You do need assumptions for that. You need an assumption that you can experience an experience.
Why would I need to assume that? I'm experiencing an experience. There's no logical process required. Observation is occurring. I can't definitely know
what is having that experience. For example, I don't know if I'm in a meat body observing a real external world, or a brain in a jar being fed stimuli by a computer, or a "soul" having a purely hallucinatory experience with no physical validity, or something else entirely. And I can't definitely know if the experience I'm having has any relevance to anything. Again, for example I could be a brain in a jar, with everything that I see and experience being fed to me by a computer.
But the experience itself...is being experienced. That I can know, because I'm experiencing it. In fact, it's
all that I know.
Otherwise, how can you say that what you experience is actually an experience and not something completely different?
I'm not sure what you mean. What else could it be? I assume you're not trying to play semantic games. I am observing. The observation that I am experiencing, is my experience. I'm not assuming that that experience necessarily has exterior validity, or even that there is any "exterior." The experience itself is all that I know, because my experience that I'm having...is all that I'm experiencing.
What do you mean when you say my experience might not be an experience?
For instance, Plato believed that experiences were illusions and did not actually exist. What he believed to be real were pure ideas, without any empirical basis.
I think you might be using the word "empirical" incorrectly.
Empirical"based on, concerned with, or verifiable by observation or experience rather than theory or pure logic."I am observing an experience. It is by definition empirical. I could well be experiencing "illusions" with no external validity. But that would not change the fact that I'm experiencing them.