Much of modern philosophy begins in doubt. Descartes rather famously claimed that he knew he existed because he could not doubt it. Ever since that time, skeptical arguments have always been prominent. If self evident truths are the most certain truths we can know, then any doubts will appear to a greater extent in anything deduced from them. There is no good reason to doubt self evident truths not even from the strongest skeptical arguments that Descartes considered.
Self evident truths can be doubted if they are not indubitable. This includes such things as moral values, the law of non-contradiction and the results of logically deductive arguments! But the mere possibility of doubt is not the same as the reasonable possibility of doubt. I am capable of jumping off the CN Tower. Doing so would be completely unreasonable. In a similar way, the ability to doubt something does not mean that doubting it is at all reasonable. Descartes method of doubt is simply to doubt everything that can be doubted. I am including his own method.
In order for doubt to be reasonable, it must be based on a reason. The standard skeptical worry upon seeing a computer is that there might not be an actual computer there. Every single sense might be simultaneously deceiving us. This is indeed a possibility. However, this possibility contains no reason to believe that it is actually true. Without such a reason, it is entirely unreasonable to believe in any skeptical position.
The natural response is that skepticism is not a position, but the a loss of confidence in our ordinary self-evident beliefs. Since the skeptical possibility has not been discounted, our confidence in our non-skeptical understanding of the world should be decreased. But this is by no means correct. Without a good reason to doubt our beliefs, there is no reason to lose our confidence in those beliefs. Admittedly, we cannot prove that skepticism is wrong at least not with our present resources. But that is no reason to actually consider skeptical beliefs or lose any of our confidence in our ordinary non-skeptical beliefs. Any belief that would lose our confidence in our beliefs will do so because of a reason. But that reason will also be a reason for a skeptical belief. Since there is no such reason, we do not have to lose any of our confidence in our ordinary self evident beliefs.
There is one final objection to this line of reasoning. We could claim that there mere possibility of being wrong counts as a reason for skepticism. But the only reason that our beliefs can be doubted is that they are not indubitable. But we cannot claim that our reason for doubting our beliefs is simply that we are able to doubt them. We would need some further reason. Since we are not given one, there is no reason to doubt any of our self-evident beliefs. This line of argument is a failure.