From https://plato.stanford.edu/entries/beardsley-aesthetics/
Three books and a number of articles form the core of Beardsley's work in aesthetics. Of the books, the first, Aesthetics: Problems in the Philosophy of Criticism (1958; reissued with a postscript, 1981), is by far the most substantial, comprehensive, and influential. More than that, it's also the first systematic, well-argued, and critically informed philosophy of art in the analytic tradition. Given the wide range of topics covered in Aesthetics, the intelligent and philosophically informed treatment accorded them, the historically unprecedented nature of the work, and its effect on subsequent developments in the field, a number of philosophers, including some of Beardsley's critics, have argued that Aesthetics is the most impressive and important book of 20th century analytic aesthetics.
In Aesthetics, Beardsley develops a philosophy of art that is sensitive to three things: (i) art itself and people's pre-philosophical interest in and opinions about art, (ii) critics' pronouncements about art, and (iii) developments in philosophy, especially, though not exclusively, those in the analytic tradition. To explain each of these elements further: (i) In the late 1940s and early 1950s, the time at which Beardsley developed his philosophy of art, there were developments in the arts—new forms in music, painting, and literature had appeared and were appearing—but there was also a well established and relatively large canon of works almost universally regarded as aesthetically superior and worthy of attention. (ii) Art criticism had become an industry, with major schools of all sorts flourishing: Marxist, Formalist, psychoanalytic, semiotic, historical, biographical. (iii) And philosophy had changed in rapid and unexpected ways. Analytic philosophy, with its emphasis on language and strong empiricist tendencies, had gained ascendancy in American universities in little more than 20 years, and dominated the philosophical scene.
Beardsley responded to each of the three. His position on developments in the arts is probably best described as open-minded moderation. He welcomed new developments, and reference to new works and works that lack the luster of fame, notoriety, or ready recognition appear frequently in Aesthetics and his other work. He didn't automatically embrace the latest fad, fashion, or movement, however, but tried, as he said, to get something out of a work.
As for art criticism, the school of criticism that attracted Beardsley, and that his philosophy of art ultimately underwrites, is the so-called New Criticism. The New Criticism made the literary work the center of critical attention, and denied, or at least greatly devaluated, the relevance of facts about the origin of literary works, their effects upon individual readers, and their personal, social, and political influence. Close reading is what is required of a critic, not biographical information about the author, a rundown of the state of society at the time the work was written, data about the psychology of creation, predictions about the effects of the work on society, and certainly not a piece of autobiography detailing the critic's own personal response to the work. Though based in literary criticism, the New Criticism could be, and should be, extended to the other arts, Beardsley thought: all art criticism should make a serious effort to recognize its objects as special, autonomous, and important in their own right, and not subservient to ulterior aims or values; all art criticism should attempt to understand how works of art work, and what meanings and aesthetic properties they have; all art criticism should strive for objective and publicly accessible methods and standards to test its pronouncements.
Developments in philosophy were a different story. Beardsley embraced a general form of analytic philosophy not heavily influenced by either logical positivism or ordinary language philosophy, the dominant movements of the time. For him, an analytic approach to the philosophy of art meant no more than critically examining the fundamental concepts and beliefs underlying art and art criticism. Doing philosophy of that sort required clarity, precision, and a good eye for identifying, exposing, and evaluating arguments, but left aesthetics, as a systematic study, a real possibility.