Suppose we want to assert a proposition P. In order to claim that P is true, I must have some criterion by which to judge its truth; some test or measure that we can use to determine if our belief in P is justified or not. Many such criteria are possible: one might be "P is true if I directly observe P with my own senses." Another might be "P is true if it is believed by the vast majority of people".
But suppose we offer such a criterion (let's call it C). Does it really justify the belief? Our claim that it does is in fact another claim; the claim (let's call it Q) that "Criterion C justifies our belief in P". Mustn't we now justify claim Q, with yet another criterion? If we apply the same criterion C to judge the truth of Q, we are engaging in circular argument, because Q contains C as part of itself, so we must use a new criterion, and so on.
It looks like there's no way out of using a criterion of truth, if we ever want to argue for a criterion of truth! And if Sextus Empiricus is right, we always have to use a criterion of truth if we want to be justified in saying that a particular claim is true. But then we are faced with circularity or regress. Either we argue in a circle and say that a criterion applies to itself, or we say there's an infinite regress of criteria.
Because of this argument, the view that one must have a criterion of truth to be justified in believing a proposition leads inevitably to skepticism. There are several proposed methods to escape the problem, including common sense and critical philosophy.
The method of common sense espoused by such philosophers as as Thomas Reid and G. E. Moore points out that whenever we investigate anything at all, whenever we start thinking about some subject, we have to make assumptions. There isn't any way to avoid that. If you try to support your assumptions with reasons, you're going to end up assuming something else. So since we know in advance that we are going to have to make some assumptions, whenever we do philosophy, then what we have to do is clear: we have to assume those things that are most obvious, the matters of common sense that no one ever seriously doubts.
Now bear in mind, by "common sense" here these philosophers don't mean old adages like "Chicken soup is good for colds." They mean much, much more basic claims than that. Claims like "Human beings typically have two eyes, two ears, two hands, two feet" and so on. Or "The world has a ground and a sky" or "Plants and animals come in a wide variety of sizes and colors" or "I am conscious and alive right now". These are all the absolutely most obvious sorts of claims that one could possibly make; and, said Reid and Moore, these are the claims that make up common sense. They are, you might say, the principles of common sense. And once again, the point is that since we know we are going to have to make some assumptions, then we might as well assume what is most obvious, namely the principles of common sense.
Another escape from the diallelus is critical philosophy, which denies that beliefs should ever be justified at all. Rather, the job of philosophers is to subject all beliefs (including beliefs about truth criteria) to criticism, attempting to discredit them rather than justifying them. Then, these philosophers say, it is rational to act on those beliefs that have best withstood criticism, whether or not they meet any specific criterion of truth. Karl Popper expanded on this idea to include a quantitative measurement he called verisimilitude, or truth-likeness. He showed that even if one could never justify a particular claim, one can compare the verisimilitude of two competing claims by criticism to judge which is superior to the other.