Thus every statement (or ‘basic statement’) remains essentially conjectural; but it is a conjecture which can be easily tested. These tests, in their turn, involve new conjectural and testable statements, and so on, ad infinitum; and should we try to establish anything with our tests, we should be involved in an infinite regress. But as I explained in my Logic of Scientific Discovery (especially section 29), we do not establish anything by this procedure: we do not wish to ‘justify’ the ‘acceptance’ of anything, we only test our theories critically, in order to see whether or not we can bring a case against them. 
Category: Conjectures and Refutations
A serious empirical test always consists in the attempt to find a refutation, a counterexample. In the search for a counterexample, we have to use our background knowledge; for we always try to refute first the most risky predictions, the ‘most unlikely … consequences’ (as Peirce already saw); which means that we always look in the most probable kinds of places for the most probable kinds of counterexamples—most probable in the sense that we should expect to find them in the light of our background knowledge. Now if a theory stands up to many such tests, then, owing to the incorporation of the results of our tests into our background knowledge, there may be, after a time, no places left where (in the light of our new background knowledge) counter examples can with a high probability be expected to occur. But this means that the degree of severity of our test declines. This is also the reason why an often repeated test will no longer be considered as significant or as severe: there is something like a law of diminishing returns from repeated tests (as opposed to tests which, in the light of our background knowledge, are of a new kind, and which therefore may still be felt to be significant). These are facts which are inherent in the knowledge-situation; and they have often been described—especially by John Maynard Keynes and by Ernest Nagel—as difficult to explain by an inductivist theory of science. But for us it is all very easy. And we can even explain, by a similar analysis of the knowledge-situation, why the empirical character of a very successful theory always grows stale, after a time. We may then feel (as Poincaré did with respect to Newton’s theory) that the theory is nothing but a set of implicit definitions or conventions—until we progress again and, by refuting it, incidentally re-establish its lost empirical character. (De mortuis nil nisi bene: once a theory is refuted, its empirical character is secure and shines without blemish.) [325-6]
The idealism of piecemeal engineering
Utopian rationalism is a self-defeating rationalism. However benevolent its ends, it does not bring happiness, but only the familiar misery of being condemned to live under a tyrannical government.
It is important to understand this criticism fully. I do not criticize political ideals as such, nor do I assert that a political ideal can never be realized. This would not be a valid criticism. Many ideals have been realized which were once dogmatically declared to be unrealizable, for example, the establishment of workable and untyrannical institutions for securing civil peace, that is, for the suppression of crime within the state. Again, I see no reason why an international judicature and an international police force should be less successful in suppressing international crime, that is, national aggression and the ill-treatment of minorities or perhaps majorities. I do not object to the attempt to realize such ideals.
Wherein, then, lies the difference between those benevolent Utopian plans to which I object because they lead to violence, and those other important and far-reaching political reforms which I am inclined to recommend?
If I were to give a simple formula or recipe for distinguishing between what I consider to be admissible plans for social reform and inadmissible Utopian blueprints, I might say:
Work for the elimination of concrete evils rather than for the realization of abstract goods. Do not aim at establishing happiness by political means. Rather aim at the elimination of concrete miseries. Or, in more practical terms: fight for the elimination of poverty by direct means—for example, by making sure that everybody has a minimum income. Or fight against epidemics and disease by erecting hospitals and schools of medicine. Fight illiteracy as you fight criminality. But do all this by direct means. Choose what you consider the most urgent evil of the society in which you live, and try patiently to convince people that we can get rid of it.
But do not try to realize these aims indirectly by designing and working for a distant ideal of a society which is wholly good. However deeply you may feel indebted to its inspiring vision, do not think that you are obliged to work for its realization, or that it is your mission to open the eyes of others to its beauty. Do not allow your dreams of a beautiful world to lure you away from the claims of men who suffer here and now. Our fellow men have a claim to our help; no generation must be sacrificed for the sake of future generations, for the sake of an ideal of happiness that may never be realized. In brief, it is my thesis that human misery is the most urgent problem of a rational public policy and that happiness is not such a problem. The attainment of happiness should be left to our private endeavours. [484-5]
Nothing can be proved
The critical attitude, the tradition of free discussion of theories with the aim of discovering their weak spots so that they may be improved upon, is the attitude of reasonableness, of rationality. It makes far-reaching use of both verbal argument and observation—of observation in the interest of argument, however. The Greeks’ discovery of the critical method gave rise at first to the mistaken hope that it would lead to the solution of all the great old problems; that it would establish certainty; that it would help to prove our theories, to justify them. But this hope was a residue of the dogmatic way of thinking; in fact nothing can be justified or proved (outside of mathematics and logic). The demand for rational proofs in science indicates a failure to keep distinct the broad realm of rationality and the narrow realm of rational certainty: it is an untenable, an unreasonable demand. 
