I would like to state outright that I am not an anti-objectivist. I am just someone who, after learning some about objectivism, has some unresolved issues.
First off, I must state an axiom that I have not heard elsewhere. Perhaps it is not axiomatic, but I consider it beyond refute:
One or more fundamental constituent(s) exist.
I consider this irrefutable because, without a fundamental constituent, there is instant paradox. It would imply that there are no true concrete entities because all such entities would be made of other entities which are made of other entities. Nothing would have shape because shape is defined by a border, thus there would be no concretes. A collection of concretes separated by space does not possess shape, they are simply a collection of concretes with a specific spatial arrangement. One could IMAGINE drawing lines between each concrete and giving it a shape, but this is artificial. Only that which is not composed of parts INHERENTLY has shape (i.e. has a border all by itself, without human conceptualization). Therefore, I submit that the universe is, objectively, only fundamental constituents changing location by interacting (touching) each other.
Now, I believe my definition of exist is in agreement with the objectivist community:
Exist: Shape and location
Therefore, the computer in front of me exists because it has a perceivable shape and I can establish a distance between it and the wall. The leprechaun I am imagining does not exist because I cannot establish a distance between the leprechaun in my head and the wall. It has shape but no location. I divide objects into two categories:
Concrete Object: Shape and location
Abstract Object: Shape
And concepts:
Concrete Concept: Relationship among concrete objects
Abstract Concept: Relationship among abstract objects
Therefore, the circles and squares of geometry are abstract objects. They are conceptually 2-D, I can visualize something in 2-D but such an object has no location. There is not a two dimensional object anywhere in the universe. I try to touch the square on the paper but I just touch ink and paper. Geometry is the study of abstract objects. On the other hand, physics is the study of concrete objects. The concrete objects of physics are conceptually composed of the abstract objects of geometry, but these geometrical shapes have no existence on their own.
Now, I have difficulty with the statement that “consciousness exists”. I think my difficulty is a tendency to veer toward what you call “reductionism”. To state that consciousness exists begs the question “what is consciousness?”. If it is defined as the motion and interaction of fundamental constituents (FCs) resulting in goal-directed/purpose-driven activity, then it does not exist. The word used this way is a concept, it is a relationship among concretes, specifically their spatial arrangement and motion. Now, I do not “deny consciousness”, for me this is simply a matter of consistency of definitions. We have one definition of exist and it simply cannot be used another way. I cannot establish a distance between consciousness and the wall, it does not have location, it does not exist.
However, I do not deny goal-directed activity (life). To even make this inquiry requires it. It is axiomatic because of language. Language is simply a set of rules/laws. Rules inherently produce goal-directed activity whereas having no rules does not. The universe must obey laws/rules because this is the only way to produce inquiries about laws/rules. This is purely an issue of defining the words we use in speech in a single way and always using it that way.