Қателікке ұшырау мүмкіндігі: ғылыми мәлімдемелердің логикасы

Property of a statement that can be logically contradicted

[[File:Black Swans. jpg|thumb|upright=1.3|alt=Pair of black swans swimming|Here are two black swans, but even with no black swans to possibly falsify it, "All swans are white" would still be shown falsifiable by "Here is a black swan"—a black swan would still be a state of affairs, only an imaginary one. The purpose of his methodology is to prevent "the policy of immunizing our theories against refutation". It also supports some "dogmatic attitude" in defending theories against criticism, because this allows the process to be more complete. This negative view of science was much criticized and not only by Johnson Laird. In practice, some steps based on observations can be justified under assumptions, which can be very natural. For example, Bayesian inductive logic is justified by theorems that make explicit assumptions. These theorems are obtained with deductive logic, not inductive logic. They are sometimes presented as steps of induction, because they refer to laws of probability, even though they do not go beyond deductive logic. This is yet a third notion of induction, which overlaps with deductive logic in the following sense that it is supported by it. These deductive steps are not really inductive, but the overall process that includes the creation of assumptions is inductive in the usual sense. In a fallibilist perspective, a perspective that is widely accepted by philosophers, including Popper, every logical step of learning only creates an assumption or reinstates one that was doubted—that is all that science logically does.

Popper distinguished between the logic of science and its applied methodology. Despite the fact that Popper insisted that he is aware that falsifications are impossible and added that this is not an issue for his falsifiability criterion because it has nothing to do with the possibility or impossibility of falsifications, Stove and others, often referring to Lakatos original criticism, continue to maintain that the problems of falsification are a failure of falsifiability.

In Popper's view of science, statements of observation can be analyzed within a logical structure independently of any factual observations. According to Rynasiewicz, in this semantic perspective, falsifiability as defined by Popper means that in some observation structure (in the collection) there exists a set of observations which refutes the theory. An even stronger notion of falsifiability was considered, which requires, not only that there exists one structure with a contradicting set of observations, but also that all structures in the collection that cannot be expanded to a structure that satisfies contain such a contradicting set of observations.

In response to Lakatos who suggested that Newton's theory was as hard to show falsifiable as Freud's psychoanalytic theory, Popper gave the example of an apple that moves from the ground up to a branch and then starts to dance from one branch to another. It is a basic statement, because it is possible to separately determine the kind of environment, industrial vs natural, and the relative fitness of the white bodied form (relative to the black bodied form) in an area, even though it never happens that the white bodied form has a high relative fitness in an industrial area.

A famous example of a basic statement from J. B. S. Haldane is "[These are] fossil rabbits in the Precambrian era." This is a basic statement because it is possible to find a fossil rabbit and to determine that the date of a fossil is in the Precambrian era, even though it never happens that the date of a rabbit fossil is in the Precambrian era. Despite opinions to the contrary, sometimes wrongly attributed to Popper, Popper rejected Hume's explanation of induction and proposed his own mechanism: science progresses by trial and error within an evolutionary epistemology. Hume believed that his psychological induction process follows laws of nature, but, for him, this does not imply the existence of a method of justification based on logical rules. In fact, he argued that any induction mechanism, including the mechanism described by his theory, could not be justified logically. Similarly, Popper adopted an evolutionary epistemology, which implies that some laws explain progress in science, but yet insists that the process of trial and error is hardly rigorous and that there is always an element of irrationality in the creative process of science. The absence of a method of justification is a built in aspect of Popper's trial and error explanation. As rational as they can be, these explanations that refer to laws, but cannot be turned into methods of justification (and thus do not contradict Hume's argument or its premises), were not sufficient for some philosophers. In particular, Russell once expressed the view that if Hume's problem cannot be solved, “there is no intellectual difference between sanity and insanity” and actually proposed a method of justification. He rejected Hume's premise that there is a need to justify any principle that is itself used to justify induction.