Why true knowledge isn’t power
This unbalanced (and immature) attitude is obsessed with the problem of power, not only over other men, but also over our natural environment — over the world as a whole. What I might call, by analogy, the ‘false religion’, is obsessed not only by God’s power over men but also by His power to create a world; similarly, false rationalism is fascinated by the idea of creating huge machines and Utopian social worlds. Bacon’s ‘knowledge is power’ and Plato’s ‘rule of the wise’ are different expressions of this attitude which, at bottom, is one of claiming power on the basis of one’s superior intellectual gifts. The true rationalist, in opposition, will always be aware of the simple fact that whatever reason he may possess he owes to intellectual intercourse with others. He will be inclined, therefore, to consider men as fundamentally equal, and human reason as a bond which unites them. Reason for him is the precise opposite of an instrument of power and violence: he sees it as a means whereby they may be tamed. 
The humanistic approach to science
I admit that the natural sciences are in danger of stifling mental growth, instead of furthering it, if they are taught as technologies (the same is probably true of painting and of poetry); and that they should be treated (like painting and poetry) as human achievements, as great adventures of the human mind, as chapters in the history of human ideas, of the making of myths (as I have explained elsewhere), and of their criticism. 
Without criticism no progress
But the most important misunderstandings and muddles arise out of the loose way in which dialecticians speak about contradictions.
They observe, correctly, that contradictions are of the greatest importance in the history of thought—precisely as important as is criticism. For criticism invariably consists in pointing out some contradiction; either a contradiction within the theory criticized, or a contradiction between the theory and another theory which we have some reason to accept, or a contradiction between the theory and certain facts—or more precisely, between the theory and certain statements of fact. Criticism can never do anything except either point out some such contradiction, or, perhaps, simply contradict the theory (i.e. the criticism may be simply the statement of an antithesis). But criticism is, in a very important sense, the main motive force of any intellectual development. Without contradictions, without criticism, there would be no rational motive for changing our theories: there would be no intellectual progress. 
Popper’s absolute theory of truth
The objective theory of truth leads to a very different attitude. This may be seen from the fact that it allows us to make assertions such as the following: a theory may be true even though nobody believes it, and even though we have no reason for accepting it, or for believing that it is true; and another theory may be false, although we have comparatively good reasons for accepting it.
Clearly, these assertions would appear to be self-contradictory from the point of view of any subjective or epistemic theory of truth. But within the objective theory, they are not only consistent, but quite obviously true.
A similar assertion which the objective correspondence theory would make quite natural is this: even if we hit upon a true theory, we shall as a rule be merely guessing, and it may well be impossible for us to know that it is true. 
The belief that science proceeds from observation to theory is still so widely and so firmly held that my denial of it is often met with incredulity. I have even been suspected of being insincere – of denying what nobody in his senses can doubt.
But in fact the belief that we can start with pure observations alone, without anything in the nature of a theory, is absurd; as may be illustrated by the story of the man who dedicated his life to natural science, wrote down everything he could observe, and bequeathed his priceless collection of observations to the Royal Society to be used as inductive evidence. This story should show us that though beetles may profitably be collected, observations may not.
Twenty-five years ago I tried to bring home the same point to a group of physics students in Vienna by beginning a lecture with the following instructions: ‘Take pencil and paper; carefully observe, and write down what you have observed!’ They asked, of course, what I wanted them to observe. Clearly the instruction, ‘Observe!’ is absurd. (It is not even idiomatic, unless the object of the transitive verb can be taken as understood.) Observation is always selective. It needs a chosen object, a definite task, an interest, a point of view, a problem. And its description presupposes a descriptive language, with property words; it presupposes similarity and classification, which in its turn presupposes interests, points of view, and problems.