The first fundamental assumption and solipsism

The first assumption that we must make is that we appear to exist. However, we need to be careful when using the word "exist" because it describes a status that is independent of the mind.

objective: a thing or class of things external to or independent of the mind;
exist: to have objective reality or being.
(Oxford dictionary)

In the following, when we talk about existing, it will only be an apparent existance that is relative to our mind.

Our apparent existence may appear to be a trivial thing to assume. Indeed it may appear to be self evident (or obvious) and not an assumption at all. But how would a person argue that it is obvious that he or she exists? Perhaps they would say "I know I exist because I am thinking and I remember things I have thought".

In fact Rene Descartes (1596-1650) said "I think therefore I am" meaning I know I exist because I can think. A similar statement was also made earlier by Saint Augustine (354-430).

But the person has merely shifted the burden of the proof from being about existing to being about thinking and remembering. How would the person then argue that they are thinking and remembering? Perhaps they might try "I know I think because I have thoughts" which leads immediately to a question about having thoughts. Giving an example such as "I just thought about us talking" wont do because it is no more than a claim of having a thought, rather than proving that they have had a thought. Neither will circular arguments such "I know I had a thought because I thought it" because the reason given (I thought it) requires the action of thinking, which is the thing they are trying to prove (I know I think because I have thoughts). We could go on in this manner, but at some point we will arrive at a statement that we have to assume is true (e.g. "I just know I think"). This assumption is then the basis for claiming existence, and implies that our apparent existence is an assumed thing.

Without making any further assumptions, the point we have reached is the basis for solipsism, the belief that only the self exists. In solipsism all the information we receive from our senses is accepted without knowing or verifying its source. We might feel a pain sensation whenever we have the sensation of moving towards something we label as a fire, but these are just sensations that reoccur in a consistent manner. We don't actually know where they arise from. This view of the world is an entirely subjective one.

solipsism: the view or theory that self is the only object of real knowledge or the only thing really existent;
subjective: existing in the mind only, without anything real to correspond to it.
(Oxford dictionary)

The status of the assumption of our apparent existence, and the knowledge that rests upon it, is revealed by considering its contrary. If we do not exist, even apparently, there is nothing further to discuss. So clearly assuming our apparent existence is essential for any meaningful discussion of any knowledge or belief.