There are many accounts of induction and confirmation and I will say a little more about them shortly. First, however, I want to collect a number of generalizations about what is to be found in that literature:
• Most accounts of induction and confirmation do not admit any simple argument that assures us that evidence must underdetermine theory.
The impoverished hypothetico-deductive confirmation relation is exceptional in admitting such an argument.12 Most accounts do not give us the opposing result, however. Excepting cases in which a fairly rich framework is presumed, most accounts of induction do not assure us that evidence can determine theory. As a matter of principle, most accounts of confirmation leave open whether evidence determines or underdetermines theory.
• Most accounts of confirmation do not allow that theories with identical observational consequences are equally confirmed by those consequences.
One might wonder how we could ever have taken seriously an account of confirmation that tells us otherwise. Consider a revisionist geology in which the world is supposed created in exactly 4004BC complete with its fossil record. Standard and revisionist geologies have the same observational consequences, but we surely do not think that the fossil record confirms a creation in 4004BC just as strongly as the ancient earth of standard geology? In standard geology, detailed analysis points to precise datings for the standard geological eras. What in the fossil record points exactly to 4004BC as the date of creation of revisionist geology and not, say, 8008BC or last Tuesday? Indeed the fossil record would seem to strongly disconfirm the 4004BC creation.
• Many accounts of confirmation do not restrict evidence to deductive consequences of hypotheses or theories.
As Laudan and Leplin (1991) illustrate multiply, there are many cases of evidence that is not a logical consequence and logical consequences are that not confirmatory. The latter arises when both an hypothesis and all credible competitors entail the same consequence. Laudan and Leplin's (1991, p. 465) example is the hypothesis H that regular reading of scripture induces puberty in young males and the consequence E of the onset of puberty in some particular young males who read scripture.
• Many accounts of confirmation allow evidence to bear directly on individual hypotheses within a theory rather than merely supporting the entire theory holistically.
This is not to dispute Duhem's remark that hypotheses often need the support of auxiliary hypotheses if observational consequences are to be derived from them. It does dispute the idea that the obtaining the of these consequences bears inductively solely on the conjunction of all the hypotheses. Consider the observation of spectral lines in sunlight corresponding to the Helium spectrum. The inference from the presence of Helium in the sun to the observed spectrum requires numerous additional assumptions about the optics of cameras and spectrographs. But the observed Helium spectrum is strong evidence for the presence of Helium in the sun and at best tangential evidence for the optical theory of the camera.