The is-ought and induction are clearly related in Hume, and I can't really debate a book I haven't read. I'll have to read it some time.
The way I understand it, Hume's writings have a recurring theme of the gap between a priori and a posteriori arguments. The problem of induction is that he thinks it is impossible to infer universal a priori truths from a posteriori observations and is an epistemological concept. The is-ought problem is that going from empirical observations about what is to ethical statements about what ought to be is a jump from an a posteriori positive claim to an a priori normative claim without justification. The way they tie together is that the former makes the solution of the latter impossible.
I'm perfectly willing to believe that Hacking has a solid argument that you deal with the problem of induction, which means the is-ought problem is solvable. It wouldn't be a solution of that problem though; it's similar to proving a system of equations has a solution without solving it.
That being said, I also have no problem talking about a priori normative claims as long as we acknowledge them as such. For instance, I have no issue with the statement:
Ought is a desired state. In ecological economics we begin with the desired state and ask what is the control surface or institutions by which we can arrive at that desired state. How could institutions or value be considered in a way that accounts for the real biophysical limits and costs in a safe operating space.
The question about how to develop solutions for reaching the desired state is positive and scientific. Picking that desired state is normative and not scientific, unless you have a solution to the is-ought problem (which I'd be interested in hearing).
Phew, that's a lot of writing! But onwards to Welras.
Let's talk about mathematical modeling. Mathematics is firmly in the a priori world. Mathematical modeling is a bridge between the two, and I'm sure Hume would not approve. But let's be clear as to what the intent of using models are. You'll have to forgive me for the huge block of text, but Milton Friedman has a good discussion of both the methodology of modeling and addresses the
"Ideal types" in the abstract model developed by economic theorists have been regarded as strictly descriptive categories intended to correspond directly and fully to entities- in the real world independently of the purpose for which the model is being used. The obvious discrepancies have led to necessarily, unsuccesful attempts to construct theories on the basis of categories intended to be fully descriptive. This tendency' is perhaps most clearly illustrated by the interpretation given to the concepts of "perfect competition" and "monopoly" and the development of the theory of "monopolistic" or "imperfect competition." Marshall, it is said, assumed "perfect competition"; perhaps there once was such a thing. But clearly there is no longer, and we must therefore discard his theories. The reader will search long and hard - and I predict unsuccessfully - to find in Marshall any explicit assumption about perfect competition or any assertion that in a descriptive sense the world is composed of atomistic firms engaged in perfect competition. Rather, he will find Marshall saying: "At one extreme are world markets in which competition acts directly from all parts of the globe; and at the other those secluded markets in which all direct competition from afar is shut out, though indirect and transmitted competition may make itself felt even in these; and about midway between these extremes lie the great majority of the markets which the economist and the business man have to study."28 Marshall took the world as it is; he sought to construct an "engine" to analyze it, not a photographic reproduction of it.... It is frequently convenient to present such a hypothesis by stating that the phenomena it is desired to predict behave in the world of observation as if they occurred in a hypothetical and highly simplified world containing only the forces that the hypothesis asserts to be important. In general, there is more than one way to formulate such a description - more than one set of "assumptions" in terms of which the theory can be presented. The choice among such alternative assumptions is made on the grounds of the resulting economy, clarity, and precision in presenting the hypothesis; their capacity to bring indirect evidence to bear on the validity of the hypothesis by suggesting some of its implications that can be readily checked with observation or by bringing out its connection with other hypotheses dealing with related phenomena; and similar considerations. Such a theory cannot be tested by comparing its "assumptions" directly with "reality." Indeed, there is no meaningful way in which this can be done. Complete "realism" is clearly unattainable, and the question whether a theory is realistic "enough" can be settled only by seeing whether it yields predictions that are good enough for the purpose in hand or that are better than predictions from alternative theories. Yet the belief that a theory can be tested by the realism of its assumptions independently of the accuracy of its predictions is widespread and the source of much of the perennial criticism of economic theory as unrealistic. Such criticism is largely irrelevant, and, in consequence, most attempts to reform economic theory that it has stimulated have been unsuccessful.