Knowledge by negation may include getting to learn an object's range of existence in space and time, its variety of reaction patterns, what it can and cannot do.
We are able to measure and stipulate a large number of qualities merely by external examination, without getting to observe the thing in itself.
Such clear definition of the externals, and elimination of that which it is not, certainly reduces speculation and sheds light on the unknown.
And, in sub-atomic physics, the Heisenberg Principle has made a system out of uncertainty itself.
To be sure, often a descriptive word suffices instead of an explanation, and we think we understand without really comprehending.
Like the European doctor who discovered hypnotism in the last century and called it 'life magnetism'; his successes were no less impressive in spite of the fact that they had nothing to do with his explanations.
Today the phenomenon is still largely esoteric, in that we simply do not know what it is, but we have learned what it can and cannot do.
We have defined its frontiers, and it has become a useful tool.
In other words, the ability to define the limits of what we do not know enables us to build a positive edifice for what we do know.
It is comprehension by way of negation.
As the Rambam ruminated in Hilkhot Teshuva, how can we speak of God's knowing?
The paradox of our existence lies in the fact that our mental comprehension of what a thing is and our consciousness that the thing exists are two separate realms of awareness, so that we only grasp things from outside.
We obviously do not have God's knowledge of a thing itself.
For He and His knowledge are one and unchanging.
To which another Sage, the Ravad, responded by asking why bring up the problem if there is no answer.
The philosophic issue here was already familiar in Rambam's time.
As some medieval scholars put it: Were I able to know Him I would be God.
My lack of knowledge is not the result of insufficient learning or inadequate effort, it is the intrinsic inability of man to really know.
Nevertheless, my intellectual efforts make it possible for me to grasp the limits of my knowledge of God and give me a "negative" understanding of the Divine.
The human intellect cannot do more.
It cannot create anything, it can only make tools to grasp what is given.
Wisdom, however, which is Divine, can create–it forms something out of nothing.
And this, of course, cannot be understood, it can only be concluded by way of elimination.
–Rabbi Adin Steinsaltz
From "Sanctity and Restraint" in The Candle of God by Rabbi Adin Steinsaltz