The Basic Logic of Non-Duality

Q: IF:

I am Consciousness, and that which I am "conscious of" (know) is not-me (thus, there is (1) me=Consciousness and (2) not-me; so this appears to be duality)
Everything that is not-me is an object. 
Thus: Not-me = Everything = Objects
All objects are apparent because we can only know them as
projections in the mind.

Thus: Not-me = Everything = Apparent Objects = Projections in the mind
The mind and its projections are one; there is no separation/difference.

Thus: Not-me = Everything = Apparent Objects = Projections = Mind
A: So far so good. 

Q: and...
We only know the mind as Consciousness (me); there is no separation/difference.

Mind = Me-Consciousness
A: This is not quite right and needs some explanation. The mind is an object in me, consciousness. When you say "we know the mind as consciousness," that's correct if you are saying that as me consciousness, the mind is known, the mind appears. You are correct when you say there is no separation, since objects appearing in me are not actually separate, real objects. BUT, when you say there is no difference, that's not correct. There is a difference: 
The object is dependent on the subject (me consciousness), but the subject is not dependent on the object. 
Do you see that? Objects all depend on me for their existence. But I exist without any objects. The existence or non-existence of objects doesn't change me one way or another. I am always pure and devoid of objects. Objects appear but don't touch me, they don't make a ripple, they don't leave a trace. 
The objects are all me, but I am not an object. 
The equation only works in one direction because the objects do not enjoy an independent, autonomous existence. The objects are all made of the one essence (consciousness), since that's all there is. I can see that you are getting to that in your thinking. That's good. But consciousness never "becomes" objects. Objects don't have consciousness in them, they are simply a form that consciousness appears as. 
We use the clay and the pot example. All pots are clay. But clay isn't a pot, doesn't ever have to be a pot, and is not dependent on pots to be. Which one is the essence? It's the clay. A pot is clay appearing in the form of a pot. 

Q: THEN: (reversing the equation),

A: So my point is that you can't reverse this equation. It's not the same in both directions. 
Q: Me-Consciousness = Mind = Projections = Apparent Objects = Everything = Not-me
A: You can say that the Not-me is Me-consciousness, but you can't say that the Me-consciousness is Not-me. The Me-consciousness is the clay-essence, and the Not-me is a pot-object appearing in Me-consciousness. It is the Me-consciousness appearing in the form of Not-me – appearing in all these infinite forms. Forms include your body, your mind, thoughts, experiences, you name it. 
Q: or...
Me = Not-me
A: So I guess you get now why that equation is not correct. Honestly, this is why Vedanta is so great – because we smart people can come up with some really logical reasoning on our own, but it's the mind's job to fool us into keeping the illusion of the duality-world going. How do you crack that nut using the very tool that is built to create the illusion? Vedanta gives the tools that get around that problem. 
Q: Meaning, nonduality: subject and object are one/not-two/non-different/non-separated.
A: The meaning of non-duality is that there is just one consciousness, free of all forms that appear within it. Anything that appears is simply consciousness appearing in a form. The really good news is, I am free of all that appears within me. 
I'm just going to comment on one more thing you said that is up in the "so far so good" section: You said, “All objects are apparent because we can only know them as projections in the mind.”
Actually, all objects are apparent because they do not have an existence independent of consciousness. Remember always that the mind is an apparent object, too! Projections in the mind are objects, too. The mind, the projections in the mind, all of that is totally dependent on your knowing it. How is the mind known? It is known by me, consciousness. Can the mind be, without being known by me consciousness? I am the primary one – the mind depends on me. Everything depends on me. 
Keep up the good work. 

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