Verisimilitude (or truthlikeness) is a philosophical concept that distinguishes between the relative and apparent (or seemingly so) truth and falsity of assertions and hypotheses. The problem of verisimilitude is the problem of articulating what it takes for one false theory to be closer to the truth than another false theory.
This problem was central to the philosophy of Karl Popper, largely because Popper was among the first to affirm that truth is the aim of scientific inquiry while acknowledging that most of the greatest scientific theories in the history of science are, strictly speaking, false. If this long string of purportedly false theories is to constitute progress with respect to the goal of truth, then it must be at least possible for one false theory to be closer to the truth than others.
Popper assumed that scientists are interested in highly informative theories, in part for methodological reasons — the more informative a theory, the easier it is to test, and the greater its predictive power. But clearly informative power by itself is rather easy to come by, and we do not want to gain content by sacrificing truths. So Popper proposed that closeness to the truth is a function of two factors — truth and content. The more truths that a theory entails (other things being equal) the closer it is to the truth.
Intuitively at least, it seems that Newton's theory of motion entails a good many more truths than does, say, Aristotle's theory — despite the fact that both are known to have flaws. Even two true theories can have differing degrees of verisimilitude, depending on how much true information they deliver. For example, the claim "it will be raining on Thursday next week," if true, is closer to the truth than the true yet logically weaker claim "it will either be raining next Thursday or it will be sunny."
Popper's formal definition of verisimilitude was challenged by Pavel Tichý and David Miller, who argued that Popper's definition has an unintended consequence: that no false theory could be closer to the truth than another. This result gave rise to a search for an account of verisimilitude that did not deem progress towards the truth an impossibility.