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In Prolegomena §9:

Freilich ist es auch alsdenn unbegreiflich, wie die Anschauung einer gegenwärtigen Sache mir diese sollte zu erkennen geben, wie sie an sich ist

Translated to:

Of course, even then it is incomprehensible how the intuition of a thing that is present should allow me to cognize it the way it is in itself

Up until now Kant refers mostly to intuitions of objects or Gegenstände, but now he suddenly changes vocabulary to thing, or Sache. I searched for object and thing in Caygill's Kant Dictionary, and there is a pretty long entry on object, explaining the differences between Ding, Objekt and Gegenstand. However, there is no mention of Sache, and the entry for thing is simply this:

thing [Ding] see APPEARANCE, OBJECT, PERSON

So, how can I best interpret Sache?

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    The German text of $9 makes no difference between the words 'Ding', 'Gegenstand','Sache'. They all mean 'object', 'thing'. - The important technical term is in the first line 'things as they are in themselves' or 'for short 'thing-in-itself'.
    – Jo Wehler
    Apr 24, 2022 at 5:56

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There are two possibilities to take this:

  1. You can understand Sache as synonym for Ding, ie. in the sense of a representation of a particular object of experience, so that the translation thing is indeed appropriate here.

  2. You can understand Sache more generally in the sense of state of affairs. We do have a specific word with Sachverhalt in modern German but in the use of his time it was common to use this as an abstract reference and understand Sache meaning a wider state of affairs, which would also make sense at this point.

Considering the usually very careful choice of words of Kant when it comes to Gegenstand vs. Ding it could well be that he expressively wanted to state here that it is unintelligible how any present state of affairs, if presented via intuition, should be able to inform us about how things are in themselves.

Indeed, this makes sense as he points out in that part that if the intuition was of the thing itself, it would effectively mean that the representation and its object would be identical. That, in turn, would mean that it wasn't an intuition (Anschauung) at all, as that has to be an intuition of something different from itself. Therefore, he argues, this logical and conceptual contradiction means intuition in general cannot be about the things in themselves.

Also, intuition cannot, as such, constitute particular Dinge (particular objects of experience). For that, understanding and an apperception under a concept are necessary.

This has to be speculation at this point though.

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