People in the information sciences are fond of high-dimensional vector spaces as models of document content. These are in fact only approximations of reality, however; and in the specific case of semantics, they are probably an oversimplification. We already know something about how the neural circuitry in our brains work when we process the meaning of language; we can find no clean finite-dimensional linear space in the tangle of our synapses.
Neural imaging like PET does support the theory that linguistic concepts correspond to particular clusters of neurons connected in fairly complex feedback loops. Our understanding here is still quite limited, though. We do not know how many such clusters exist or how widely they are distributed. Visual concepts are in a different part of the brain than auditory concepts, for example; and overall, we have not yet found any obvious switchboard, say in the hippocampus, that could somehow tie everything together neatly.
In our computational semantic model, we assume that all concepts are independent and equal. That seems to work in semantic dictionary applications when we have thousands of concepts of concepts as dimensions, but an espistemologist here would have the lurking suspicion that our actual semantic space has to be some kind of complex manifold with all kinds of holes and twisting surfaces like a deranged n-th-order Moebius strip. Meaning is messy.
Our linear Euclidean model may therefore be valid only in a small local region of our actual semantic space, but in practice, that is really where all our apps have to live. One cannot presume to comprehend all possible content in text. We can only slice off a small piece of the pie of meaning, and until world peace and perfect enlightenment break out, that is a good start.