Celia Green writes:

Since old-fashioned philosophy has been to so large an extent forgotten, perhaps I may summarise its principal findings, which were all related to what we may call the principle of total uncertainty. It is impossible to be sure that what we are looking at is really there, impossible to be sure that our apparent memory of even the most recent event is not a delusion, impossible to be certain that the object we leave in a room is identically the same when we return and not merely a precise reproduction of the one we left, and impossible to be sure that anything is ever causally related to anything else, no matter how many times they are perceived in close conjunction.

This principle of uncertainty gave rise to a famous philosophical dilemma, known as the Problem of Knowledge. The problem in question was to distinguish some kind of knowledge or of mental activity to which the principle of uncertainty did not apply. A considerable amount of thought was expended over a long period on attempts, frequently convoluted and never entirely conclusive, to delineate such an area of knowledge. This might have led people to suspect that there was in fact no such area...

This is the actual situation. In my opinion, appearances do provide a form of knowledge, but only a very superficial sort: So long as the appearance is there, you know it is there. And even then, when you reflect on an appearance, some possibility of error reenters the situation. (Husserl's long analyses of certainty and uncertainty in phenomenology may be the most insightful thing ever written on this topic.)

The comments elsewhere on this page ask you to think in terms of probability. But what justifies these probabilities? The argument for persistence of objects is that, so far in your life, they are usually still there when you look for them again; also, that the data about the world is consistent with the hypothesis that objects do persist and that it contains many other people who have experienced this. But if you examine your experiences logically, all that you really know is that so far, you have had a series of experiences consistent with this interpretation. You do not know that these appearances - of objects and of people - correspond to persistent realities with an existence independent of your perceptions, nor do you know that your experience will continue to be consistent with this hypothesis.

Nor do you know that this hypothesis is the most probable interpretation of your experience, because you don't actually know the set of all possible worlds and the conditions under which your life-experience typically occurs to a possible being. It could be that your experience is actually most characteristic of a certain type of dream experienced by 29-dimensional hyperfnords, and that across the whole multiverse it is only rarely that such experiences are veridical (that they are literally true). In that case, the rational interpretation of events would be to say that the objects and people of your experience aren't real, they don't exist when not attended to, they are just a product of your dreaming mind and you could wake up at any moment.