Unfortunately for the Tower of Objectivity, using objective reality as the foundation of our existence comes with a gaping hole: its independent existence cannot be verified, by virtue of the fact that you, as a subject, must be derived from it. The existence of objective reality, in other words, must be taken as an article of faith.
This is best exemplified by Rene Descartes, whom we have to thank for the phrase "I think, therefore I am" ⬈. He constructed a thought experiment in solipsism, which I will briefly cover here.
Definition Solipsism (noun):
The belief that you are the only truly conscious being in the universe and that all other subjects are figments of your consciousness.
Descartes supposed that there was a demon who controlled his every sense, and made him believe, through the careful manipulation of his perceptions, that there was an objective reality, when in fact it was all just up in his head.
After trapping himself in this neat little conceptual box, Descartes proceeds to spend 40 pages chasing his tail, after which he more or less assumes the existence of God, and then uses Him as an omni-tool to escape. At least, this is what I got out of his writing. I probably missed a detail or two...
Once you've trapped yourself into thinking that you're the only fully conscious being out there, how do you get out?
The answer to this may be found in the closely related Turing Test ⬈. The gist of the test is that if you were chatting with two individuals through a computer (and one of the them was actually just another computer), and you were unable to determine which of the two was the computer, then for all practical purposes that other computer must be conscious being. [1]
[1]This chain of reasoning doesn't prove that the computer is conscious. For the counterargument, consider John Searle's [1-1]Chinese Room ⬈.
[1-1]I'm required to tell you my joke that I don't think John Searle is a fully conscious human being, and that inside his head there's actually just a Chinese Room.
Having established an understanding of existence which puts the subjective as its foundation, it is possible to go on and [re-]construct interstitial realities out of it again, using the results from the Turing Test to combat our self-imposed solipsism. The chain of reasoning goes that while you cannot prove that the other "seemingly" conscious beings in your subjective existence are actually conscious, you similarly cannot prove that they aren't actually conscious, and so in this ambiguity you are free to choose either. As it turns out, there's more you can do with the world if you think that other conscious beings exist to some extent beyond yourself, and so almost everyone ends up falling into that understanding eventually.
This leads us back to interstitial reality, that there exist things that, by virtue of the fact that they are subjectively held by a bunch of subjects, gain a level of existence with greater permanence and tangibility than just one subject's opinion.
You can build a notion of objective reality on top of this notion of interstitial reality by taking objective reality to be the asymptote towards which all interstitial objects approach: that ofsubject-invariance. The idea here is that if literallyeveryone perceives the same subjective fact, then that fact mustbe indistinguishable from an objective fact. And, in the same way that a being being indistinguishable from a conscious one allows us to treat it as conscious, these facts then become objective.
This completes our subjectivity-based Tower of Existence. In particular, I'd like to emphasize that the rarely encountered "interstitial reality" is the one being used as a bridge between the more traditional objective/subjective dichotomy.
I'd also like to emphasize that the two constructions of the Tower of Existence are duals of each other, in that you can pretty much arrive at the same conclusions no matter which way you go, though one may often be easier than another to reach.