I have shown that all self-evident sentences are true. But some sentences are not self-evident, even though they are true. These sentences are found by reasoning from self-evident sentences. Such reasoning can be either deductive or inductive.
We determine whether or not a sentence is true by asking why that sentence is true. For self-evident sentences, the justification comes from the senses, reflection or some combination thereof. For all other sentences, the justification (reasons) comes from other sentences. For example, suppose that I was counting my pennies. I can see all 102 pennies on the table. I remember counting them and coming up with 102. It is hardly self-evident that there are 102 pennies. But my memory of counting them is a good reason to believe that there are 102 pennies especially if a second count of those pennies also comes up with the same number.
No sentences are brute facts. The reason for this is simple. If any sentences were permitted to be a brute fact, then there would be no way to distinguish between sentences I strongly wish were true and sentences that actually are true. In both cases, I believe that the sentences are true. But if I can simply avoid justifying my sentences, then there is no way to determine which is which.
Deductive reasoning is the kind of reasoning in which a set of sentences guarantee the truth of the sentence that needs justification. For example, If I know that I am sitting down, then I know that there is something I am sitting on. The truth of the second sentence I am sitting on something is guaranteed by the truth of the self-evident sentence I am sitting down. Any argument that begins with self-evident premises and only uses deduction to arrive at a conclusion is a demonstration. Demonstrations are extremely important in philosophical reasoning.
Inductive reasoning is the kind of reasoning in which a set of sentences support but do not guarantee the truth of the sentence that needs justification. For example, if I know that I am sitting down, then it is likely that I am sitting on a chair. But it is quite reasonable to believe that I am sitting on a bench, on a log or on the floor. So while the statement that I am sitting on a chair is supported, it may not be true. This sort of reasoning appears in science and history. Such reasoning can become so strong that disbelieving it is irrational.
This is the end of my exposition on self-evident truths. Further exploration would include a defense of the previous exposition or a exploration of that exposition in detail. Such things would include a defense of definition against Wittgenstein and his modern followers, an exploration of the relationship of illusion to self-evident truths and a more precise account of just what self-evident truths are.