There are a number of ways that something can be self-evident. In ordinary language, we say that something obvious is self-evident. Philosophically, however, further distinctions must be made. In modern philosophy, something is self-evident when understanding what it means immediately results in knowing that it is true. In Aristotelian philosophy, another meaning of self-evident was used. There are four different ways of understanding self evidence – logical, indubitable, undeniable and impractical.
Something may be self-evident to one person, but not to another person. For example, I know that 2468+5589=8057. But I figured that our using a calculator. Some individuals are so skilled at math that they know the answer simply by understanding the question. But I understand the question as well. So the difference is not one of understanding, but one of degree of understanding. The math expert simply understands implications that I require a calculator to do.
Something may also be self-evident in a number of ways. First, it may be logically self-evident. Denying the statement causes a logical error. So if the box is blue and red is not blue then the box must not be blue. The last statement is self-evident given the previous statements. Second, something may be indubitable. That is, it cannot be doubted. When I see a computer in front of me, then the statement I see a computer in front of me is self evident. Such a thing cannot be doubted. Third, something may be undeniable. Attempting to deny the statement meaningfully will result in affirming it. A good example of this is the law of non-contradiction. I might claim that some contradictions are true, but my statement assumes that its logical opposite – no contradictions are true – is false. But the assumption is simply a restatement of the law of non-contradiction! Therefore, such a law cannot be denied. Fourth, something may be practically self-evident. This may be read in two ways. First, the general activities of life confirm the statement and deny its opposite. For example, it is self-evident that we need food to live. Second, attempting to disprove the statement will prove it instead. For example, attempting to prove that there is no such thing as goodness will result in an appeal to the good life or to good reason.
All of these various kinds of self-evidence are not equal. But they are all things that are the most certain to us. So there are a number of objections to the use of self-evidence. First, how could a conflict over whether or not something is self-evident be resolved? Second, couldn’t the world be made in such a way that self-evident truths are simply wrong? Third, how do we determine whether or not something is really self-evident or not? Fourth, are there a sufficient number of self-evident truths to build a philosophy on? I think that these are the central concerns of philosophers who deal with self-evident truths. (I am excluding for moment those who simply deny that there are such truths.)