Monday, September 6, 2010

What Are The Error Bars On That?

I have been summarizing the physicalist views of two authors, Jeffrey Poland and Andrew Melnyk. In this post, I give my own opinions about Melnyk's view. Caveat lector!

Melnyk thinks that physicalism should take as its basis the current consensus physics of practicing physicists. At first I thought this a reasonable approach, but the more I thought about it the less I liked it. I see two very serious problems with it:
  • - What if the best current theories of physics are not even logically consistent with each other?
  • - What if the ontological basis of current physics is itself problematic?
On the first point, I think many physicists would agree that General Relativity (GR) and current particle physics theories (especially the Standard Model - SM) are logically inconsistent. This is a big problem for Melnyk, because he says the attitude that we should take toward physicalism is the "scientific realist (SR) attitude," that is, to "assign the hypothesis a higher probability than its relevant rivals." (p. 227) But if two theories are logically inconsistent, then we can't assign their joint probability as anything other than zero.

(Some might argue with my characterization of these theories as inconsistent. However, it is easy to see that, historically, there have been many times when our best physical theories were logically inconsistent: for instance, around 1900 Maxwell's electrodynamics was inconsistent with Newtonian mechanics. So physicalism must at least recognize the possibility that, at some given time, a fundamental inconsistency might exist in the physical theory basis.)

On the second point, I would say that we are in exactly this situation with respect to quantum mechanics. The ontological status of the quantum wave function (or state vector) is a matter of considerable dispute. Does it represent something physical, or does it represent our state of knowledge? The latter is my own view, but this seems to create a huge difficulty for physicalism: If all large-scale phenomena are based on (realizable as) quantum phenomena, and quantum phenomena are only understandable as probabilities of certain large-scale phenomena (output of sensors, counters, and other experimental apparatus), then physicalism is in very great danger of circularity.

I don't know what to do about the second problem - this seems like a very serious problem to me. But I have a suggestion about the first. I think Melnyk is simply wrong about the SR attitude being the view of practicing scientists. After all, how could we physicists simultaneously endorse GR and the SM while acknowledging their inconsistency? I think scientists' (or at least physicists') attitude is better described as the "good approximation (GA) attitude." That is, GR provides a good approximation to how the universe works at the largest scales, and the SM provides a good approximation at the smallest scales. Physicists - in spite of what they might themselves say - are not actually interested in whether a theory is true. They are interested in whether it works.

In fact, they have to be. Let me explain. I'll ignore GR for the moment and pretend that all we need for a fundamental theory of physics is a theory of particles and their interactions. Now, the Standard Model consists of some equations that contain various parameters that must be experimentally determined: the speed of light, Planck's constant, the electron's charge, the masses of the quarks, and so forth. Let's suppose that there is a true theory of the universe that is exactly the equations of the SM with some values of those parameters. Let's call that theory SM-true. Our current theory has the same equations, but with some "best fit" values of those same parameters. Call that theory SM-bf.

Now, the probability that SM-bf and SM-true are the same theory is precisely zero. There is zero chance that the specific values that we have deduced from experiment are identical to the true values. It is like trying to hit an infinitesimally small bull's-eye with an infinitely thin dart. (Mathematically, the true value is a set of measure zero in the space of possible parameters.) Certainly, the relevant rivals of our SM-bf would include other SM-like theories with other values of those parameters. But the probability of each of those rivals is zero, too! So the SR attitude is useless in deciding among these rivals.

If you go look up the values of those parameters, you will see them listed with experimental uncertainty after the value. These are what we sometimes call the "error bars." What those uncertainties mean is this: we have no confidence that the parameter takes on the exact value listed, but we have high confidence that the true value lies within the range specified by the value and the experimental uncertainty.

I think endorsing a theory by taking the GA attitude should mean that we believe the universe will behave approximately as described by the theory, where "approximately" means "within the range of expected outcomes as determined by the range of experimental uncertainty in the parameters of the theory, as long as the values of relevant external parameters are within a specified range." Here "external parameters" refer to physical values that are characteristic of the particular situation in question, rather than parameters appearing in the theory. External parameters might include relative velocity, center-of-mass energy, and so forth.

