This from the Comments. The numerals are my intercalation.
But the question remains, exactly what does Kant mean by ‘appearance’ (Erscheinung)? [1] Can I speak of this Appearance? [2] Is this Appearance the visible surface of my desk? [3] Is it numerically identical to what F sees when she looks at the desk? (Surely it is, since you claim it is “public, intersubjectively accessible” – and [4] in what passage does Kant say that Appearances are ‘public’ and ‘intersubjectively accessible’? What are the German terms corresponding to the English?)
Ad [1]. Yes, in the same way that you can speak of your desk or this desk.
Ad [2]. No, the appearance or phenomenon is the empirically real desk itself with all its parts (and their parts . . .) and properties. Notice that I wrote 'desk itself,' not 'desk in itself.' The desk itself is a phenomenon, not a noumenon; it is an empirically real object of "possible experience" (moegliche Erfahrung). The visible surface you see is not identical to the desk itself.
Ad [3]. The desk itself is a Kantian phenomenon and therefore intersubjectively accessible via outer perception. So when F is in your study, she sees the same desk that you see. But your mental states are numerically different from hers, and hers from yours. Your epistemic access is via your mental states and her access is via hers. You can introspect yours but not hers and vice versa. If A1 is your act of visual perceiving at time t, and A2 is her act of visual perceiving at time t, then it is obvious that A1 is not identical to A2. It should also be obvious that what A1 presents to you and what A2 presents to her are typically different aspects of the same desk. Suppose you are looking at the desk from above and she is underneath the desk looking up at its underside.
Since 'appearance' is causing you confusion, let's use 'phenomenon.' The Kantian phenomenon is the desk with all its parts and properties. But this one desk appears differently to you and your wife.
Ad [4]. Carefully read section 32 of the Prolegomena. There we learn that appearances = things of sense = phenomena. Phenomena are sensible things such as your desk. They are full-fledged denizens of the mundus sensibilis. Phenomena are the empirically real objects of sensory intuition (Anschauung). They are obviously public in that two or more empirical subjects can have knowledge of one and the same phenomenon such as your desk. The main thing here is that phenomena are not private mental data. It therefore should be obvious that Kant is not promoting a form of subjective idealism. The world of phenomena for Kant is an intersubjectively knowable world.
Study also Prolegomena, section 13, Remark II wherein Kant explains why he is not an idealist.
And then there is CPR A45-46/B62-63. Do you have the Akademie Ausgabe in your library? If so, check out Ak. XX, 269. That's a passage from Fortschritte.
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