Popper was a fallibilist, not a skeptic.
Fallibilism is the heart of one influential response to skepticism. Fallibilists hold that people often have sufficiently strong justification to know that there is for example a tree in the yard. According to fallibilists, a skeptical argument about knowledge relies on setting the standard of justification for knowledge too high. We can have knowledge even though we cannot have the certainty that the skeptics wrongly associate with knowledge. For fallibilism there is no possibility of a definitive, once and for all certification. All contingent, empirical propositions whatsoever, including reports of immediate experience, are uncertain on the ground that every such proposition involves the application of a general predicative term to its subject and thus makes a comparison with previous and perhaps faultily remembered instances of the term’s application. Skepticism simply taken it for granted that for a belief to be knowledge, it must be impossible to doubt it, there is certainty.
But fallibilism is not without problems. It is no easy task to explain what it is about our experiential evidence that makes it a good reason for thinking that we are in the presence of ordinary objects rather than the victims of some sort of deception. Some epistemologists contend that our justification for our external world beliefs depends upon an inference to the best explanation of our experiences. But adequately spelling out just why our beliefs are even fallibly justified remains an unfulfilled task.
The traditional view is that knowledge is true belief that is justified, but no fallibilist view about justification can accept this account of knowledge. Fallibilism about justification is the view that justified false beliefs are possible, perhaps clarified in terms of the claim that no matter how good our evidence is for what we believe, we might still be wrong. Given this view, it turns out to be unavoidable that there could be cases of justified true belief that are not cases of knowledge. Given fallibilism, the truth condition for knowledge is not supplied by the justification condition; justification does not entail truth. Similarly, truth does not entail justification; one can lack evidence for a proposition that is true.
On the other hand, the proponents of the justification condition for knowledge do not share an account of the exact conditions for epistemic justification. Competing accounts include epistemic coherentism, which implies that the justification of any belief depends on that belief’s coherence relations to other beliefs, and epistemic foundationalism, which implies that some beliefs are justified independently of any other beliefs. Recently, some philosophers have proposed that knowledge requires not evidence but reliable belief formation. This is the reliabilism about the justification condition for knowledge. Whatever the exact conditions for epistemic justification are, proponents of the justification condition maintain that knowledge is not merely true belief.
The problem of induction is posed by Hume’s argument for the shocking conclusion that any evidence belief is unreasonable. That argument rests upon two premises: (1) Hume’s inductive scepticism and (2) the justificationist principle that it is reasonable to believe only what you can justify. Popper’s answer to Hume was critical rationalism, which accepts (1) but rejects (2), jettisoning truth as the aim of inquiry, or going in for some peculiar epistemic theory of truth.
In Popper, though potentially falsifiable, a theory may be currently untestable. If a theory is potentially falsifiable, currently testable, and has been tested, then there are two possibilities: (i) If a test is positive, the theory is corroborated. Corroboration does not mean proven true; Popper’s fallibilism prohibits us from claiming that we have discovered the truth. Nor should even consistently corroborated theory be viewed as highly probable or even more probable. This was the point of Popper’s critique of inductive logic. It is a radical implication: Even perfect corroboration carries no evidential weight. (ii) If a test result is negative, the theory is refuted or falsified.
Popper's critical rationalism means that we may reasonably believe what is false – though if we find out that what we believe is false, it is no longer reasonable to believe it. Similarly, according to critical rationalism reasonable beliefs need not be reliable beliefs, beliefs produced by a reliable belief-producing process, though if we find out that a belief-producing process is unreliable, it is no longer reasonable generally to adopt beliefs of that kind. Critical rationalism can contain a notion of ‘conjectural knowledge’: to know is reasonably to believe what is true. Critical rationalism says that the fact that a hypothesis is well corroborated is a good reason to adopt it, tentatively, as true. Justificationism is demand that a reason for believing something must be a reason for what is believed. This is what Popper denies. If you assume justificationism, you will also assume that lying behind critical rationalism there must be a metaphysical principle linking corroboration with truth or probability.
Popper was long a lonely advocate of scientific fallibilism: that, although science aims at the truth, most theories have turned out to be false and current theories are also likely to be false. This seems a bleak vision indeed and fails to do justice to the evident progress in science. Popper realized that the picture would be less bleak if a succession of false and falsified theories could nevertheless constitute steady progress toward the truth. Further, even if actually refuted by some of the data, the general observational accuracy of a false theory might be good evidence for the theory’s approximate truth, or high degree of truthlikeness. That our theories, even if not true, are close to the truth, may be the best explanation available for the accuracy of their observable consequences. Popper proposed a bold and simple account of truthlikeness: that theory B is more truthlike than theory A if B entails all the truths that A entails, A entails all the falsehoods that B entails, and either B entails at least one more truth than A or A entails at least one more falsehood than B.