If you take the position of empiricism, there are various things that you think you know, but can't justify. Perhaps the best known is Hume's Problem. Hume pointed out that there is nothing in perception that tells you that the universe has reliable regularities or that the future will be like the past.
There are many regularities that are experienced but that can't be used for predictions. For example, most people have seen lots of crows and they were all black, but there are non-black crows. This is a regularity that is perceived but is not something that can be relied on for prediction. Thus, it is a proof by example that experience does not contain information that tells you you can predict from what you have observed.
This means that an empiricist not only cannot justify science, he can't even justify normal thought processes that involve anticipating or predicting things in nature. This doesn't mean that an empiricist can't do science, it only means that if he is consistent, he has to admit that he can't justify science within his epistemology. Essentially, the empiricist is cornered into doubting the rationality and reliability of all knowledge that he has not already himself experienced, including any predictions about things he has not seen. This is a form of skepticism.
There is another important bit of information that is not available from experience alone. Consider the difference between seeing a tree and dreaming that you see a tree. In both cases, the perception might be identical, but in one case there is a tree there and in the other case there is no tree there. What this tells us is that the existence of the tree is not revealed by experience. There is nothing in perception that tells you there is really a tree there.
Consequently, to be consistent, an empiricist must be agnostic about whether there is a tree there or not, because he claims that all knowledge comes from what is perceived, and there is nothing in the perception that tells him the tree is there.
A consistent empiricist therefore, cannot be a (dogmatic) physical realist. The alternative is idealism. A consistent empiricist can remain agnostic about the realism/idealism debate, but if he also takes Occam's Razor as a guide to investigation, he is led to the position that since it is not necessary to postulate the existence of the tree, it is better to assume that the tree does not exist. Therefore, empiricism plus ontological parsimony leads to idealism.
Therefore, empiricism does have the seeds of both idealism and skepticism.
ADDENDUM:
Another answer to this question says that empiricism presupposes a material world. This is not correct. Many empiricists such as George Berkeley have been idealists, and all of the philosophically sophisticated empiricists have admitted that their epistemology makes it difficult to justify a belief in the material world.
In the comments, someone says "An empiricist simply admits their knowledge is tentative, based on plausability and regularities". This does not work, because an empiricist has no justification for relying on plausibility and regularities at all--even a little bit. Here is how Hume argued the point:
- The principle that we can infer from regularity is not a priori.
- The principle is not found in the data of perception. There is nothing in perception that tells you that what happened in the past will happen again in the future.
- The principle is not a rule of inference (deductive or not, probabilistic or not). If it were, then how would you justify the rule? The rule isn't a priori, it isn't found in sense perception, and if it is justified by another rule, then you have entered a vicious regress.
The quoted comment is a species of falsificationism. This does not work until you have negotiated Hume's trilemma. You have to come up with some way to justify believing in regularity even tentatively or probabilistically. There is no way to do that.
Hume's argument is intended to apply generally, to rationalism as well as empiricism. Rationalists can resolve the problem by claiming that the rule is, in fact, a priori, either dogmatically or via Kant's arguments, but there is no escape for empiricism. Empiricists have been trying for two centuries using falsification, probability, inductive logic, defanging the regression, and other tactics. None of these efforts succeeded. An empiricist just cannot get around the basic problem that there is no data in sense perception to connect past events to future ones.