Can art be of importance without meaning? Must "good" art convey the zeitgeist of the times in which it was created? Does "depth of meaning" correlate directly to "goodness" of art?
A definition of terms here would be of value but the terms in question are so based on individual and subjective opinion that the defintions would be questioned.
Abstract painting, particularly the nonobjective painting of many artists since the 1940s is arguably devoid of meaning. In fact many artists want it that way. They prefer to see purely compositional factors, the tenets of design as the measure of their works. Does this relegate them to the level of design, not truly "high art."
Abstract paintings can do two things. 1) They can ascend to the highest level of design, and 2) They may transcend it to "high art." Just as Kurt Schwitters paper snips transcend the craft of hobbyists cutting paper, and Joseph Cornell's boxes transcend the craft of cabinet makers or box designers – so can an abstract paintings transcend design.
The criteria of meaning needs some discussion in my opinion. The "meanings" that some narrow-sighted critics refer to as being the paramount criterion of "high art" revolve around historic, philosophic, and religious dimensions. These meanings purportedly reflect the highest ideals and aspirations of man and god (God?).
I appreciate meanings as much as the next person. I like the classical, epic struggles of mythology, the ancient renditions of the history of the world, the religious icons of every century, the struggles of mankind and every individual in mankind. These are wonderful meanings and certainly worthy of artistic depiction.
Now consider the meaning of a man / woman who struggles to create pure beauty. The artist. The artist who wants to create not only "high art" but does so without the tools of religious thought, without the maps of cultural revolutions, without the applause of an informed and socially motivated political movement, without the traditions of a craftsmens guild. Consider this courageous individual.
These individuals not only attempt real, although only mortal, creation at its highest level – they do so in a unique and hardwon individual style. In addition, their work is meant to free, enhance and amplify your perception of art and beauty in all of its mysterious manifestations.
That "is" meaning. You can witness this meaning in its visual record of each abstract painting. No, not every painting is a masterpiece – and it can't fall back on cliche 'or a social nomenclature. It stands as a testament to a real struggle to push something to the highest level of art with no help from all the other "manifold meaning packages" that were the reason for art in previous centuries.