On 9/3/13 we'll be discussing the first three essays in Conjectures and Refutations: The Growth of Scientific Knowledge (1963). The book is a retrospective in part, presenting the ideas in the philosophy of science that had established his reputation back in the 1930s.
The first essay, "On the Sources of Knowledge and Ignorance," is a historical overview of epistemology, describing Socrates, Bacon, and Descartes as "epistemological optimists," meaning that under normal circumstances--if you're seeing and thinking clearly--your faculties will provide you with truth. While Popper sees this optimism as preferable to the pessimism that says that we're too defective to recognize truth and so need authority to tell us what it is, it still fetishizes certainty. Instead, Popper recommends the doctrine of fallibility: a real respect for objective truth means that we seek it, realizing that more often than not we miss it by a wide margin, and relentlessly try to correct our errors by testing.
The second essay, "Science: Conjectures and Refutations," tells us more about what such "testing" entails. The point is not to look for evidence verifying our theories, but to construct tests that would, if successful, falsify the theory. Popper's problem in this essay is demarcation: which theories are really scientific, and which are pseudo-science (which, he notes, may still be worth discussing; he's not recommending throwing out everything that's not science)? If there's no test that could potentially show that a theory is false, then it's not a scientific theory. He mentions, for instance, Freudian claims about the unconscious. Freudians saw this view as endlessly confirmed by their clinical observations, but Popper saw this as a weakness: any psychological observation of a patient can be interpreted in light of the theory and so seen as a confirming instance. A real scientific theory needs to take risks: it needs to make specific predictions that--if they were not fulfilled--would show that the theory is wrong.
This criterion of falsifiability is Popper's big idea, and he wants to make sure we understand that this is just a matter of determining what statements are scientific, not what statements are meaningful, which was the concern of the Logical Positivists following Wittgenstein, whom Popper considered his philosophical nemesis. Another target of the essay is Hume on the problem of induction. Hume, on Popper's account, saw science (and any perception of causality) as perception of regularities, and claimed that this recurrent seeing of things in conjunction (e.g. every time I hit the ball it moves) was not logically sufficient to guarantee the universality of a natural law; it was more just a matter of habit. Popper thinks this is backwards: we do not see regularities first, and in fact would need some notion of causality to recognize something as a "regularity" at all. Instead, we jump to hypotheses: we see something happen once and, in interpreting what that "something" is (e.g. which two events were linked causally), we then have a criterion for what would count as a future repetition of the event, and we expect it. If our expectation if frustrated, we modify the hypothesis. So science's method of attempted falsification is just adding a self-critical step (actually trying to frustrate the hypothesis) to the method of conjecture already built into ordinary experience.
There are a few essays in the collection relating science to philosophy, including the third one we read, "The Nature of Philosophical Problems and their Roots in Science," where Popper directly takes on this view he attributes to Wittgenstein (both in Wittgenstein's early and late writings) that any statement not ultimately rooted in the empirical is strictly nonsensical in the manner of "the tree is five." Popper does think that philosophy that's gotten away from its roots in live questions in science and mathematics can be just a bunch of hot air, and that our current method of learning philosophy which is just by reading philosophers encourages this sort of academic incest. For instance, he cites Plato's theory of Forms, and says this was motivated by Pythagoras's discovery of irrational numbers: These numbers, that we see right there in nature (look to our discussion of "logos" for more on this), can't even be described in full, and so obviously are not a human invention... hey, what if that's not just how numbers work, but all ideas? But we don't learn about this background, but instead just get Plato's "theory," and by relating this to numerous other similarly unrooted (for us students) "theories" think we're doing something productive but are really just lost in a thicket of ideas.
If you know the extra-philosophical motivation, however, you can see that Plato--and Kant, Hegel, and the rest--were (in many cases, anyway) responding to real problems, and it's this sensitivity to problems that Popper wants to emphasize. Calling these problems part of physics or philosophy or whatever is a matter of convenience after the fact to group similar kinds of work together, but Popper thinks there is no specific method proper to dealing with the problems that philosophers have recognized.