> That's only an empirical generalization if you can cache out "valuable/effective/legitimate" in genuinely empirical terms (at minimum, in terms of observer-independent observations free from value judgments).
I can cash it out empirically as "generates accurate empirical predictions and suggests fruitful avenues for future investigation" (fruitful in the sense of ultimately leading to more detailed and accurate empirical predictions). That the measure of a theory is the accuracy of its predictions is of course a subjective human position (there are an infinity of possible measures on which to evaluate theories, and a priori no reason to prefer one over another), but again that's (a cautious Neurath's boat extension of) the common-sense way that we all evaluate theories in practice in everyday settings.
No, that's not even close to cashing out the generalization in empirical terms. To do this you'd need to specify exactly which observations would confirm or disconfirm it. Without the parenthesized parts, your gloss of the generalization remains vague and value-laden. With the parenthesized parts it is virtually tautological, since it's in the nature of empirical knowledge to generate accurate empirical predictions. It's surely not news to anyone that if forms of knowledge which lead to detailed empirical predictions are superior to other forms of knowledge, then empirical knowledge is superior to other forms of knowledge.
What you really seem to want to do, then, is argue from the nature of empirical knowledge itself to the conclusion that it is better than other methods of empirical knowledge. But that requires rational argument to back up the italicized statement above, not (just) an inductive generalization. And then we come back to the problem that it is impossible to find suitable premises for such an argument which can themselves be known empirically.
(For reference, the generalization we're talking about here is that "a bunch of empirical knowledge turns out to be valuable/effective/legitimate and all the supposed non-empirical knowledge I've seen turns out not to be valuable/effective/legitimate".)
> But that requires rational argument to back up the italicized statement above, not (just) an inductive generalization.
Why? Everyone evaluates ordinary, everyday knowledge in terms of its empirical predictions, so everyone seems to accept the italicised statement in practice, even if they'd argue for some sophisticated alternative in the abstract.
I can cash it out empirically as "generates accurate empirical predictions and suggests fruitful avenues for future investigation" (fruitful in the sense of ultimately leading to more detailed and accurate empirical predictions). That the measure of a theory is the accuracy of its predictions is of course a subjective human position (there are an infinity of possible measures on which to evaluate theories, and a priori no reason to prefer one over another), but again that's (a cautious Neurath's boat extension of) the common-sense way that we all evaluate theories in practice in everyday settings.