships.

So, however an adequate theory of meaning change (sense and reference) may work out, the current lack of a solution does not impact the kind of theory of rationality I am advocating here. At the very least, even if the problem of logical incommensurability remains unsolvable, this does not detract from the rational commensurability of rival scientific theories. In the end, even for Kuhn [1977a: 185, 199], any purported logical incommensurability does not prevent rational dialogue on the comparative merits and demerits of rival theories. Kuhn had explicitly conceded that his five criteria for rational theory choice apply across paradigms (or 'disciplinary matrix', as he later preferred to call them.)[32]

Book cover: Against Method by Paul K. Feyerabend

For Feyerabend also, during his rationalist phase before going over to radical epistemological relativism, logical incommensurability did not stand in the way of conducting crucial experiments to test rival theories. Feyerabend [1970: 226] argued that the truth of an evidence-statement resulting from a crucial experiment is not determinable by a rival theory's postulates alone, but by the interpretation of an experience by such postulates. When scientists conduct crucial experiments, he said, they are in fact conducting two experiments and not one. During a crucial experiment, each research programme is tested for its ability to anticipate and novelly derive phenomena interpreted in its own terms.[33] So, even without recourse to direct semantic comparison, Feyerabend conceded, Newton's program led to predictive failure while Einstein's led to predictive success.

The other problem that I had mentioned requiring detailed solution; that of implicit rationality, may be considerably easier to solve than the problem of logical incommensurability. It arises for those who wish to deem science a rational enterprise. The problem is that different scientists have, by and large, professed that their theories have been arrived at, developed or appraised by a number of different methodologies. These methodologies, opponents of Lakatos claim, bear little or no resemblance to the MSRP. Induction from 'facts', falsificationism and conventionalism are some of the more popular autobiographical offerings of scientists. If the MSRP is the most adequate methodology, then in what sense can scientists be said to have appraised theories rationally? The solution to this problem lies, I think, in making an important distinction between how an individual scientist or scientific community thinks it appraises theories and how in actual fact it evaluates them. It is then open for a Lakatosian to argue that scientists had appraised their theories rationally, although they had given the wrong reasons for thinking so.

This approach becomes credible when we appreciate the complex relations between theory and practice. Kuhn's elucidation of how scientists are inculcated into their scientific community's ways of doing things sheds light on scientists' thinking about their own practices. Coupled with the fact that most scientists working on the ground are unfamiliar with the discipline of epistemology and the various theories in the philosophy of science, it is understandable that scientists will adopt the particular philosophical outlooks for which they have had the most contact. Many successful scientists, for example, repeated the standard account they read in their text books; that theories are inductions from 'facts'.[34] Despite the popularity of Popperian falsificationism among scientists from the mid-nineteenth century, Kragh [2013] illustrates well how some well-respected cosmologists promulgated naïve falsificationism while paying it lip service in practice.


  1. [32] For a discussion of Kuhn's weakening of his incommensurability thesis, see Musgrave [1971] and Sankey [1993].
  2. [33] See Franklin [1984] for a practical example of this.
  3. [34] This account originates with the early proponents of the Scientific Revolution, such as Francis Bacon and Isaac Newton, so they are in respectable company.

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