If inductive evidence is ampliative evidence, then it is clear what would count as a successful outcome of the inductivist project. Given hypothesis h, and evidence e, one must show that evidence e makes p(h if e, e), greater than p(h if e). Evidence e can be anything one cares to name, including repeated sightings of white swans, black raven, or blue hats.
Popper and Miller proved in 1983 that, following from the rules of probability, no e can satisfy this requirement. Until this proof is answered, inductivists are tilting at windmills.
” … if the hypothesis h logically implies the evidence e in the presence b [background knowledge] (so that he is equivalent to h) then p(h, eb) is proportional to p(h, b) … suppose that e is some such evidence statement as ‘All swans in Vienna in 1986 are white’, h the supposedly inductive generalization ‘All swans are white’ and k the counterinductive generalization ‘All swans are black, except those in Vienna in 1986, which are white’. Then p(h, eb) = p(h, b)/p(k, b). No matter how h and k generalize on the evidence e, this evidence is unable to disturb the ration of their probabilities …. Supporting evidence points in all directions at once, and therefore points usefully in no direction. (Popper & Miller, Why Probabilistic Support is not Inductive, Phil. Trans. of the Royal Society of London. Series A, Mathematical and Physical Sciences, Vol. 321, No. 1562 (Apr. 30, 1987))
This is no problem for critical rationalism as long as one maintains that corroboration is not epistemologically valuable. Salmon had earlier said that corroboration is either empty or inductive. In response, I say it is empty: corroboration gives no reasons to think a theory or hypothesis is true. This does not requiring that I bite the bullet–I am happy to admit that there is no such thing as epistemologically valuable corroborating evidence.
Salmon’s response is that, without using corroboration to promote theories, the falsificationist is left with no way of determining which remaining theories should be preferred over others. Criticism, while perhaps necessary, is then not sufficient for finding theories that are true (or an objective degree of verisimilitude that is higher than all rivals). The picture Salmon presents is that, without induction, we would be drowning in a sea of theories.
Salmon thinks as an inductivist–most theories we can think of fail immediately, or clash with noncontroversial theories. An infinite number of theories can be eliminated for strictly logical reasons–they are incoherent, not universal in scope, contradict unproblematic theories or the set of all currently accepted existential statements, and so on.
Long before we get to corroborating anything, we would be lucky to have a handful of theories left. It’s possible to invent empirically adequate theories that have Goodman-predicates, but these theories require (1) an explanation for the apparently arbitrary behavior predicted by the Goodman-predicate (Deutsch) and (2) a problem that introducing the Goodman-predicate attempts to solve (Bartley) before they can be taken seriously.
Thus, I mst point out that falsifying instances are but one criticism of theories. We should be thankful that scientists are imaginative enough to produce such a number of theories that can be counted on one’s digits without taking off one’s shoes.