By taking the GA attitude, we can endorse a theory even if we are sure (by reason of logical inconsistency, for example) that it is not a true theory. Thus, we can say that GR is a good approximation at large values of some external length parameter, and SM is a good approximation at small values of that parameter, while not claiming that either one is (or is an approximation to) a true theory.

Melnyk mentions the possibility of treating physicalism as approximately true (p. 225), but dismisses it on the grounds that notions of approximation to the truth are "notoriously hard to explicate satisfactorily." But, given the difficulties of Melyk's own account, and given the fact that physicists have to deal with approximations to the truth all the time, and have developed tools for doing so quantitatively, I think that this must be a more promising avenue than his own.


  1. In mathematics you can divide proofs into constructivist and non-constructivist. A non-constructivist proof shows that a theorem is true or false, but does nothing to explain anything deeper. Proofs by contradiction are often non-constructivist. By contrast, a constructivist proof builds the mathematical object that is the point of the theorem, thus giving more insight and value to the theorem.

    I view physics as basically non-constructivist. That is, physics uses mathematics to describe what happens in some interaction, but it isn't very good at telling us why the predicted action happens.

    For example, Newton created a very serviceable theory of gravitation. If you put the correct numbers into his equations, out came very respectable predictions of planetary behavior. And, as a bonus, his equations explained why the planets moved the way they did: the inverse square law. But why does gravity obey the inverse square law? How does gravity work at all? No answers from Newton on this.

    Einstein came along a few centuries later and updated Newtonian Gravitation with General Relativity. His theory gave better answers, and it also deepened the understanding of gravity: masses distort space-time, which is shy gravity works the way it does. Fair enough. But how does mass distort space-time? And what is mass, anyway? And what exactly is space-time, really?

    Physics uses the tool of mathematics to describe the behavior of objects, and in this it is very successful, and getting better all the time. But the universe is not math. Math can approximate and describe the universe, but it's not so good at explaining. I don't think you have to go too far before you can ask why- and how- questions that physical theories can't answer. And it seems to me that these physicalist philosophies need to be rooted in theories that explain the how- and why-, not just the what.

  2. I think you're right to focus on Melnyk. He's very bright and almost the only person to even try to defend naturism. When he was writing the book, I suggested the verisimilitudeneity approach, but he'd have none of it. I still think it's the most reasonable approach. I think the merely numerical approach you mention for values won't work, though, for the ontology side of a theory. An entity can't be approximately there. And the central thesis of physicalism is that there is NO non-physical thing. That can't be only approximately true.

  3. Hi, Trent, and thanks for joining the discussion. I find your attitude fascinating because it is so different from my own.

    I admit that I failed to address the ontological issue. I do think that there is a sense in which an entity can be "approximately there." Think of an atom: we can use the picture of atom-as-little-billiard-ball for many purposes (e.g. deriving gas laws from kinetic theory, a good example of realization in action), even though we know (or believe) that an atom is REALLY a complex system of neutrons, protons, and electrons. So a physicalism that is based on atoms need not be discarded once the deeper structure - the "correct" ontological basis - is discovered. We only need to admit that atom-as-little-billiard-ball is only an APPROXIMATELY correct picture of the true physical bases.

    "And the central thesis of physicalism is that there is NO non-physical thing."

    This is wrong. The central thesis is that any non-physical thing is REALIZED by a physical thing. For Melnyk, physical things are ONLY those that are described in the proprietary language of physics. So anything from a chair to an emotion is non-physical.

    In his chapter on reductionism, he goes to great lengths to explain this point. The whole point of realization physicalism is that non-physical things can be EXPLAINED in terms of physical things. But you don't provide explanations for things that don't exist!

    For example (mine, not his), a rainbow can be given a physical explanation in terms of the refraction of light by water droplets. But that doesn't deny that the rainbow, as a phenomenon, exists.