Should have said existent physical object. Each point in thingspace is a possible configuration of matter, but not all possible configurations of matter necessarily exist (see the post on Logical Zombies). It's a Big Universe so maybe all possibles exist, but my point was to differentiate the abstract "this is an abstract possible configuration of matter" from the "this is a particular instance of this configuration of matter".

For the last part.. yes, I think, kind of? The concepts are being processed by a physical brain, which means in a significant sense the judgement must be being made by a physical object, but at the same time the physical embodiment of that concept in the brain is key to the judgement so the concept is vital.