The Limits of Causal Explanation

Woodward's interventionist conception of causal explanation is perhaps the most expansive and well-worked out view on the market. He conceives of a causal explanation as providing information about how the explanandum would vary under appropriate possible manipulations. Among other things, this allows an explanatory role to phenomenological laws or other generalizations that support the right kind of counterfactuals, even if they do not invoke any kind of fundamental or continuous causal process.

Given the recent debates on mathematical explanation of physical phenomena, it's worth wondering if Woodward's account extends to these cases as well. In a short section in the middle of the book, he concedes that not all explanations are causal in his sense:

it has been argued that the stability of planetary orbits depends (mathematically) on the dimensionality of the space-time in which they are situated: such orbits are stable in four-dimensional space-time but would be unstable in a five-dimensional space-time ... it seems implausible to interpret such derivations as telling us what will happen under interventions on the dimensionality of space-time (p. 220).

More generally, when it is unclear how to think of the relevant feature of the explanadum as a variable, Woodward rejects the explanation as causal.

Still, some mathematical explanations will qualify as causal. This seems to be the case for Lyon and Colyvan's phase space example, but perhaps not for the Konigsberg bridges case I have sometimes appealed to. To see the problem for the bridge case, recall that the crucial theorem is

A connected graph G is Eulerian iff every vertex of G has even valence.

As the bridges form a graph like the figure, they are non-Eulerian, i.e. no circuit crosses each edge exactly once.



I would argue, though, that as with the space-time example, there is no sense in which a possible intervention would alter the bridges so that they were Eulerian. We could of course destroy some bridges, but this would be a change from one bridge system to another bridge system. It seems that to support this position, there must be clear set of essential properties of the bridge system that are not rightly conceived as variable.

Globe and Mail Drops the Ball

If you needed any more evidence that the general public, including Toronto's Globe and Mail newspaper, doesn't know what "philosophy" means, check out this profile of a self-described "cyberphilosopher" and his campaign to expose the dark side of the parent-child relationship:

The philosophy behind this is codified and has its own lingo. For example RTR (Real-Time Relationship) means you're willing to confront a spouse or parent if you feel they're hurting you. "If you don't want to be a slave, stop acting like a slave," he writes.

One might have hoped for at least one sentence in the article explaining that this has nothing to do with philosophy.

Science Communicators?

Today's Guardian includes an interesting piece by Jim Al-Khalili on the role of what he calls "science communicators" in the public sphere. While one of their obvious functions is to communicate scientific developments in a way that an educated public can understand, he suggests a broader role:

I do feel strongly however that those scientists who have a voice must be doing more than simply popularising their field to attract the next generation into science. Yes, this is vital; but it is also vital that we help defend our rational, secular society against the rising tide of irrationalism and ignorance. Science communicators, for want of a better term for now, have a role to play in explaining not just the scientific facts but how science itself works: that it is not just "another way of viewing the world"; and that without it we would still be living in the dark ages.

Perhaps here is another place where philosophers of science can also make a contribution? There was good evidence of the potential for this at the PSA. While I missed several sessions on science and the public, there was a great series of papers relating to medical issues and broadly feminist epistemology. Susan Hawthorn, for example, gave an illuminating reconstruction of history and current practice of ADHD medicine, and Intemann and de Melo-Martin offered a critical reconstruction of the science behind the highly publicized HPV vaccine.

Post-blogging the PSA: Gauge Freedom and Drift

It's taken me a few days to recover from the excellent PSA. I talked to many people who had a great time and who thought this year's program was exceptionally well-balanced to reflect both old classics and new debates in philosophy of science.

On the first day I was happy to attend two sessions which reflect the interpretative difficulties arising from the central role of some mathematics. In the first session, Richard Healey summarized his paper "Perfect Symmetries", followed by Hilary Greaves' and David Wallace's attempts to critically reconstruct Healey's central argument. Very roughly, Healey aims to distinguish cases where a symmetry in the models of a theory explains observed empirical symmetries in physical systems from cases where there are theoretical symmetries with no analogous explanatory power. In the latter case, the theoretical symmetries may just amount to 'mathematical fluff' or 'surplus structure' that lack physical significance.

