Karl Popper's philosophy of science

Assume that we have deliberately made it our task to live in this unknown world of ours; to adjust ourselves to it as well as we can; to take advantage of the opportunities we can find in it; and to explain it, if possible (we need not assume that it is), and as far as possible, with the help of laws and explanatory theories. If we have made this our task, then there is no more rational procedure than the method of trial and error - of conjecture and refutation: of boldly proposing theories; of trying our best to show that these are erroneous; and of accepting them tentatively if our critical efforts are unsuccessful.

Science: Conjectures and Refutations, VII, p51.

Theories are our own inventions, our own ideas; they are not forced upon us, but are our self-made instruments of thought: this has been clearly seen by the idealist. But some of these theories of ours can clash with reality; and when they do, we know that there is a reality; that there is something to remind us of the fact that our ideas may be mistaken. And this is why the realist is right.

Three Views Concering Human Knowledge, 6, p117.

Against the view here developed one might be tempted to object (following Duhem) that in every test it is not only the theory under investigation which is involved, but also the whole system of our theories and assumptions - in fact, more or less the whole of our knowledge - so that we can never be certain which of all these assumptions is refuted. But this criticism overlooks the fact that if we take each of the two theories (between which the crucial experiment is to decide) together with all this background knowledge, as indeed we must, then we decide between two systems which differ only over the two theories which are at stake. It further overlooks the fact that we do not assert the refutation of the theory as such, but of the theory together with that background knowledge; parts of which, if other crucial experiments can be designed, may indeed one day be rejected as responsible for the failure. (Thus we may even characterize a theory under investigation as that part of a vast system for which we have, if vaguely, an alternative in mind, and for which we try to design crucial tests.)

Three Views Concering Human Knowledge, 5, p112. (Popper refers to Duhem's Aim and Structure of Physical Theory. This is the most frequent objection to Popper, even though he anticipated it right from the start, in his Logic of Scientific Discovery. In short, if a theoretical prediction is falsified, despite Duhem's objection we can still be certain that our system of theories is false.)