Are there any self-evident concepts? This question must be asked before we can delve further into particular self-evident truths. I know that there are self-evident concepts because I know particular examples of such concepts and if they did not exist, then self-evident knowledge would be impossible.
Self-evident knowledge requires that there be self-evident concepts. To say that a particular proposition is self-evident is to say that it is known with certainty. In order to understand any proposition, there are certain concepts that we must know. For example, to understand the proposition science is a form of knowledge, we must know the meaning of the concepts that form that proposition. But mere knowledge of those propositions is not enough. We must have a completely certain knowledge of the concepts in order for the proposition to be believed with certainty. If our knowledge was not certain, then any single way of combining those concepts would lead to less certainty rather than more. Therefore, such knowledge requires that the concepts themselves be self-evident.
There are in fact certain concepts that we know are self-evident. The first example is the concept red. This concept is understood by anyone who has seen something red. We might define the word by saying that it is a certain frequency of light, but that is not what we understand by that word. We understand that redness is a particular sensation we receive from particular objects that are red in color. Their redness is the ability to give us that sensation. So the fact that this redness is a particular frequency of light has nothing to do with what redness is. The second example is good. We know that some acts are good and others are not good. But know that some ways of thinking are reasonable; and reasonable simply means a good way to think. We might even analyze goodness through philosophy. But our knowledge of what goodness is does not come from that analysis. If our “analysis” declared that killing innocent people was good then we would determine that our analysis was wrong. Both good and red are understood differently, we understand red by sensation and good by mental reflection. But our knowledge of them as concepts cannot be made more certain. Therefore, these are both self-evident concepts.
These two arguments will not establish that there are self-evident concepts without knowing what self-evident concepts are. What they do establish is the hypothesis that such concepts do exist and it is worth finding proof that they do exist. Proving that self-evident concepts exist requires explaining what those concepts are.
Self-evident concepts themselves need to be understood. In order to do so, and to demonstrate that they exist, it is important to explain what such concepts are. Once that is clear, it will be obvious why they must exist.