Then it was time for some biology and the symposium "(Mis)representing Mathematical Models in Biology". The session began with biologist Joan Roughgarden's summary of different kinds of models in biology, followed by Griesemer, Bouchard and Millstein talking about different issues in their interpretation. Both Griesemer and Millstein emphasized the importance of a biologically grounded understanding of the components of a biological model, and argued that a merely mathematical definition of such components would block our understanding of biological systems. Millstein was especially emphatic (to quote from a handout from a previous presentation of hers) "Selection and drift are physical, biological phenomena; neither is a mathematical construct." That is, when we look at the changes in some biological system over time, we cannot think of the changes as resulting from a genuine process of selection with some additionally mathematically represented divergence from some ideal that we label as "drift". Instead, drift itself must be countenanced as a genuine process that makes its own positive contribution to what we observe in nature.

While it is a bit of a stretch, there is at least a suggestive analogy between these debates in physics and biology: in both cases, we have a useful and perhaps indispensable mathematically identified feature of our theories whose physical and biological status can remain in doubt, even for our best, current scientific theories. Here, it seems to me, we see some of the costs of deploying mathematics.

The Deep Blue of Poker

New Scientist reports on the success of a new (Canadian!) poker program, Polaris, at beating some top poker players. As with Deep Blue, this success is not exactly decisive as it was restricted to one-on-one play of Limit Texas Hold 'Em. This is surely the easiest version of poker to master.

The article mentions both the lack of perfect information and the contextual nature of the best play as complications in programming poker programs: "One of the fundamental problems for any poker player is that the best strategy varies, depending on your opponent's style of play." While it would be easy to see how simple calculations would handle the lack of information, I am more interested in seeing how programmers can deal with the interactions between playing style and optimal no-limit betting!

New Book: Collected Works of Carnap, Vol. 1

One of the best parts of the PSA was the reception hosted by Open Court as part of their launch of the Collected Works of Carnap. The first volume was actually there, and should soon be available for purchase. This volume is perhaps one of the most important as it provides English translations of Carnap's early work for the first time, including his doctoral dissertation. There is an extensive introduction and carefully compiled textual notes.

Real fans of Carnap will like the detailed chronology of Carnap's life. Some things that I never knew before: (i) in WWI, Carnap was initially assigned to the Carpathian mountains because of his skiing ability, (ii) in 1929 Carnap was advised not to publish his paper "On God and the Soul" because "it will make it impossible for him to get a job at a philosophy department anywhere in Germany" (xxxv), and (iii) in 1936 Carnap turned down an offer from Princeton to take up a position at the University of Chicago.

The whole team of editors is to be thanked for their excellent work. Only 12 more volumes left for them to complete!

Is the Standard Model in Trouble?

Maybe everyone who cares about this has already heard, but over the last week there has been an important posting on experiments done at Fermilab that the scientists are having difficulty interpreting. As Physics World reports,

Physicists at the Tevatron collider at Fermilab in the US, which is enjoying extended status as the world’s most powerful particle collider while CERN’s Large Hadron Collider (LHC) awaits repair, have reported signals in their data that hint at the existence of new fundamental particles. Last week members of the CDF experiment, one of the Tevatron’s two huge particle detectors, posted a preprint detailing a large sample of proton–antiproton collisions that cannot be accounted for either by quirks of the CDF detector or by known processes in the standard model of particle physics (arXiv:0810.5357, submitted to PRD).

I am certainly not the person to explain what the anomaly is or how it can be interpreted, but there are a number of interesting features of this development from an HPS perspective. Among other things, there seems to be some disagreement among the members of the large research group about going public with the result at this stage. Looking ahead, there will surely be many accounts of the data, and apparently an attempt to replicate the results at DZero.

For more from the physics blogosphere, see Not Even Wrong.