So many of the questions that arise in addressing this question are difficult to address. But here are some caveats: it is not a question of right or wrong or of true and untrue or even of important or unimportant, relevant or irrelevant (which could change from one decade to another). The answers that I intend to explore all can be argued but without proving anything. That examples may be at once 'absolute' and 'illustrative' doesn't matter. Whether there is recognizable subject matter is not to the point.
What I am interested in is very much a question of my own generation, but I think that it may interest others, if they read this. I have been reading the last part of Bertrand Russell's Autobiography, when he was in his seventies, eighties, and nineties. One cannot help but notice how much more, in old age (he died in 1970, age 98), he was impelled to reiterate the great Causes of his life, even verbatim. Very few of us are aristocrats or famous philosophers, but the sense of urgency in old age may lead to essays that are simply boring: I hope not.
In the mid-20th century decades, not only was theoretical mathematics opposed to accounting, and descriptive musical compositions, like Leroy Anderson's Sleigh Ride or von Suppe's Light Cavalry Overture, opposed to music not at all descriptive, like J. S. Bach's Art of the Fugue or Anton Webern's string quartets, but in particular in the visual arts Absolute was opposed to Illustrative.
In the visual arts, perhaps theosophy is in some sense the subject matter of the purest Mondrian of the 1930s, but, on the other hand, the abundant recognizable objects in Judy Chicago's Banquet do not make it any less illustrative of its verbal, even philosophical, ideas (the linked images are surely copyright) than Mondrian's work is. French art of every post-Renaissance period is abundant in representations of well set tables, and the Matisse family as much as any other cared for this side of French domesticity, but for Matisse as a painter the well set table became 'absolutely' a Matisse painting (there are many images available, too). Simply, it isn't recognizable objects, or their absence, that differentiates Absolute and Illustrative.
Also, this question has nothing to do with loose, impressionistic painting rather than exact, linearly executed painting. When de Beers got Raoul Dufy to do some open-color water colors for their full-page advertisements in up-market periodicals in the 1950s, those water colors did not ask to be appreciated in the same terms as the first open-color that made him famous. And, on the other hand, the obvious relationship of Matisse's Joy of Life (the Barnes one, that for so long was so hard to get to see) to pastoral idylls by Puvis de Chavannes does not dilute or compromise its place in the category of Absolute art. By the way, however, where the de Beers advertisments are concerned, this essay has almost nothing to do with the interest or virtues of advertising art, or any other applied arts. Whatever one thinks of the huge Dutch paintings of tables laden with food or with "fur and feathers" ready for the kitchen, they are quite different, in the terms I'm trying to address, from Zurbarán still lifes, which are also quite exact. Indeed, even among the Dutch food paintings as a category, some of them are Absolute.
(Why not go to Google's wonderful Art Project for images to consider? Only 20th-century works are generally copyright, especially the fashionable ones which Google couldn't get. Zurbarán is most easily accessed by his name—though they sometimes go by first name—and the Dutch by going to Dutch museums. It is utterly wonderful, and with some practice you can handle the elaborate interface.)
It is at least a quarter century since I read C. S. Lewis's attempt to differentiate literary from not-so-literary writing. The useful thing I remember from it is that it is a question of how the work itself demands (in the case of literature) to be read. Also I remember someone writing of architecture (perhaps Nicholas Pevsner) that though a great tithe barn may be wonderful and beautiful, and a work commissioned from a well known architect may be forgettable or ugly, the line that the writer drew between Building and Architecture is just that, between vernacular building and the personal ideas of an architect who thinks of himself as such. You may say, there are difficulties here, but I would agree with the importance of the non-judgmental distinctions.
The Cleveland Museum of Art has one of my favorite Poussin paintings, a Holy Family. Surely, as a religious subject, Illustrative. But it is this painting that made me remember that C. S. Lewis essay. Sometimes what the artist did is so unmistakably meant to be understood and enjoyed as Absolute art that the latter prevails. Even a painter considered more pious than Poussin, Raphael Sanzio himself, may do one Holy Family after another whose intellectual visual content is deliberately prevalent; it was his tondo, the Madonna della Sedia, that riveted my attention as a small child; he had, of course, patrons who valued what later came to be called Absolute painting, at least as much as the subject.
By Absolute, of course, is meant that the work's value is not engaged with the associations of its subject matter. I have often wondered whether it was that Raphael print, given to me as a reward for perfect attendance at Sunday School, that put me on the way to specializing in Greek art. I have learned to appreciate all sorts of illustrative art, often illustrative of literature or expressive of mystical ideas, as with Odilon Redon, or even political ideas or the spirit of an age, like the railway stations and social life in Manet and the Impressionists, but the Absolute works have conditioned the way I see them.
What most interests me is understanding why, when almost all the rest of humanity is interested in art as illustrating or standing for something else, and in discussing or explaining art betray their way of seeing it (even to the point of explaining Edward Weston's Peppers sexually, just to cite one), a few of us, myself included, have become formed, without any special training (and indeed over the objections of Sunday School teachers in the case of Tintoretto's Susannah and the Elders, the Vienna painting when it was on tour in the USA), to enjoy almost all art for its absolute qualities, feeling that I see the artist's own mind, even admitting that our Norman Rockwell, at his best, can be taken as an artist more than as an illustrator. Is the tendency innate?
And I'd like to propose that differentiating the absolute qualities in visual and musical and poetic works is worth thinking about. Who wants to be distanced from Sumerian and Greek, from Chinese and Islamic, and any other works of visual art simply because they may represent or illustrate cultural beliefs different from one's own? Who doesn't want to have the pleasure of understanding why Chardin's painting of a boy blowing soap bubbles is as much more satisfying than any Dick and Jane illustration of soap bubbles as Raphael's Madonna is than what usually comes on a commercial Christmas card?
It is so difficult to write clearly enough!
P.S. But, key idea, non-objective and absolute are not the same idea. Some artists have been more than others inclined to the Absolute, though. Go to Art Project (see above) and think about it. It is not formal emphasis, either, that governs Poussin, but his own vision that governs his own use of it.
It's like, the statement Rose is Rose is Absolute, but a rose placed on a wedding altar is a symbol of something else, and "Roses of Picardy" is a song less about roses than about the sadness following World War I.
Chardin's boy blowing soap bubbles is in the Metropolitan Museum in NY, and you can just Google that subject. It is a good example of a painting with absolute values dominating that sells like hot cakes for its subject matter's associations.