One of the early questions that I asked is whether or not self-evident truths are sufficient to build a proper philosophy on. I whether or not there is a method to determine self-evident truths. I think that these questions are related. There is no a priori method to determine whether or not self-evident truths are sufficient because there is no general method to determine self-evident truths.
There is no general method to determine self-evident truths because self-evident truths are not all of one kind. As mentioned in my earlier post on self-evident truth, there are at least four categories of self-evident truths. There is no reason to believe that these categories are jointly exhaustive either. The only thing that self-evident truths share in common is that they are all certain in various ways. But because they are all of different kinds, no general argument can determine whether or not a particular truth will actually be self-evident.
There is a further and much more central reason to believe that no general argument for self-evident truths can exist. Any such argument would either beg the question or be non-deductive. If an argument claimed that a particular truth was self-evident because of reasons and those reasons were deductive, then the argument would beg the question. Self-evident truths are certain. So any argument for them would have to have premises no more certain than their conclusion. So no general argument for self-evident truths is possible. But if there were a general method to determine whether or not a truth was self-evident, then that method would also be a general argument for self-evident truths. Therefore, there is not and cannot be such a method.
Without knowing the full scope of self-evident truths ahead of time, there is simply no way to determine if they are sufficient for philosophical purposes. We can either assume that they are and build a philosophy on them, or we can include other truths in our foundation. But there is no a priori way of determining whether or not self-evident truths are sufficient for building a philosophy on.
Given all of this, I have chosen to build my philosophy on self-evident truths. I have done so in order to maintain a foundation that is as certain as it is possible to be. This was also Aristotle’ s motivation. So the remaining questions do not deal with the nature of self-evident truths in general, but self-evident truths in particular. Before dealing with issues of particular self-evident truths, there are issues related to the knowledge of particular truths. First, are there any self-evident concepts. Second, are there any self-evident operations on concepts. It is these kinds of questions that must be answered next.