Anthony O'Hear's An Introduction to the Philosophy of Science is an excellent book; but the purpose here is not a general review. Instead, there is one important point that will be considered, where O'Hear settles on what seems to be a decisive criticism of Karl Popper's theory of falsification as the key to scientific method.
The first problem for a Popperian to consider, though, is whether he can really talk of a severe test [of a theory] without the use of inductive reasoning....
For a severe test is one which is unlikely on past evidence. Without using some sort of inductive assumptions, how can one move from past experience to calculations of present (or future) probability?.... All we have, on non-inductive grounds, are reports of past experience, and generalization from them is forbidden. [pp. 39-40]
This account seems to involve a certain confusion. What are "inductive assumptions"? Are they principles that are presupposed by induction, or principles that are supposed to depend on induction? Hume's entire critique of induction was that, logically, it was wholly unable to establish the regularity of nature, the conformity of the future to the past and present, or any other "inductive" generalizations. Unless Hume was wrong, which O'Hear does not seem to maintain, this rules out "inductive assumptions" depending on or being established by induction. On the other hand, if "inductive assumptions" are presupposed by induction, then what is their justification? In such a case, induction itself would depend on principles that are logically independent of, and prior, to it. That is what Hume himself thought. Where do they come from? O'Hear is not likely to accept Hume's answer that they depend on psychological conditioning and so subjective expectation. But if we say that they are justified because they are not falsified by the practice of induction, this completely turns around O'Hear's point to one where induction is only possible with "Popperian assumptions."
The source of the problem here may be O'Hear's statement that "generalization from them [reports of past experience] is forbidden." Are any kinds of generalizations or conjectures "forbidden" by Popper? Of course not. We can make any kind of assumptions that we like. What is "forbidden" is the idea that past experiences prove something on the basis of logical considerations alone. This is merely to acknowledge the Problem of Induction and Hume's conclusion that induction has no logical force. What then happens when we generalize, not just from past experience, but as a matter of theoretical conjecture, to the principle of the uniformity of nature itself? We would seem to have formulated an "inductive assumption" in a very Popperian way. With an eye to Hume, we might even formulate the Principle of Causality itself -- that events have explanations in terms of antecedent conditions and the laws of nature. And we might even venture the proposition that frequently confirmed theories are more likely to be true than untested ones, on the basis of a theory of probability: Successful predictions eliminate areas of the "phase space" of physical theories, which means that successful theories describe a larger number of possible universes. That makes them, in a quantitative theory of modality, more probable, i.e. more probable to be true in this universe.
These all can be called "inductive assumptions," but they owe nothing to induction. Quite the opposite. With them, however, O'Hear's objection here to Popper disappears. Thus, when O'Hear says, "...we would need something like an inductive jump, from past to future" [p. 40], there actually is no reason not to postulate the validity of that jump: It is just a higher order rule, with the same logical status, as all the other contents of scientific theories. O'Hear finishes the section thus:
The Popperian will say that the Popperian method aims at the truth. The critic will reply that the method aims at the truth only in the sense of ruling out false theories, and that is does not give any positive reasons for believing in the theories which have survived severe tests. To which the Popperian will agree, adding that we may still act on such theories in the hope that they are true. And the critic will say that he had hoped for more than a hope in science. Once again we are back where we started. [p. 41]
A Popperian does not have to agree: We are not back where we started because there is no reason why the logical system of science should not itself contain the "positive reasons for believing in the theories which have survived severe tests." It doesn't help to say that this would have been taken care of by "inductive assumptions," when induction could not establish such assumptions anyway, while just such assumptions can be included by a Popperian in scientific theories, subject to falsification, along with anything else. This circumstance should be recognized when Popper's theory is viewed, not just as an answer to the Problem of Induction, but as an answer to the Problem of First Principles. After all, Hume's scepticism ultimately focused on the Principle of Causality. Is Popper justified in assuming the Principle of Causality? Indeed, he is justified in assuming anything as long as it is tested. But the Principle of Causality has the curious property of being confirmed by every test which depends on the idea of a Law of Nature, which means all of them.
The practice of science depends on several principles like the Principle of Causality, including the idea that confirmed theories are probably, but not certainly, true. These are higher order principles than the content of particular scientific theories, but they belong to the same logical system and so can be handled by Popper the same way as anything else in science.
While O'Hear makes a mistake in ruling out the possibility of what he calls "inductive assumptions" in Popper, it is still true that we wonder if there are positive reasons for First Principles that are grounded independently of scientific testing. But this is simply to ask all over again Kant's question about the possibility of synthetic a priori propositions, where the focus again was the Principle of Causality and the regularity (law-like-ness) of nature. If there are synthetic a priori propositions, and if Fries's theory of non-intuitive immediate knowledge is true, then Popper's "logic of scientific discovery" is simply one way of determining the Kantian quid facti of such propositions, while the Kantian quid juris is something that need not be a matter of concern for science, just for "Critique of Science": the metalanguage of philosophical knowledge.
Since O'Hear was certainly unaware of Popper's Friesian connection, he would also be unaware of the Friesian answer to the Aristotelian Problem of First Principles: that First Principles do not need to be proven, not because they are self-evident (the Aristotelian or Rationalistic answer), but because they are grounded in non-intuitive immediate knowledge. What Popper clearly still employs, whatever his view of the theory of non-intuitive immediate knowledge, is the sense that the lack of logical proof for principles like causality or the regularity of nature does not leave us with a lack of "positive reasons" in a way that we need to worry about for the practice, or the conclusions, of science.
Criticism of Karl Popper in Martin Gardner's Are Universes Thicker Than Blackberries?
Philosophy of Science