Who does not share the experience of beauty?
How would we know that exactly?
I would agree with you only that we know (I certainly know but I can only assume that other people do as well) the things we happen to have in mind (and only at the moment we have them): pain is my favourite example, but beauty when I have the impression of beauty is just as good an example; colours; feelings; so many other things we may not even have names for them. However, it does not follow that the pain I experience today is identical to the something else I have the impression of remembering also as pain. The thing is, what I experience now is the memory of something I take to be pain, not pain itself (which is fortunate since memory of pain is already unpleasant enough). So, how could I possibly know that the two are the same sort of things? Same for beauty. I think that what matters is that we believe (not know) they are the same. This is good enough for practical purposes. This also explains behaviours. Now, if we move away from the requirement of knowing, and look at our beliefs, it is also interesting that the things we believe are beautiful in the material world, say a flower, are actually never identical. So we have to assume for it to work at all that people somehow code for beauty. So, presumably, we not only know beauty as the immediate impression of beauty, but we also probably have some reference inside our brain, whatever this is exactly. This doesn't seem to be much different from how computers work. They have certain codes that stand for certain things in the material world. What the computer knows is the code. So we may have what amount to a code inside our brains that stands for beauty. However, if we assume that this code can only have come to my brain through the material processes of the material world, we have no good reason to claim that the code in my brain is really identical to the one in your brain, let alone that of Plato. All that is needed is that we somehow believe we broadly understand what other people say. If so, contrary to your claim that there is such a thing as Beauty, somehow identically and magically accessible to each of us as to Plato, we may only have access to particular codes in our brains standing for particular experiences individually determined by our body and our environment as we move through life. We are naturally very easily fooled by the uniqueness of our individual experience of our own personal beauty code so that we tend to take it for some sort of absolute, or universal. But there is no evidence for this. The only evidence is beauty as we may experience it now, probably just a code. And then a very interesting system of beliefs whereby we work out a model of what we think is the real world, which we then take for the real world itself.
EB