Clarity

I think the English is clear. I'm curious, though, about a skeptic being one who ACCEPTS the appearance of things as their reality. (Special philosophical meaning? Or is this just describing an open-minded early stage of the epistemological process?)

The ancient skeptic does not affirm or assert that the reality of something is reduced to the way it appears (appearance is understood here in a loose way), but just points out that he doesn't know how things really are and, moreover, if there's such a thing as the reality or nature of something. This is why he must restrict himself to reporting his own appearances, that is, the vari

Without any surrounding context, I would draw the following abbreviated meanings from the sentence.--

The Skeptic bases his value judgments on the various ways that things appear to him.

When the Skeptic says "that is", he means "that appears to be".

(I don't claim to be your most intelligent reader, though.)

EDIT: I did not see the previous posts.

Davkett, your interpretation is totally correct. Now, do you think the sentence is clear?

Sextus

Yes.

Do you think it would be just as clear to say 'the reason...is that' as opposed to 'the reason why...is that' ?

Well, you're the native speaker and I respect your opinion. You think it's clear to say:

"The reason the Skeptic uses the verb "to be" in the sense of "to appear" is that, having suspended judgment about the existence of anything good, bad, or indifferent, he limits himself to basing his value judgments on the different ways things appear to him".

Sextus

Yessir.