It was an interesting discussion, but WRT "previously examined definitions of science", quoted from the article, I did not see anything in the general area of science discussed or anything resembling an application of the scientific method along the lines of falsifiable logical predictions based about testable experiments and so on. I think a discussion along those lines with the same characters would be interesting, although this small excerpt was pretty far away from those specific topics.
The metaphors Tagore is using are confusing, at least to me, but this is definitely in the realm of "Philosophy of Science." It's funny because I can't really spot a practical consequence of the difference in their model of the world, functionally speaking.
Einstein says he believes there is a reality which exists independent of the human mind. When we leave the kitchen the table remains, even though we can't see it. It seems like for Einstein this is less of a metaphysical belief and actually a scientific postulate. I could imagine him saying, "It might not be true, but I don't know how one can do meaningful science with any other premise."
Tagore, OTOH, imagines a "Universal Mind", compatible with certain aspects of our own mind, that "anchors" reality for us. It's this universal mind we're discovering when we're doing science, not some foreign reality.
To be honest, these two pictures of the world seem isomorphic as far as science is concerned. That seems like it might've been part of Tagore's point, when he said "In a similar manner if there be some Truth which has no sensuous or rational relation to the human mind, it will ever remain as nothing so long as we remain human beings." Here is a thing which could very well be true but nevertheless couldn't be demonstrated scientifically.
In many ways his worldview reminds me of True Arithmetic (http://en.wikipedia.org/wiki/True_arithmetic), which circumvent's Gödel's Incompleteness Theorem at the cost of being undecidable and recursively innumerable. As soon as we constrain our set of arithmetical axioms to something that a "finite mind" can handle, so to speak, we wind up with true-but-unprovable theorems.
True Arithmetic encapsulates the whole universe of Truth when it comes to arithmetic, but in a way that makes it impossible for us to do any meaningful work. Once we constrain ourselves in a way that allows us to do meaningful work, it becomes impossible to ever reach True Arithmetic.
This debate interweaves lots of metaphysics and epistemology, which are things scientists can and do discuss. See, e.g., realism vs. positivism vs. instrumentalism vs. empiricism.
Interesting, my take on Einstein's POV is that there is a reality (God, Nirvana, etc.) that is independent of reality as we know it, and therefore has nothing to do with anything -- thus Einstein's claim that it is his religious belief, and not something that can be proven scientifically.
The kitchen table argument is quite fascinating. One could argue that nothing exists without oneself to observe it; i.e. when walks away from the kitchen, does the kitchen continue to exist, or has the reality of the living room now come into Mind? i.e. all that exists is what we are currently experiencing and everything else is a delusion.
Or, delusions are endless, as the Zen masters teach.
You can play a lot of thought experiments about scientific experiments to test if the table disappears. As far as I know at this time, they all devolve into the brain-in-a-vat or the bad-actor solution (although I may have the names mixed up). The brain in a vat is we're brains in a vat connected to a really high end "second life" computer server. The bad actor argument boils down to some god is testing our faith by trying to fool us (usually heard about fossils, or the earth being round, etc)
