The Logic of Scientific Discovery
The Logic of Scientific Discovery was published by Karl Popper in 1934. One of the most important themes was demarcation of empirical sciences from other forms of knowledge, of scientific statements from other forms of truthful, or truth-seeking statements. Popper began this important work with a definition and then the problem of demarcation:
A scientist, whether theorist or experimenter, puts forward statements, or systems of statements, and tests them step by step. In the field of the empirical sciences, more particularly, he constructs hypotheses, or systems of theories, and tests them against experience by observation and experiment. I suggest that it is the task of the logic of scientific discovery, or the logic of knowledge, to give a logical analysis of this procedure; that is, to analyze the method of the empirical sciences. But what are these ‘methods of the empirical sciences’? And what do we call ‘empirical science’?”
The aim here is to delineate the empirical from the non-empirical sciences.
Popper then investigates the “problem of induction” which he defined as the question of whether inductive inferences are justified. He opposed the belief that empirical science can be identified by its use of inductive methods. Induction, for Popper, could never lead to the certainty that he knows science possesses. All systems of induction, he believes, lead to logical inconsistencies. Thus Popper proposed a deductive method of testing, that “a hypothesis can only be empirically tested–and only after it has been advanced.” Popper then divides his problem into “the psychology of knowledge which deals with empirical facts, and the logic of knowledge which is only concerned with logical relations.” Thus, for the deductive method, Popper proposed two broad tests: First, is the hypothesis consistent with empirical evidence? Second, is the hypothesis internally consistent (that is, not self-contradictory)?
The Logic is concerned here with statements. Popper is striving for a rule that when he is confronted with any statement he would be able to classify it as scientific, metaphysical, logical, mathematical, or otherwise. He wants a criterion that validates these types of statements but at the same time distinguishes among them. He proposes a method of validation that has four steps. The first step is to deduce, or predict, the consequences of any hypothesis. Then, if the deduced consequences are logically consistent with each other, the next step is to identify the logical form of the theory (i.e., is it scientific, tautological, empirical, etc.?). With this information, the third is a pragmatic step and determines whether the hypothesis, in comparison with other theories, advances our understanding. If the hypothesis does not does not advance human knowledge, then why pursue it or test it? Finally, the hypothesis is tested empirically. Note that only hypotheses that have empirical consequences will reach this final step. The appeal to empirical evidence for Popper is absolute and irrevocable. Nature is to be the final arbiter of any hypothesis and will either verify or falsify the hypothesis on the basis of its predicted consequences.
With this method, Popper intended to delineate clearly between philosophical and scientific statements. “I still take it to be the first task of the logic of knowledge to put forward a concept of empirical science, in order to make linguistic usage, now somewhat uncertain, as definite as possible, and in order to draw a clear line of demarcation between science and metaphysical ideas–even though these ideas may have furthered the advance of science throughout its history.” Given that both metaphysics and science produce meaningful statements the problem became how to use experience to distinguish between them. For Popper, scientific statements must by testable by experience, in other words, experience must be able to conclusively refute, or falsify, any deduced consequence of the hypothesis for that hypothesis to be considered science.  Thus Popper proposes not a positivist science, but a negativist science. Experience is either consistent with our theories or it falsifies them; little is proven. And so, he concludes, “there can be no ultimate statements in science: there can be no statements in science which cannot be tested, and therefore none which cannot in principle be refuted, by falsifying some of the conclusions which can be deduced from them.” 
- Karl R. Popper, The Logic of Scientific Discovery (New York: Basic Books, 1959; reprint, Harper & Row, Harper Torchbooks, 1968), 27.
- Popper’s emphasis; Popper, Logic, 30.
- Popper, Logic, 38-9.
- Popper, Logic, 38-9.
- Popper, Logic, 47.