A standard conception of the transition from classical to relativistic physics is that although Einstein's theory of relativity supersedes Newton's theory, what we have is an improvement or generalization whereby Newton's theory is a special case of Einstein's (to a close approximation). We can therefore say that the later theory is closer to the truth than the older theory. Kuhn's view that ‘mass’ as used by Newton cannot be translated by ‘mass’ as used by Einstein allegedly renders this kind of comparison impossible. Hence incommensurability is supposed to rule out convergent realism, the view that science shows ever improving approximation to the truth.

(source: Stanford Encyclopedia of Philosophy)

When saying that "incommensurability is supposed to rule out convergent realism" is incommensurability referring to semantic incommensurability only?

Or may the sentence be applied to methodological and observational incommensurability as well?


This question has been up for a while so I thought I'd offer an answer (even if incomplete).

I haven't read Kuhn's original work though in all of the cases in which I have heard his incommensurability argument made, it has been on semantic grounds. This is a common example, the idea that the meaning of the term 'mass' changes during the transition from the Newtonian to 'Relativistic' paradigm.

Another example Kuhn uses is one from his own experience in aiming to study Aristotelian physics. Since he was a physicist, he was to teach a course on the history of science as the university he was working for began an initiative to educate all students (including those studying humanities and arts) about science. He found he had trouble when studying the historical (Aristotelian) accounts of nature and 'physics'. He found it laughable that these ideas were entertained by thinkers as intelligent as Aristotle since they were so obviously wrong but later came to realise that the source of his confusion was the fact that he was interpreting the ideas with his modern understanding of terms like 'motion'. 'Motion', to Aristotle, meant something completely different. More like a synonym for the general word 'change' than anything specifically to do with change of spatial coordinates. He drew the conclusion that we will always have trouble appraising the theories of the past because of this and how terms change like this. This argument is specifically made distinct to the concept of methodological incommensurability though it could have been that Kuhn believed in both forms of incommensurability. Please note that this is a brief statement of the point he made and likely doesn't do it justice. See here for more.

One thing I might add is that it's wrong to say that the meaning of the term 'mass' changes as it is carried from Newtonian to Relativistic physics. Students of physics learn Newtonian physics long before they learn Relativistic physics and therefore, even if it was the case that the meaning of this term has changed, modern physicists would understand this difference. As a student of physics, I learned Newtonian mechanics long before I approached special relativity and when you first learn relativity, there is a clear distinction made between the idea of a 'rest mass' (which is equivalent to the newtonian idea of 'mass') and the idea of 'relativistic mass', a completely separate concept. In physics, talk of 'mass' is usually presumed to be talk of 'rest mass' since it isn't given the caveat of being specifically relativistic. Since old theories still make for good models, most quantities, terms and meanings in physics go this way. Students still learn about Maxwell's equations, Newtonian gravitation and Kepler's laws, about kinetic theory and Faraday's law. Therefore, students go on to develop new theories with an understanding of the terms used in these old theories, some of which are from much older paradigms and therefore the understanding between paradigms is conserved.

There is even much debate as to whether the term 'relativistic mass' should be used at all since the quantity itself seems distinct from any 'kind' of mass as the term was traditionally used. This article by Steven Weinberg in response to the arguments made in The Structure of Scientific Revolutions makes all of these points well. He concedes some points to Kuhn but sets the record straight on how the science is actually practiced.

  • Yes but relativistic mass actually exists, and rest mass is the relativistic mass of a thing that is in a state that nothing is ever in -- a thing that has no internal energy. And the fact that one can make that observation keeps relativistic mass from being a completely separate concept from rest mass. The fact that modern science approaches its actual content by layers of approximation is just a testament to its complexity, not a real belief that any of those stages represent a genuine understanding.
    – user9166
    Aug 23 '18 at 15:44
  • This demonstrates your lack of understanding. An object at rest has internal energy... from its rest mass... Oct 2 '18 at 12:36
  • This demonstrates nothing, and the choice of language demonstrates there is no point in talking to you.
    – user9166
    Oct 3 '18 at 18:38

The point here is not to take Einstein as an example, but to point out that even in the most conservative of shifts, there is always some new content that is not compatible with the old content. You cannot mark out Einstein as an absolute exception to incommensurability, just because it carries Newton forward as a special case. There is still something new in the theory that makes parts of Netwon absolutely wrong, or there would be no shift. Mass acquired by adding energy is not mass for Newton. It just cannot be.

The argument is better proven by other cases, like the ones that originally motivated it: the move from circles to ellipses in astronomy, the re-introduction of atomism as the basis for heat flow, etc. The point isn't that this is a good example, but that even in the most strained example, the observation is still not completely wrong. There is still a change in the meanings of basic terms, even when there is only a tiny change in predictive value, which makes for entirely new approaches (like the observations of lensing that let us identify 'dark matter'.)

There is physics now being done, especially astrophysics that has no basis whatsoever in Newton, and which Newtonians would not see as an extension of their theories, but would see as just plain wrong. Einstein did not just refine physics, he created new meaning incompatible with the existing meaning.

To rule out convergent realism, you need some examples, not for every change to be a good example. But we already have a dozen. However, since the theory is stated in terms of 'every revolution' you need some evidence that there are not any absolute exceptions to the theory. This example does show that in a minor way, it still applies.

  • That argument is more like a pessimistic meta-induction than Kuhn's argument. Part of Kuhn's argument is literally that our language and standards change between theories and one key example is the change in the meaning of mass between Newtonian and Relativistic physics. No such change occurred. Physicists of today are trained up in the application of Newtonian mechanics. No such change has occurred that would prevent modern physicists from understanding or making use of Newton's theories or even Kepler's theories of planetary motion. Aug 23 '18 at 11:46
  • @JoeLee-Doktor The fact that your interpretation of Kuhn does not in any way fit the data lets you tell me that your interpretation is right, and mine is wrong? No, people did not stop being able to use every known fact from Alchemy when Chemistry started. To propose that would be nonsense. And Kuhn did not propose it. Nor did we lose the ability to use Netwon when Einstein came along, or Ptolemy when Kepler did. We just really had to interpret various facts of the old theory as incorrect.
    – user9166
    Aug 23 '18 at 14:36
  • @JoeLee-Doktor At some point, consider Kuhn's actual arguments with Popper and his other contemporaries. He fends off this constant insistence that he has declared all outdated processes and tools impossible to use in a new paradigm over and over again. But there is no part of Newton that really means the same thing once you know that speed changes mass, or that gravity affects time. Newton did not think his theories were just approximations. We do.
    – user9166
    Aug 23 '18 at 14:45
  • I wasn't using the utility of Newton's theories as an argument against Kuhn. That's a moot point. I'm saying that these terms and the symbols in the equations do mean the same thing. I know they mean the same thing. When you learn one after the other there's no need to learn what these new terms mean you can use the theories either way. Unless you can properly unpack "there is no part of Newton that really means the same thing" then there's no conversation to have. Sep 13 '18 at 22:50
  • @JoeLee-Doktor Mass does not mean the same thing, it includes energy. Length and time do not mean the same thing, because Newton's length and time don't change when objects move relative to one another. So very few of the derived formulas continue to mean the same thing, except when the variations all cancel out. That is not deep. Protest all you want, the two theories are not talking in the same terms, at least not precisely.
    – user9166
    Sep 20 '18 at 0:19

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