I need to go a bit further than what I did in my blog post on conceptual anachronism. It is the worst nightmare of the historian, mostly because his or her craft is centrally about context. For them, there is a wrong answer, when looking at history unfairly with a modern lens. Philosophers make this mistake, too, but they tend to do it with style and blissful ignorance like you’ve never seen. The problem with philosophers doing it is double: 1) The philosopher’s project is often (only!) ostensibly lacking in investment in historical accuracy; but the truth is that this false impression makes it more difficult to pick up on his or her error —and this, in my opinion, means partial exculpation for the indicted philosopher. 2) The creative fashion in which conceptual anachronisms are employed is so unclear that the error may seem debatable. I have a particular instance in mind. It arose this past week, in a seminar I am taking under Jordi Cat, called “Unity of Science.” One of the readings, “Two Concepts of Intertheoretic Reduction” (in The Journal of Philosophy vol. 70 (Apr. 12, 1973) No. 7) by Thomas Nickles (a philosopher whose work I enjoy and admire), may contain such a conceptual anachronism. I have to explain a few things, first, so let me lay out the context and then explain the problem.

First of all, I had no clue what Nickles was talking about in this article, if he was on to some novelty. Cat put down his sledgehammer and presented, what he calls, a “charitable” reading. In the following, everything I say will have to do with this charitable reading of the paper, which is, really, my only understanding of the paper. Going off of the charitable reading, Nickles means to point out that there are two modes of reduction, the first being, in essence, Ernst Nagel’s, as presented in *Structure of Science: Problems in the Logic of Scientific Explanation*. The second, the novelty, is that reduction can work backwards, as is employed in the everyday lingo of the physicists: “Relativistic mass, in the equation of special relativity, *reduces* to Newtonian mass, when relativistic mass travels at low speeds.” To be clear, the proposal is a mathematical reduction, such that, as v→o (in other words, v<<c):

m_{o}=m’/√(1- (v^{2}/c^{2}))

Becomes:

m_{o}=m’

This is how any physicist speaks on an everyday basis. The question the reader might have is, what does this have to do with conceptual anachronism? Play with the math a little bit, before continuing on, and think about it. Nickles’ claim is that, to paraphrase: Okay, so the later paradigm doesn’t logically follow from the earlier, but there is a sense in which the older, strictly speaking, is a specific case of the more ‘advanced’ paradigm, where the ‘advanced’ is much more general (and presumably he would claim more accurate). Let’s first examine why the former does not logically necessitate special relativity. The problem comes from Thomas Kuhn’s point about incommensurability. Items in the Newtonian system do not correspond to the Einsteinian system. You can think about it philosophically, that space in Newton’s system is homogenous and isotropic (not to mention absolute, though I wonder about this in the times since Laplace, Lagrange, and so on have altered Newton’s mechanics), while Einstein’s space is has curvature (positive, negative, or zero), is not homogeneous and exhibits anisotropy, not to mention is relative. You can also think about it in a more linguistic sense, examining the differences in terms and their meanings within the context of their respective paradigms. What Nickles wants to point out is that the mathematics defeats the incommensurability that the logic faces. Ah-ha! Your intuition should tell you that something is wrong, and that in what was just said is the key to finding the conceptual anachronism. If you are a little unfamiliar with the mathematics, but you have a pretty good idea that that is where the trick is, then you are right.

There was a slick use of relativistic mass to hide the incommensurability in the mathematical forum of the reduction. Here’s the thing: Why didn’t Nickles get sufficiently mathematical and just use talk about functions, which is semantically appropriate? Why didn’t Nickles choose to talk about special relativity from the standpoint of mass as a function of velocity: m(v)? Had he done this, he would have seen that, as v→o (in other words, v<<c), mass does not stop being a function of velocity. Taking a look at the Newtonian system, mass is a constant, no matter what. A way of drawing a comparison between the two sets of attempts to reduce one paradigm to the other is this: The problem with the logic reduction was that mass means much more in the later paradigm than it did the in the earlier, making them incommensurable; the same is true of the mathematics, and the trick that Nickles accidently employs is that he mathematically sweeps under the rug the fact that mass (mathematically speaking!!) means more in the later paradigm than it did in the earlier. Even from the standpoint of mathematics, there is an incommensurability, in that functions are not constants, and so on and so forth. Therefore, the way around the puzzle-solving problems is ad hoc rationalization, and this is not limited to the linguistic concepts of the paradigmatic structure, which make it impossible to logically derive the newer paradigm from the older one; the ad hoc rationalization extends to the mathematics.

The point of all of this is that conceptual anachronism plays a role in philosophy of science, too, in a similar but different way that it does for the historian. The similarity is that both disciplines need to avoid the artificial imposition of modern notions upon former periods. The difference is that philosophers can find ways of cheating that are so complicated enough that they are not aware that what they are doing is cheating. Moreover, it might not be obvious to anyone that there has been any cheating. I think the parallel moral of the above is that incommensurability touches all areas of the conceptual framework, altering them, and I really can’t think of an instance in which such is not the case. Paradigm shifts tend to involve brute force, trying to make it so that the critical problems of one paradigm are either destroyed or placed into a new and meaningful context in which normal science can continue to work on them. This means a reconfiguration of concepts (general structural framework and qua words endowed with semantics), philosophy (methodological and regarding the conceptual structure), and the mathematics. In general, this line of thinking can be instrumental in raising awareness for when one might be misstepping, committing a conceptual anachronism in philosophy, but it certainly won’t alert one to all cases in which conceptual anachronism has been committed.