[Continuing my earlier blog on Nancy Cartwright’s book How the Laws of Physics Lie.]

One thing about the philosophy of science is that it tries to cover a very wide spectrum of disciplines – not just physics, chemistry and biology but other subjects such as psychology and medicine. I have grave doubts about this approach; while applying a given method or concept across the entire spectrum may be beneficial in some sense, I think the individual sciences are too different for the same philosophical approach to work on all of them.

Nancy Cartwright certainly espouses the wide-spectrum approach. She regularly quotes examples from botany and medicine, despite the fact that her book is about the laws of physics. This may, however, be done partly to contrast physics with the other sciences. For instance, she maintains that a physical law such as the law of gravitation is not a causal law because it “provides no account of what makes things happen”. In contrast, she argues, laws such as “smoking causes cancer” and “aspirin relieves headache” are causal. But these sorts of statement are so woolly that they can surely hardly be classed as laws at all. I find myself screaming “How much smoking? What kind of cigarette? What sort of cancer? In what sort of body?” etc. Surely we all know at least one  person who has smoked all their life but not contracted cancer – so how can this be causal?

Her problem with laws such as that of gravitation may be simply because of the way in which it is often presented – in algebraic form. An algebriac equation can be changed around so as to make any quantity the subject, so there is no sesne of a “flow” of causation in the bald algebraic statement. But when I was at school, we learnt our physical laws in verbal form first. The law of gravitation would have been rendered something like this: “The gravitational force exerted by one body on another is proportional to the product of the masses divided by the square of the distance between them”. The term “exerted by” surely indicates causality here. No-one would say that the force is causing the masses to exist. And in the case of electromagnetic induction, we would say that “the induced emf is proportional to the rate of change of flux, and acts in a direction so as to oppose the change of flux”. Clear causality there, surely? And these are laws that always apply – every single time – and not just in certain circumstances, as in the case of smoking and cancer.

I think another part of the problem might be that Cartwright, like many “mainstream” philosophers, is stuck in a qualitative groove, and is used to dealing with statements about discrete entities that can be regarded as having, or not having, various properties – a very discrete world, where everything either is or isn’t something, with nothing in between. The grey world of continuously-varying quantities seems to take such people by surprise. In the book, she complains over and over again that the laws of physics do not “state the facts”.  She is very keen on “the facts”, but does not explain what they are, or how, and whether, we might know them. But she wants laws to be “true” – she wants them to make predictions that are at one with “the facts”. Earlier, I showed that this cannot be done in the case of the sort of “facts” that modern physics addresses – where the laws make predictions about quantities that are continuous variables, capable of taking any rational value, and possibly irrational ones too.

She actually addresses the question of approximations quite early in the book, on page 14. She says that “realistically-oriented philosophers are inclined to think that approximations raise no problems in principle. The “true” solution is the rigorous solution, and departures from it are required only because the mathematics is too difficult or too cumbersome …”

The second sentence here is disappointing. As I showed earlier, approximations are all we get – and not because the maths is too difficult, but because measurement, which can supposedly verify or falsify a law, returns not a number, but a confidence interval; and confidence intervals cannot be equal or unequal. So she says a sensible thing, but for the wrong reasons; and in any case, she then goes on to disagree with the view she has just set out.

Cartwright does not actually mention the Principle of Superposition by name, but she makes vague references to it. On page 59 she says that there is a presumption that “the explanatory laws ‘act’ in combination just as they would ‘act’ separately. I think this is probably somehting more than “a presumption”; I think it has probably been tested quite thoroughly. For instance, in the Thomson e/m experiemtn for the electron, it would be quite surprising (and very noticeable) if the deflection of the electron beam when either the magnetic or the electric field is turned off, were not explainable by exactly the same equations (including numerical values) as when the two fields act together. I could be wrong here, of course, adnd have to admit that i have not verified it myself (yet). But I bet you someone, somewhere, has.

When discussing how the cooking time of potatoes is affected by the salinity of the water and the altitude, she produces complicated-looking expressions in formal logic for each individual case but claims that “neither of these tells us what happens when we both add salt to the water and move to higher altitudes”.

Really? Surely this is a classic example of a function of two variables. We can express the cooking time T as a function of the salinity S and the altitude A in differential form as follows:

dT =  – k dS + m dA

where k and m are constants; then integrate to find

T = T0 kS + mA

 where T0 is a constant, i.e. does not depend on salinity or altitude. When both the salinity and the altitude are varied, this equation will tell us what happens, as long as we know the values of the constants, which can be found empirically.

About halfway through the book, we finally encounter some pretty heavy equations, and some circuit diagrams. Unfortunately that is the point at which I stop for now. I am fed up with reading it, I have more important things to do, and besides it is due back in the library. I will come back to it later. Maybe.

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