Transitivity is derived from the Latin word transitivus which means “a passing over.” The intransitive does not pass over. The word transitivity characterizes three types of states or qualities. A) Having the nature of a transitive verb, i.e., a verb that requires a direct object to complete its meaning. B) Something transitive affects something else, it is a transitional or intermediate phase. C) In mathematics and space and time, representation and abstraction. These classifications engender principles that serve as the basis for precise criteria for the proper employment of each. They make sure that the means are intrinsic to artistic ends. One medium should, therefore, not pass over into the territory of another. Similarly, one medium should not have another as its content. The specificity of the medium should be its own subject. And for ultimate purity, the medium should dematerialize. Upholding an intransitivity of media plays a central role in maintaining qualitative judgment and in distinguishing high art from popular culture and kitsch.
Proponents of intransitive media contend that each medium, while not completely discrete, is best suited for specific types of expression. For example, Gotthold Lessing wrote “that succession of time is the province of the poet just as space is that of the painter.”  Although he believed, “that as two equitable and friendly neighbors do not permit the one to take unbecoming liberties in the heart of the other’s domain, yet on their extreme frontiers practice a mutual forbearance by which both sides make a peaceful compensation for those slight aggressions which, in haste and from force of circumstance, the one finds himself compelled to make on the other’s privilege: so also with painting and poetry.”  He cites Homer as a poet whose pictures emerge consecutively rather than through a static enumeration of details. Clement Greenberg, writing later, pushed for greater autonomy of each medium. He wrote, “Discussion as to purity in art and, bound up with it, the attempts to establish the differences between the various arts are not idle. There has been, is, and will be, such a thing as confusion in the arts. From the point of view of the artist engrossed in the problems of his medium and indifferent to the efforts of theorists to explain abstract art completely, purism is the terminus of a salutory [sic] reaction of the mistakes of painting and sculpture in the past several centuries which were due to such a confusion.”  To Greenberg, painters attained autonomy for their medium by eliminating the illusion of depth to reveal the material surface of the flat picture plane.
With the same goal of media independence theorists argued that one medium should not be the content of another. For example, Francois Truffaut introduced the auteur theory in an article that denounced the prevalence of adaptations of novels for the screen. The medium of the cinema, he believed, should be self-sufficient. Conversely, artists complained that their works were compromised when they were represented in other media. For example, Barnett Newman stated that the history of modern painting has been a struggle against the catalogue.
From the reductive process toward medium specificity, critics like Greenberg and Michael Fried, in protecting the autonomy of art, considered it essential to distinguish painting and sculpture from mere objects. To this end, Greenberg advocated an elimination of the tactile to create the appearance “that matter is incorporeal, weightless, and exists only optically like a mirage.”  By the end of the 1960s, Conceptualism pushed this de-materialization even further whereby some sought to abolish the object completely to transcend to the realm of pure ideas.
While all mediated relationships are transitive, not all transitive relationships are aesthetic. To have an aesthetic experience, the medium must become a totally integral part of the completed whole. It is, therefore, not a mere means to an end. Dewey stated that aesthetic experience is distinguished from the non-aesthetic by whether or not the means are intrinsic or external to the end. According to this definition, any act which becomes inseparably fused with its object has an aesthetic quality. Dewey went so far as to acknowledge that even business can be considered an art, if it is carried out not for money but to do a job well . For this reason, Dewey criticized rigid classifications including those which intransitively separated the media as leading away from aesthetic experience. He wrote, “They inevitably neglect transitional and connecting links.”  Allowing the media to pass over into the other territories and interact would generate a new vitality in art. As Marshall McLuhan wrote, “The crossings or hybridizations of the media release great new force and energy as by fission or fussion.”  Acclaiming this tendency, Allan Kaprow wrote in 1958, “Young artists of today need no longer say, ‘I am a painter’ or ‘a poet’ or ‘a dancer.’ They are simply ‘artists.’”  Similarly, in 1965, the artist Donald Judd declared that the most interesting new art was neither painting nor sculpture.
Walter Benjamin wrote how media of mechanical reproduction change the art object to a more democratic form. In this vein, theorists have argued that when older media become the content of media of mechanical reproduction, the newer media transitively act as an intermediary which integrate them into daily life. Andre Bazin, for example, observed that painting is a framed and hence intransitive medium separated from the reality that it pictures. He argued that the film screen does not enclose but rather reveals the picture as related to a reality that continues outside its borders. Representing paintings within film, he believed, advantageously opened this hermetic medium to the masses.  Similarly, Edward Said has described the results of Glen Gould’s decision in the 1960’s to renounce the concert hall for the mass media of records, television, and radio. While Gould claimed that he made this choice to make his playing more pure, Said found that through these media of mass reproduction, paradoxically, Gould was able to address the world more directly rather than withdraw from it. 
Those who believe in the heteronomy of art push for greater transitivity among the media to take art beyond the concert hall, museum, and library and their institutional audiences. At the forefront, Kaprow interpreted the legacy of Jackson Pollock very differently then Greenberg’s attribution of medium specificity. He predicted it would lead beyond the frame of the canvas, off the wall and into the street, blurring the boundaries separating art from life. And he was right. New hybrid media in the form of Happenings, Earth Art, Situationism attempted to make art an integral part of life. Andy Warhol’s factory, bringing together rock music, performance, journalism, and film, has been widely celebrated for intermediating between high art and popular culture. But it can be asked, “Where will this project of breaking down the barriers between art and life lead if it is finally successful?” Will not then the heteronymous become totally autonomous?
Above copied from: http://csmt.uchicago.edu/glossary2004/transitivityintransitivity.htm