Monday, May 21, 2018

Incommensurability

Philip Kitcher has a good review of Errol Morris's The Ashtray, in which he makes some important points about the work of Thomas Kuhn.

According to the cartoon — and according to Morris: Kuhn denied the possibility of communication across the revolutionary divide. No — he said that such communication was inevitably partial. The languages of different paradigms are not straightforwardly inter-translatable. Often, no single term in one language will do for a scientifically important term in the other. What one paradigm sees as a “natural” division of the subject matter appears as odd and disjointed to its rival.

When I was in undergrad (a time when I read quite extensively in philosophy of science), I remember reading a number of criticisms of Thomas Kuhn and suddenly realizing that the reason they didn't entirely make sense to me was that the critics were assuming that 'X and Y are incommensurable' meant 'X and Y cannot be compared'. Of course, this is not true -- in fact, incommensurability implies that they can be compared. When we say that the legs and the hypotenuse of a right triangle are incommensurable, we don't mean that we can't compare them -- in fact, the Pythagorean Theorem gives you a precise account of such a comparison. Rather, the point is that in such a comparison there is no unit definable wholly in terms of a leg that measures the hypotenuse without anything left over. So to say that two theories are incommensurable in how they use the term 'mass', for instance, is not to say that you can't compare how they use the term, but instead that there is a shift of meaning between the two such that when you do compare them you find that one cannot perfectly translate what is meant by the other. 'Mass' in Newtonian physics and 'mass' in Einsteinian physics are obviously related and obviously comparable; but on comparison they do not fit each other exactly. You can identify precisely ways in which they do not fit each other. First, they are not exact synonyms. Second, if you try to get Einsteinian 'mass' from Newtonian 'mass' by adding qualifications or complications, you still don't get a direct translation until your qualifications have multiplied so much that you are just restating the Einsteinian account of mass. Third, if you try to get Newtonian 'mass' from Einsteinian 'mass' by (say) idealizing and introducing negligibility assumptions, you still don't get a direct translation until you've introduced so many assumptions that you can no longer use it for Einsteinian purposes. They are incommensurable -- you cannot intertranslate without something being lost or gained that the other theory cannot or does not countenance, because the sets of problems considered by each theory are not exactly the same, the methods used by each theory are not exactly the same, and the topics each theory treats as most important are not exactly the same.

Kuhn is hardly the first person to make the point -- Duhem argues the same, and more rigorously -- but Kuhn's version is in a generalized form so that it did not otherwise depend on the exact details of your account of how theory works. People reading him, however, regularly misunderstood what the word 'incommensurability' means, to the complete distortion of everything he says on the subject. This, combined with a dogmatic assumption about what scientific progress would have to mean -- cumulation without break -- and which Kuhn rejects, resulted in the kind of caricature Kitcher is arguing against.

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