I have a couple of questions about W’s RA paper of the “I’m pretty sure I’m missing something” sort. So if anyone has ideas of what I’m missing I greatly appreciate the help.

1. The key to W’s response to O&S seems to be the nature of step 3.

[T]he third step of robustness analysis involves interpreting the mathematical structures as descriptions of empirical phenomena. In the predation case, theorists have to decide how two coupled differential equations will explicitly map on to the properties of real or imagined predator-prey systems. (738)

But I’m not sure what this involves. The most natural way for me to read it is to say that the investigators are now deciding what the link is between the model descriptions and the models (and on to targets). But surely this has been done already when the initial model descriptions were generated.

When W explains how this answers O&S he says,

Standard issues in confirmation theory concern whether a particular kind of model, such as the logistic growth model, is confirmed by the available data. However there is a prior confirmation-theoretic question that is often asked only implicitly: If the population *is* growing logistically, can the mathematics of the logistic growth model adequately represent this growth. (740)

The way I naturally read this, such a confirmation is trivial. What is it for a population to grow logistically except that its growth can be described by a logistic function?

W goes onto say that confidence in a positive answer to the question above is bought by “demonstrating that the relevant mathematics could be deployed to make correct predictions” (740). What this means beyond “theories are constructed using the maths and predictions are compared to real-world events” I don’t know. All the above only seems to indicate that the models that go into the hopper for robust analysis were developed in normal scientific (empirical) ways (and therefore RA is not non-empirical confirmation). But this is exactly what I take Levins’ response to be at the beginning of the paper (on 733) (though W has tidied up to what Levins’ response may apply, i.e. his more complex formulation of robust theorems).

2. My other confusion concerns the “two key questions” on page 739. W takes answering these as the key to ensuring that the antecedent of the conditional holds, and that all the *ceteri *are *paribi*. They are:

1. How frequently is the common structure instantiated in the relevant kind of system?

2. How equal do things have to be in order for the core structure to give rise to the robust property?

Answering the second is essentially the fourth step of analysis, so I’m not quite sure what it’s doing here. But that is a minor complaint.

W’s discussion of the first question seems to indicate that the greater the variety of models that are put into the hopper is, the more likely it is that the robust property will be true of target systems, since it is more likely that the common causal structure will actually be present. But then he also says that “This would allow us to infer that when we observe the robust property in a real system, then it is likely that the core structure is present and that it is giving rise to the property” (739). Wouldn’t the conditional representation of robust theorems have to be a bi-conditional for this to be the case? He says that the question is best addressed empirically, so the “relevant kind of system” is indeed talking about target systems. So in applying this to the Volterra example, would it be that various pred-prey systems were examined, the various models were developed that fit those systems, and then the models were all thrown in to the hopper and Volterra came out as the robust property with the given antecedent as the core structure? And if we studied a lot of systems in generating many models, then we can be more confident that we’ve really pared the core down to the important parts for the robust property. Is that what he’s saying?

In sum: I am confused. Thoughts?