*** In the first one it is certainly unclear as to which statement you are trying to make; are you trying to say "no portion of ultimate reality is knowable or that there are portions of ultimate reality which can not be known.***
No portion of ultimate reality is knowable in the ontological sense. I contend that it is knowable in an epistemological sense, however you need to accept a number of reasonable assumptions to do so.
***And in the second, why is the adjective approximate required? Isn't an approximate structure a structure?***
I'll use an example. A cloud is an approximate structure in that it has observable properties, causal properties, functional properties, etc, but it is an approximate structure in that it can be effectively reduced to sub-structures that determine the properties of the cloud. We can virtually eliminate talk of the cloud by merely talking in terms of its reduced properties. However, we cannot quite do so because of the complexity factor which makes it a complex object in a holistic sense.
***My comment here is absolutely nothing more than an aside as the issue is how does one go about answering these kind of questions, not what the answers are!***
Why do I get the sneaky impression that you are only concerned about communicating your ideas and not learning ideas from others?
***1. First it is possible that some specific thing (or perhaps several specific things) may exist.***
I agree that it is possible that ultimate reality may have one or more properties. Those properties might be the existence of objects, processes, laws, etc.
***2. Second, it is possible that some of those things which exist have no direct consequences in the physical universe available to my studies.***
Generally, I agree. However, existence has to be defined, and causal connection with our physical universe is one of the key attributes for something to be considered to exist. As long as we accept that some causal tie-in is needed, then I don't have problems accepting (2).
***3. Third, some of those things described as having no direct consequences in the physical universe available to my studies may have consequences in the future.***
I agree. However, refering to the our physical universe might be equivalent to referring to our spacetime continuum, and therefore what is no direct consequence to the spacetime continuum is not going to affect the future. Also, what is a direct consequence in the future is also a direct consequence throughout the age of the universe.
If you can accept these exceptions, then we are in agreement.
Warm regards, Harv